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An option contract for vaccine procurement using the SIR epidemic model
Abstract
Timely and adequate supply of vaccines in disastrous situations has a key role in controlling communicable diseases. This paper develops a specific option contract for proactively provisioning required vaccine doses from two suppliers (a main and a backup). The model aims to minimize the procurement and social costs using the SIR epidemic model. A novel hybrid solution procedure is developed using the optimal control theory, Stackelberg game model and nonlinear programming approaches. To evaluate the performance of the developed solution method, a number of numerical examples are presented and their results are discussed.
... Option contracts (Patra and Jha 2022, Aghajani et al. 2020, Liang et al. 2012) and quantity flexibility contracts , Balcik and Ak 2014 are most widely studied. Another stream aims to optimize the governmentprivate FAs from a variety of perspectives, such as considering two or more (competitive) suppliers (Liu et al. 2019, Nikkhoo et al. 2018, Shamsi et al. 2018, combining physical reserve and production capacity reserve (Liu et al. 2022). Although the existing FAs could provide useful strategies for emergency supplies prepositioning at pre-disaster and emergency purchasing at post-disaster, "bounded rationality" of decision-makers has received less attention. ...
... It shows that the proposed flexible mechanism by two collaborative partners is effective in elevating the victims' satisfaction level on the supply of emergency supplies. Analogously, Shamsi et al. (2018) exert an option contract to establish a purchasing mode for vaccine doses from two competitive suppliers. The results indicate that the innovative procurement mechanism plays an essential role in guaranteeing the timely supply of vaccines and lowering the total social cost. ...
... How to measure the supplier's utility is a key question. Despite not retaining the property of diminishing sensitivity in the prospect theory, piecewiselinear loss aversion utility functions have been frequently used in production and operations management (POM), behavioral supply chain (BSC), finance, and economics (Long and Ghavamifar et al. (2022) single ✓ hybrid contract Liu et al. (2022) single ✓ option contract Patra and Jha (2022) single ✓ bilateral option contract single ✓ quantity flexibility contract single ✓ option contract single ✓ option contract Liu et al. (2019) multiple ✓ option contract Wang et al. (2019) multiple bonus contract Nikkhoo et al. (2018) two quantity flexibility contract Shamsi et al. (2018) two option contract Wang et al. (2015) single ✓ ✓ option contract this paper single ✓ ✓ ✓ option contract Fig. 1. The game timing between the agency and the supplier. ...
... Parvin et al. (2018) examine the optimal allocation of malaria medications in a three-layer centralized health supply chain system, in which the market demand uncertainty is modeled by a two-stage stochastic programming approach. Shamsi et al. (2018) develop a specific "options contract" for vaccine procurement under demand uncertainty. The authors build an analytical epidemic model to capture the establishment and spread of an infectious disease. ...
... Their experimental results indicate that the capacity bottleneck, as well as the level of supply disruptions, will be reduced significantly by implementing the "voluntary quarantine" mechanism. Shamsi et al. (2018) analytically develop a specific option contract for vaccine procurement by adopting the bi-level optimization approach with a nonlinear optimization problem. In their model, two suppliers, called the "main" and "back-up" suppliers, are explored in the presence of supply disruption. ...
... (iii) Establishing an emergency supply chain with contingency plans is necessary (Dasaklis et al., 2017), especially for the pre-pandemic stage (Choi, 2021). We suggest that firms, especially those who produce essential products, establish a plan to properly increase their production capacity, provide resource reservations, and adopt an emergency sourcing and collaboration strategy to combat both demand and supply disruption risks (Mishra & Singh, 2020;Paul & Chowdhury, 2020;Shamsi et al., 2018). ...
The recent outbreak of COVID-19 has posed serious threats and challenges to global supply chain management (GSCM). To survive the crisis, it is critical to rethink the proper setting of global supply chains and reform many related operational strategies. We hence attempt to reform the GSCM from both supply and demand sides considering different pandemic stages (i.e., pre, during, and post-pandemic stages). In this research paper, we combine a careful literature review with real-world case studies to examine the impacts and specific challenges brought by the pandemic to global supply chains. We first classify the related literature from the demand and supply sides. Based on the insights obtained, we search publicly available information and report real practices of GSCM under COVID-19 in nine top global enterprises. To achieve 3Rs (responsiveness, resilience, and restoration), we then propose the "GREAT-3Rs" framework, which shows the critical issues and measures for reforming GSCM under the three pandemic stages. In particular, the "GREAT" part of the framework includes five critical domains, namely "Government proactive policies and measures", "Redesigning global supply chains", "Economic and financing strategies under risk", "Adjustment of operations", and "Technology adoption", to help global enterprises to survive the pandemic; "3Rs" are the outputs that can be achieved after using the "GREAT" strategies under the three pandemic stages. Finally, we establish a future research agenda from five aspects.
... Vaccination, medication, education, lockdown, quarantine, using face masks, and home health care are just a few of the techniques available to combat epidemics [2][3][4]. One of the most promising treatments for dealing with epidemic diseases is vaccination [5,6]. However, several elements of COVID-19 conditions, such as unclear identification, cause vaccine production to be delayed, with varying yields. ...
... In order to measure the social cost of infected people, the disability-adjusted life years (DALY) index is used. The cost of spreading a disease epidemic in unaffected areas by an infected individual as the host is included in the DALY [5,39,40]. ...
... As a result, another goal of this problem is to reduce vaccine supply procurement costs. Shamsi G, Ali Torabi [5] and Gamchi, Torabi [24] present some solutions for such multi-objective issues. ...
Infectious diseases drive countries to provide vaccines to individuals. Due to the limited supply of vaccines, individuals prioritize receiving vaccinations worldwide. Although, priority groups are formed based on age groupings due to the restricted decision-making time. Governments usually ordain different health protocols such as lockdown policy, mandatory use of face masks, and vaccination during the pandemics. Therefore, this study considers the case of COVID-19 with a SEQIR (susceptible–exposed–quarantined–infected–recovered) epidemic model and presents a novel prioritization technique to minimize the social and economic impacts of the lockdown policy. We use retail units as one of the affected parts to demonstrate how a vaccination plan may be more effective if individuals such as retailers were prioritized and age groups. In addition, we estimate the total required vaccine doses to control the epidemic disease and compute the number of vaccine doses supplied by various suppliers. The vaccine doses are determined using optimal control theory in the solution technique. In addition, we consider the effect of the mask using policy in the number of vaccine doses allocated to each priority group. The model’s performance is evaluated using an illustrative scenario based on a real case.
... Parvin et al. (2018) examine the optimal allocation of malaria medications in a three-layer centralized health supply chain system, in which the market demand uncertainty is modeled by a two-stage stochastic programming approach. Shamsi et al. (2018) develop a specific "options contract" for vaccine procurement under demand uncertainty. The authors build an analytical epidemic model to capture the establishment and spread of an infectious disease. ...
... Their experimental results indicate that the capacity bottleneck, as well as the level of supply disruptions, will be reduced significantly by implementing the "voluntary quarantine" mechanism. Shamsi et al. (2018) analytically develop a specific option contract for vaccine procurement by adopting the bi-level optimization approach with a nonlinear optimization problem. In their model, two suppliers, called the "main" and "back-up" suppliers, are explored in the presence of supply disruption. ...
... (iii) Establishing an emergency supply chain with contingency plans is necessary (Dasaklis et al. 2017), especially for the pre-pandemic stage (Choi 2021). We suggest the firms, especially those who produce essential products, establish a plan to properly increase their production capacity, provide resource reservation as well as adopt an emergency sourcing and collaboration strategy to combat both demand and supply disruption risks (Shamsi et al. 2018, Mishra and Singh 2020, Paul and Chowdhury 2020. (iv) Rerouting the vehicles and having alternative logistics choices (e.g., using third-party logistics (Li et al. 2018)) under travel restrictions can be considered. ...
... In this case, Nosoohi and Nookabadi [75] developed an outsourcing model to analyze optimal ordering strategy under disruptions in final processing costs and customer demand. Torabi [76] studied the impact of timely and adequate vaccine delivery in catastrophic infectious disease conditions, considering two suppliers, including a main and a backup to provide the vaccine doses needed. In addition, Heydari, Govindan, Nasab and Taleizadeh [77] investigated the role of outsourcing in a supply chain and concluded that such a strategy enhances the earnings of both channel and its members. ...
... This contract can be used for humanitarian services to ensure efficient service in case of catastrophic events. Torabi [76] analyzed an option contract to create coordination between two suppliers to provide the requirements for the epidemic. Most studies surveyed the effect of this contract on traditional channels, while such a mechanism is also widely used in e-channels and actually addressed in various industries. ...
... x x x Ivanov (2022) x x x x x Llaguno et al. (2021) x Kaur and Singh (2021) x Kellner et al. (2019) x Kinra et al. (2020) x Li and Zobel (2020) x Lowe et al. (2020) x x Lücker et al. (2020) x Mamani et al. (2013) x Nagurney (2021) x Naqvi and Amin (2021) x Nuss et al. (2016) x Park et al. (2021) x Paul and Chowdhury (2020) x Paul and Chowdhury (2021) x x x Queiroz et al. (2022) x Rothan and Byrareddy (2020) x Sawik (2022) x Sawik (2023) x Ouardighi et al. (2021) x x Shamsi et al. (2018) x Sinha et al. (2020) x Torabi et al. (2015) x Torabi et al. (2018) x Vahidi et al. (2018) x Li et al. (2023) x Yusuf and Benyah (2012) x Our paper x x x x portfolio selection problem with past supplier data and four criteria: purchasing cot, logistic service, risk, and sustainability. Hosseini et al. (2019) propose a stochastic multi-objective optimization model for resilient supplier selection and demand allocation using probabilistic graphical model for computing the probability disruption of the supplier. ...
... All such models only consider a macro-economic or social policy framework and implicitly assume that production facilities are not affected by the epidemic. Shamsi et al. (2018) looks into the procurement of vaccines and uses an optimal control model to minimize the procurement and social costs using the SIR epidemic model. Whereas Enayati and Özaltın (2020) addresses the optimal influenza vaccine doses number for distribution. ...
The COVID-19 pandemic has illustrated the unprecedented challenges of ensuring the continuity of operations in a supply chain as suppliers' and their suppliers stop producing due the spread of infection, leading to a degradation of downstream customer service levels in a ripple effect. In this paper, we contextualize a dynamic approach and propose an optimal control model for supply chain reconfiguration and ripple effect analysis integrated with an epidemic dynamics model. We provide supply chain managers with the optimal choice over a planning horizon among subsets of interchangeable suppliers and corresponding orders; this will maximize demand satisfaction given their prices, lead times, exposure to infection, and upstream suppliers' risk exposure. Numerical illustrations show that our prescriptive forward-looking model can help reconfigure a supply chain and mitigate the ripple effect due to reduced production because of suppliers' infected workers. A risk aversion factor incorporates a measure of supplier risk exposure at the upstream echelons. We examine three scenarios: (a) infection limits the capacity of suppliers, (b) the pandemic recedes but not at the same pace for all suppliers, and (c) infection waves affect the capacity of some suppliers, while others are in a recovery phase. We illustrate through a case study how our model can be immediately deployed in manufacturing or retail supply chains since the data are readily accessible from suppliers and health authorities. This work opens new avenues for prescriptive models in operations management and the study of viable supply chains by combining optimal control and epidemiological models.
... This seminal work has been then extended in Mamani et al. (2013) by considering the contract design problem with multiple governments and the possibility of intranational transmission of the disease. More recently, Torabi et al. (2018), using the SIR epidemic model, devise a procedure including an optimal control model to decide on post-disaster vaccine supply with consideration of demand uncertainty. The models proposed in Torabi et al. (2018); Chick et al. (2008); Mamani et al. (2013) implicitly assume that workforce availability is not affected by the epidemic. ...
... More recently, Torabi et al. (2018), using the SIR epidemic model, devise a procedure including an optimal control model to decide on post-disaster vaccine supply with consideration of demand uncertainty. The models proposed in Torabi et al. (2018); Chick et al. (2008); Mamani et al. (2013) implicitly assume that workforce availability is not affected by the epidemic. Enayati and Özaltın (2020) address optimal influenza vaccine distribution. ...
A pandemic can wreak havoc in supply chains, as witnessed in the COVID-19 context. As workers get infected, production level drops and demand from customers goes unfulfilled. Combining in a novel way an epidemic model with optimal control theory, our model provides a plant manager with the optimal level of prophylactic effort she needs to deploy over a planning horizon to protect the workforce from a pandemic in its early stage and so maintain production levels. Given the production planning problem, the effort in terms of prophylactic measures can be optimally determined in closed form, balancing worker protection against production requirements in a single step. The manager must initially implement the strictest measures before relaxing them in time. Three extensions are presented:, (1) determine the optimal period of time over which the prophylactic measures should be maintained; (2) determine the optimal effort in terms of prophylactic measures in the case of an endemic disease; and (3) assess the effect of a stochastic exogenous shock on the total number of infected. This research provides a production planning model that allows a decision-maker to mitigate the impact of worker absenteeism at the onset of a pandemic, thus improving supply chain resilience.
... In OR applications, we also register two additional (and opposite) situations: on the one hand, works in which the calibration is implicit, because researchers borrow models already calibrated in the literature and use these models to perform further investigations -see Enayati & Özaltın (2020) ; Kaplan et al. (20 02,20 03) ; Lin et al. (2020) ; Ren et al. (2013) ; Tebbens & Thompson (2009) . On the other hand, works in which inputs are elicited are either directly assigned by the modelers or derived from experts' opinions, as in Shamsi G et al. (2018) . This happens especially when models involve poorly known compartments, e.g., a network compartment in Rahmandad & Sterman (2008) , or a mobile medical team in Rachaniotis et al. (2012) . ...
... Kaplan et al. (20 02,20 03) study the marginal behavior of the number of fatalities varying five model inputs, that comprise the number of initially infected individuals and of available vaccinators, over predetermined ranges. Shamsi G et al. (2018) use several one-way sensitivity plots to study the variation of several outputs, such as the social cost and percentage of recovered individuals, respond-ing to changes in vaccine delivery time. Tebbens & Thompson (2009) use one-way sensitivity functions to study the impact of population size and population structure on policy decision rules, such as the incremental cost-effectiveness ratio and the time until disease elimination. ...
Operations researchers worldwide rely extensively on quantitative simulations to model alternative aspects of the COVID-19 pandemic. Proper uncertainty quantification and sensitivity analysis are fundamental to enrich the modeling process and communicate correctly informed insights to decision-makers. We develop a methodology to obtain insights on key uncertainty drivers, trend analysis and interaction quantification through an innovative combination of probabilistic sensitivity techniques and machine learning tools. We illustrate the approach by applying it to a representative of the family of susceptible-infectious-recovered (SIR) models recently used in the context of the COVID-19 pandemic. We focus on data of the early pandemic progression in Italy and the United States (the U.S.). We perform the analysis for both cases of correlated and uncorrelated inputs. Results show that quarantine rate and intervention time are the key uncertainty drivers, have opposite effects on the number of total infected individuals and are involved in the most relevant interactions.
... Some scholars divide relief supplies into two categories: perishable products and non-perishable commodities, and propose different strategies (outsourcing and insourcing) to pre-position the two kinds of relief supplies (Wang et al., 2016;Yao et al., 2018). Many researchers pay attention to the pre-positioning problem of a certain type of relief supplies such as food (Zhang et al., 2019) and vaccine (Shamsi et al., 2018) because these relief supplies are critical products which are in great demand in the early post-disaster. It can be seen that the classification of relief supplies largely determines pre-positioning strategies for different types of relief supplies. ...
... Similar results can be seen in Yao et al. (2018). Shamsi et al. (2018) presented an option contract between the buyer and two competing suppliers and determined the optimal amount of the required vaccine doses provided by the two suppliers. Zhang et al. (2019) built a quantity commitment contract framework where there was a government authority and an agreement supplier. ...
It is vital to pre-position a certain amount of relief supplies at pre-disaster. But governments are often confronted with a dilemma of coordinating inventory cost and stock-out cost in pre-positioning relief supplies. Pre-positioning strategies for relief supplies depend on the natural characteristic of relief supplies and the most urgent needs at post-disaster. Therefore, we classify relief supplies by their natural characteristic and priority, and introduce an option contract into relief supplies pre-positioning system which consists of a single government and an agreement enterprise. Specially, a consumable and relatively urgent relief supplies pre-positioning (C-RUP) model and a non-consumable and urgent relief supplies pre-positioning (NC-UP) model are established. The optimal decisions of the government and the enterprise are derived, respectively. The relief supply chain coordination is achieved with the option contract. Under channel coordination, the two models can not only improve the government’s emergency ability and support capacity, but also reduce the government’s inventory risk when compared to the government single pre-positioning model. Moreover, we give out the conditions that the two sides can reach a win-win situation. Lastly, we propose important managerial insights for pre-positioning strategies related to different types of relief supplies.
... Each major natural disaster or public health crisis has had a significant impact on the economy and the safety of human lives. Sufficient emergency material reserves are crucial for the mitigation of the threat of disasters [1]. ...
Sustainable Emergency Material Reserve Systems (SEMRSs) are complex frameworks comprising three types of reserves, namely, physical, capacity, and agreement reserves, and involve various stakeholders such as local governments and enterprises. However, multiple stockpiling methods have not been considered in investigations on the influencing factors and inter-factor relationships within an emergency material stockpiling system. In this study, we achieved consensus through a questionnaire, established an evaluation system encompassing various reserve methods and participating entities, and delineated the key factors affecting SEMRSs while analyzing their causal relationships using the decision-making trial and evaluation laboratory–based analytic network process. Results reveal that (1) local governments and participating enterprises play crucial roles in ensuring the sustainable supply of emergency provisions; (2) the capacity to guarantee emergency funds serves as a pivotal link among all key influencing factors, emergency funds should be augmented, and the utilization of contingency funds should be rationalized; and (3) the integration of physical, production capacity, and agreed stockpiling methods in the emergency reserve system requires enhancement, and the incorporation of capital reserves should be considered as part of the stockpiling strategy. These insights hold significant implications for refining emergency stockpiling practices and fostering the development of SEMRSs.
... Pazirandeh (2011) presents a decision-making framework for strategic sourcing and distribution of vaccines in developing countries. Shamsi et al. (2018) propose an option contract using the Stackelberg game approach to procure required vaccine doses from two suppliers. In a similar context, Martin et al. (2020) propose three vaccine procurement contract designs to encourage pharmaceutical companies to bring vaccines to developing countries. ...
... There are several differences between the vaccine supply chain (VSC) and the traditional supply chain, which can provide unique characteristics of VSC. For instance, the non-profit identity of the buyer, high associated risks in terms of products' perishability, supply and demand uncertainties, and very limited reliable information (Shamsi G. et al. 2018). ...
... Finally, demand for vaccines during pandemics greatly outstrips supply, which causes a shortage of supply. A new decision model for vaccine supply in response to an uncertain vaccine demand can also be considered in future research (Jahani et al., 2022;Shamsi G. et al., 2018). links with added vaccine production (ω ∈ {1, ..., A 1 }) A 2 links with fixed vaccine production (γ ∈ {1, ..., A 2 }) δ a,p 1 if an element of incidence matrix of link a on path p, and 0 otherwise W t the total number of vaccine which is distributed in period t x t,p the number of vaccine production for path p in period t f a,t vaccine flows on link a in period t f ω,t vaccine flows on link ω in period t f γ,t vaccine flows on link γ Γ t,ω the upper bound of vaccine production per week t on link ω Γ t,γ the upper bound of vaccine production per week t on link γ Γ t,ω vaccine capacity per week t on links ω I t h the number of infected humans in period t I t m the number of infected animals in period t S t h the number of susceptible humans in period t V t h the number of vaccinated susceptible humans in period t S t m the number of susceptible animals in period t E t h the number of exposed humans in period t E t m the number of exposed animals in period t R t h the number of removed humans in period t R t m the number of removed animals in period t σ t the percentage of vaccine coverage in period t α h population vaccination rate Λ m animal birth rate Λ h human birth rate µ m animal natural death rate µ h human natural death rate d m animal MPX related death rate d h human MPX related death rate ρ m animal recovery rate ρ h human recovery rate ν m animal infection rate ν h human infection rate β mm animal to animal transmission rate rate β hh human to human transmission rate rate β mh animal to human transmission rate rate ϖ price of vaccine Symbol Description(continued) Θ M P X infection loss of MPX N population (human population N h ,animal population N m ) ϖ(W t ) the total purchasing cost of vaccineŝ c a (f a,t ) the total operation cost on link â π t,α (Γ t,α ) the investment cost on link α ...
After a pandemic, all countries experience a shortage in vaccine supply due to limited vaccine stocks and production capacity globally. One particular problem is that it's hard to predict demands for vaccines during the global crisis. On the other hand, vaccines are usually made and packaged in different places, raising logistical issues and concerns that can further delay distribution. In this paper, we propose an optimization model to link infectious disease dynamics and supply chain networks considering a one-to-one relationship between demand and supply for vaccines. We focus on designing a vaccine coordination system using government subsidy that considers the equilibrium behaviors of manufacturers under an actual demand for the vaccine. This study evaluates vaccine manufacturers and government behaviors that help the vaccine market to reach the socially optimal. Different decisions, such as vaccine demands and vaccine production and distribution are investigated. A study of the monkeypox pandemic in the U.S. is performed to validate our model and its results. The obtained results from testing the proposed system problem revealed that the vaccine coverage increased by up to 35%, while the unmet demand reduced by up to 60%, in comparison to when vaccine manufacturers act individually.
... Hence, designing option contracts in DRL has received increasing attention from researchers. For example, Shamsi et al. (2018) presented a new provisioning model under option contract with the goal of minimizing procurement and social costs to proactively supply the needed vaccine doses from a main supplier and a backup supplier. introduced a put option contract into DRL and proposed a relief items purchasing model, which can not only ensure the profits of suppliers, but also reduce the inventory risk of governments. ...
Disaster relief logistics (DRL) provides adequate relief supplies to victims of natural disasters (e.g., earthquakes and volcanic eruptions). This study explicitly considers supplier selection and inventory pre-positioning corresponding to static preparedness decisions, and post-disaster procurement and delivery associated with dynamic response decisions in actual DRL operations. To tackle issues triggered by shortage and surplus of multi-class relief resources, a flexible option contract is adopted to purchase relief items from suppliers. To measure the risk of demand ambiguity, a worst-case mean-quantile-deviation criterion is introduced to reflect the decision-maker's risk-averse attitude. To handle the ambiguity in the probability distribution of demand, a novel two-stage distributionally robust optimization (DRO) model is developed for the addressed DRL problem. The proposed DRO model can be transformed into equivalent mixed-integer linear programs when the ambiguity sets incorporate all distributions within L1-norm and joint L1- and L∞-norms from a nominal (reference) distribution. A computational study of earthquakes in Iran is conducted to illustrate the applicability of the proposed DRO model to real-world problems. The experimental results demonstrate that our proposed DRO model has superior out-of-sample performance and can mitigate the effect of Optimization Bias compared to the traditional stochastic programming model. Some managerial insights regarding the proposed approach are provided based on numerical results.
... The SIR epidemic model is used for analysis of the post-disaster situation considering the delivery of vaccines. Shamsi et al. (2018) propose a game formulation for vaccine procurement exploring option contracts considering a backup supplier. The aim of the buyer is to minimize cost (including social cost) and the objective of the suppliers is to maximize profit. ...
The increasing damage caused by disasters is a major challenge for disaster management authorities, especially in instances where simultaneous disasters affect different geographical areas. The uncertainty and chaotic conditions caused by these situations combined with the inherent complexity of collaboration between multiple stakeholders complicates delivering support for disaster victims. Decisions related to facility location, procurement, stock prepositioning and relief distribution are essential to ensure the provision of relief for these victims. There is a need to provide analytical models that can support integrated decision-making in settings with uncertainty caused by simultaneous disasters. However, there are no formulations tackling these decisions combining multiple suppliers, multiple agencies, and simultaneous disasters. This article introduces a novel bi-objective two-stage stochastic formulation for disaster preparedness and immediate response considering the interaction of multiple stakeholders in uncertain environments caused by the occurrence of simultaneous disasters. At the first stage, decisions related to the selection of suppliers, critical facilities, agencies involved, and pre-disaster procurement are defined. Resource allocation, relief distribution and procurement of extra resources after the events are decided at the second stage. The model was tested on data from the situation caused by simultaneous hurricanes and storms in Mexico during September of 2013. The case is contrasted with instances planning for disasters independently. The results show how planning for multiple disasters can help understand the real boundaries of the disaster response system, the benefits of integrated decision-making, the impact of deploying only the agencies required, and the criticality of considering human resources in disaster planning.
... Xie et al. (2021) analyzed subsidy selection in a vaccine supply chain with risk-averse buyers using evolutionary game methods. Shamsi et al. (2018) used optimal control theory, Stackelberg game model, and a nonlinear programming method to construct SIR epidemic model to minimize procurement and social costs in the vaccine supply chain. Pan et al. (2022) discussed the impact of public and private hospital supply on the vaccine supply chain. ...
Currently, the global spread of COVID-19 is taking a heavy toll on the lives of the global population. There is an urgent need to improve and strengthen the coordination of vaccine supply chains in response to this severe pandemic. In this study, we consider a closed-loop vaccine supply chain based on a combination of artificial intelligence and blockchain technologies and model the supply chain as a two-player dynamic game with inventory level as the dynamic equation of the system. The study focuses on the applicability and effectiveness of the two technologies in the vaccine supply chain and provides management insights. The impact of the application of the technologies on environmental performance is also considered in the model. We also examine factors such as the number of people vaccinated, positive and side effects of vaccines, vaccine decay rate, revenue-sharing/cost-sharing ratio, and commission ratio. The results are as follows: the correlation between the difficulty in obtaining certified vaccines and the profit of a vaccine manufacturer is not monotonous; the vaccine manufacturer is more sensitive to changes in the vaccine attenuation rate. The study’s major conclusions are as follows: First, the vaccine supply chain should estimate the level of consumers’ difficulty in obtaining a certified vaccine source and the magnitude of the production planning and demand forecasting error terms before adopting the two technologies. Second, the application of artificial intelligence (AI) technology is meaningful in the vaccine supply chain when the error terms satisfy a particular interval condition.
... There is a growing interest in optimizing VSCs from operational management perspectives. Torabi [8] construct a Stackelberg game model based on the susceptible infected recovered (SIR) epidemic model and developed a vaccine procurement option contract to minimize procurement and social costs. Ng et al. [9] study an influenza VSC to derive optimal solutions with the aim of improving vaccination efficiency and finding the best combination of vaccination strategies. ...
People can choose to be vaccinated to prevent diseases at their own expense. There are specific vaccines for many diseases. Meanwhile, for a particular disease, there might be multiple vaccines available to choose from. Based on that, we constructed a stylized vaccine supply chain (VSC) model for the market where domestic vaccines and imported vaccines co-exist. We explored the effect of government tariff policies on the game behaviors between a domestic vaccine manufacturer (DVM) and an imported vaccine manufacturer (IVM). This paper analyzes the short-term game and long-term evolutionary game behaviors of the VSC from both the entirely rational and boundedly rational perspectives. The analysis considers three tariff policies: no tariffs on imported vaccines, tariffs borne by the IVM, and tariffs borne by buyers. Results suggest that in the short-term game, buyers bearing tariffs on imported vaccines can enable the DVM to gain the most market share. The buyers willingness-to-pay is relatively low for imported vaccines, which makes the DVM more profitable. Imposing tariffs on imported vaccines can reduce the IVMs profit margin. However, the IVM still prefers to bear the tariffs itself. Lowering the cold chain transportation level and reducing the retail price of imported vaccines are both feasible solutions for the IVM to relieve the pressure from tariffs. It is also feasible for the IVM to increase the retail price of imported vaccines when the buyers willingness to pay for imported vaccines is high. In long-term evolutionary game, the DVM can gain more room for price adjustment if the IVM bears tariffs. The IVM can obtain greater cost tolerance if buyers bear tariffs. However, from governments prospective, tariffs borne by buyers is the optimal option, which makes the VSC stable and controllable.
... In their contract design, the buyer purchases certain options from a supplier that provides the buyer with the right to exercise the options when a disaster occurs. Using the Stackelberg game and optimal control theory, Shamsi et al. (2018) proposed an OPC for procuring vaccines under an SIR epidemic model. Liu et al. (2019b) established an OPC to determine how many items should be pre-purchased from multiple suppliers and the amounts that should be prepositioned by the government. ...
This paper proposes a novel hybrid relief procurement contract in which the specific features of option contract and quantity flexible contract are used to coordinate the supply of a relief item between a supplier and a humanitarian organization. First, a mathematical statistics approach is used to categorize different provinces according to a multi-hazard risk approach. Then, the proposed contract is elaborated. Different managerial insights are derived from conducting several sensitivity analyses in our case study. The results reveal that using the proposed contract can significantly improve the procurement process by reducing the shortage and overstocking risks in humanitarian organizations.
... [25]. The risk spread of pandemic models is widely used in finance, with contagion caused by shocks to complex financial networks [26]; how to use the SIR epidemic model to develop contracts that minimize procurement and social costs after disasters is considered [27]. Despite the SIR epidemic model being well developed, it has not been used for the risk propagation mechanism in the automotive supply chain. ...
Risk propagation is occurring as an exceptional challenge to supply chain management. Identifying which supplier has the greater possibility of interruptions is pivotal for managing the occurrence of these risks, which have a significant impact on the supply chain. Identifying and predicting how these risks propagate and understanding how these risks dynamically diffuse if control strategies are installed can help to better manage supply chain risks. Drawing on the complex systems and epidemiological literature, we research the impact of the global supply network structure on risk propagation and supply network health. The SIR model is used to dynamically identify and predict the risk status of the supply chain risk at different times. The results show that there is a significant relationship between network structure and risk propagation and supply network health. We demonstrate the importance of supply network visibility and of the extraction of the information of node firms. We build up an R package for geometric graphs and epidemics. This paper applies the R package to model the supply chain risk for an automotive manufacturing company. The R package provides a firm to construct the complicated interactions among suppliers and display how these interactions impact on risks. Theoretically, our study adapts a computational approach to contribute to the understanding of risk management and supply networks. Managerially, our study demonstrates how the supply chain network analysis approach can benefit the managers by developing a more holistic framework of system-wide risk propagation. This provides guidance for network governance policies, which will lead to healthier supply chains.
... The priority of various people groups is the most useful policy in discounting the pandemics' impacts on vaccines' distribution (Uscher-Pines et al. 2006). This policy plays an essential role in reducing the total social cost related to an infected person (the medicine drugs, hospitalization cost, and other disease costs) (Torabi 2018). Healthcare providers, vital services providers, and people with a high risk of outbreaks are priority groups for vaccination recommended by WHO. ...
Vaccination is one of the most efficient ways to restrict and control the spread of epidemic outbreaks such as COVID-19. Due to the limited COVID-19 vaccine supply, an equitable and accessible plan should be prepared to cope with. This research focuses on designing a vaccine supply chain while aiming to achieve an equitable and accessible network. We present a novel mathematical formulation that helps to optimize vaccine distribution to inoculate people with various priority levels to achieve an equitable plan. The transshipment strategy is also incorporated into the model to enhance the accessibility of COVID-19 vaccine types between health facilities. The nature of COVID-19 is dynamic over time due to mutations, and the protection level of each vaccine type against this disease is not exact. Besides, complete information about the demand for different vaccine types is not available. Hence, we use Multi-Stage Stochastic Programming as a reliable strategy that is organized to manage stochastic data in a dynamic environment for the first time in the vaccine supply chain network. The scenarios in this approach are generated using a Monte Carlo simulation method, and then a forward scenario reduction technique is conducted to construct a suitable scenario tree. The practicality and capability of the model are shown in a real-life case of Iran. The results show that the performance of the Multi-Stage Stochastic Programming is significantly improved compared with the two-stage stochastic programming regarding the total cost of the vaccine supply chain and the number of the shortage units.
... They used the epsilon-constraint method, multi-objective genetic algorithm (MOGA), and multi-objective particle swarm optimization (MOPSO) to solve their model. Torabi (2018) developed an option contract to prevent the required dose of vaccine. They designed a model with the aim of minimizing purchasing and social costs, which had two suppliers (main and backup). ...
In this paper, a new responsive-green-cold vaccine supply chain network during the COVID-19 pandemic is developed for the first time. According to the proposed network, a new multi-objective, multi-period, multi-echelon mathematical model for the distribution-allocation-location problem is designed. Another important novelty in this paper is that it considers an Internet-of-Things application in the COVID-19 condition in the suggested model to enhance the accuracy, speed, and justice of vaccine injection with existing priorities. Waste management, environmental effects, coverage demand, and delivery time of COVID-19 vaccine simultaneously are therefore considered for the first time. The LP-metric method and meta-heuristic algorithms called Gray Wolf Optimization (GWO), and Variable Neighborhood Search (VNS) algorithms are then used to solve the developed model. The other significant contribution, based on two presented meta-heuristic algorithms, is a new heuristic method called modified GWO (MGWO), and is developed for the first time to solve the model. Therefore, a set of test problems in different sizes is provided. Hence, to evaluate the proposed algorithms, assessment metrics including (1) percentage of domination, (2) the number of Pareto solutions, (3) data envelopment analysis, and (4) diversification metrics and the performance of the convergence are considered. Moreover, the Taguchi method is used to tune the algorithm’s parameters. Accordingly, to illustrate the efficiency of the model developed, a real case study in Iran is suggested. Finally, the results of this research show MGO offers higher quality and better performance than other proposed algorithms based on assessment metrics, computational time, and convergence.
... At the same time, DES paradigm was used for the analysis of resulting data of ABS paradigm. Shamsi et al. (2018) constructed a specific option contract for proactively provisioning required vaccine from two suppliers (main supplier and a backup supplier). This model goal is to minimize procurement and social cost. ...
The black swan event caused by the novel coronavirus (COVID-19) has majorly exposed the vulnerabilities of the supply chain of many of the firms. However, healthcare sector is one of the significant areas which majorly got disrupted during this pandemic event. The majority of the studies focus on the reviews on supply chain disruption modelling to analyse the risk and their effect on supply chains. This study provides a systemic literature review of various supply chain disruption models in the healthcare sector, analyses them based on different parameters identified from the literature. Some of our key findings include (1) analysis of quantitative and analytical modelling approaches used for dealing with disruption in healthcare sector; (2) managerial implications that derive potential future research avenues and insights for practitioners in the domain of healthcare supply chain disruption in post-pandemic era to improve international competitiveness and operational excellence.
... The proper distribution of emergency supplies is essential for controlling the spread of epidemics (Deng, Shen, & Vorobeychik, 2013;Kasaie & David Kelton, 2013;Liu & Ming, 2016). Most of the studies on the allocation of emergency supplies during large-scale epidemics are based on the SIR model of infectious disease, which is used to dynamically allocate medical supplies based on their demand (Shamsi et al., 2018). Vaccines are crucial during epidemics, as they can delay the spread of an epidemic; however, the allocation of vaccines is relatively concentrated (Westerink- Duijzer, Schlicher, & Musegaas, 2020;Yarmand, Ivy, Denton, & Lloyd, 2014). ...
During cross-regional epidemic outbreaks, patients with suspected infection have a high demand for testing resources, while patients with confirmed infection have a high demand for treatment resources. The allocation of testing resources affects the demand for treatment resources in multiple regions and at different periods, which features a time-lag correlation. In this study, we developed a joint allocation model for allocating testing and treatment resources with consideration of their time-lag correlation to minimize the loss of patients and maximum the fairness of allocation in all regions. We devised a sequential solution generation strategy (SSGS) and combined it with the NSGA2 and MOPSO algorithms to solve the proposed joint allocation problem. We demonstrated numerically that NSGA2 coupled with SSGS yields a better solution. Furthermore, we compared the solutions of our joint allocation model with those of an independent allocation model. Our numerical results show that the joint allocation scheme, which considers the time-lag correlation between the two types of resources, has better performance—with a lower loss of patients and higher fairness of allocation. In particular, when the impact of the allocation of testing resources on the demand for treatment resources was increased, the joint allocation scheme performed better in terms of both the objectives.
... Some disruptions, such as machines needing repairs or a fire in the factory of the manufacturer or their supplier, only disrupt one supply chain (Li et al., 2017;Son and Orchard, 2013;Paul et al., 2014Paul et al., , 2015, while others, such as an earthquake, Hurricane, or other natural disasters, affect partners in a particular location (e.g. a state or district of a country or the entire country) Chen et al., 2015). On the other hand, a major epidemic such as the 2014 Ebola outbreak in West Africa and the 1991-94 Cholera outbreak in South America, and pandemic disruption such as severe acute respiratory syndrome (SARS) in 2003 and H1N1 in 2009, affect a large region or the entire world simultaneously and have more severe impacts (B€ uy€ uktahtakın et al., 2018;Huff et al., 2015;Min, 2012;Shamsi et al., 2018). However, the current pandemic, COVID-19, has broken all previous records for its levels of interruption, as it has already affected almost all supply chains around the world, and its impacts are greater than those of any prior pandemic (Chowdhury et al., 2020a, b;Laing, 2020;van Barneveld et al., 2020;Sen, 2020;Koonin, 2020). ...
Purpose – The recent coronavirus disease 2019 (COVID-19) pandemic poses numerous challenges to supply chains. This pandemic is quite unique when compared to previous epidemic disruptions and has had a severe impact on supply chains. As a result, the operational challenges (OCs) caused by COVID-19 are still unknown
among practitioners and academics. It is critical to comprehensively document current OCs so that firms can plan and implement strategies to overcome them. Consequently, this study systematically identifies and ranks COVID-19-related OCs.
Design/methodology/approach – This study uses an integrated methodology combining expert interviews and the best-worst method (BWM) to analyze the results. The data have been collected from the electronics industry of Bangladesh, an emerging economy. This study also conducts a sensitivity analysis to check the robustness of the results.
Findings – The results reveal 23 COVID-19-related OCs under five categories: sourcing, production and inventory management, demand management and distribution, return management and after-sales service, and supply chain-wide challenges. The quantitative investigation reveals that overstock in finished goods inventory, low end-customer demands, order cancellations from dealers and retailers, high inventory holding costs and lack of transportation are the top five OCs.
Practical implications – The findings will help practitioners to understand the OCs and allow them to prepare for future major disruptions and formulate long-term strategies for operations during and after the COVID-19 pandemic.
Originality/value – This study contributes to the literature on supply chain complexity and challenges by considering a major pandemic outbreak. Moreover, the study also contributes to the knowledge on emerging economies, which have been largely neglected in the current literature.
... A special type of cost-sharing and coordinating can improve cost-benefit in public health and provide incentives for both players. Shamsi et al. (2018) extend Chick et al. (2008) by (i) considering a backup supplier to overcome uncertainties and (ii) adding a new social cost objective. An option contract is developed between a buyer, a governmental organization, and two vaccine suppliers. ...
We reviewed research papers related to pandemics/epidemics (disease outbreaks of a global/regional scope) published in major operations management, operations research, and management science journals through the end of 2019. We evaluate and categorize these papers. We study research trends, explore research gaps, and provide directions for more efficient and effective research in the future. In addition, our recommendations include the lessons learned from the ongoing pandemic, COVID-19. We discuss papers in the following categories: (a) warning signals/surveillance, (b) disease propagation leading to pandemic conditions, (c) mitigation, (d) vaccines and therapeutics development, (e) resource management, (f) supply chain configuration, (g) decision support systems for managing pandemics/epidemics, and (h) risk assessment.
... Davis et al. (2013) proposed a stochastic programming model to determine how supplies should be positioned and distributed among a network of cooperative warehouses for HSC coordination. Shamsi et al. (2018) developed an options contract model to proactively procure necessary vaccine from the suppliers using a Susceptibility-Infection-Recover (SIR) epidemic model. Fathalikhani et al. (2018Fathalikhani et al. ( , 2019 used the Stackelberg games, where the humanitarian NGO's were considered as leaders and donors were represented as followers. ...
Procurement of aid material such as vaccines by a humanitarian agency (HA) is often fraught with uncertainties. For example, an epidemic outbreak can increase the demand for materials (such as vaccines) in a very short period. Most of the HAs depend on external donations (funding) to procure necessary vaccines to meet this demand. Hence, it is financially infeasible and operationally inefficient for the HA to procure large quantities of aid material in anticipation of a demand spike during an epidemic outbreak. Thus, the procurement processes for aid materials such as vaccines need to be flexible enough to meet these demand fluctuations. HAs can achieve this flexibility by employing a procurement mechanism portfolio that includes upfront buying, capacity reservation, spot market purchase, etc. However, the challenge lies in identifying the optimal combination of multiple procurement mechanisms and how they can be utilized to coordinate the humanitarian supply chain. In this study, we explore the feasibility of quantity flexibility contracts along with discount incentives combined with spot market procurement in humanitarian supply chains for aid material procurement. We also derive the conditions under which the contract can achieve systemic coordination between the supplier and HA. Furthermore, we also illustrate that under optimal conditions, the procurement of aid material using multiple procurement mechanisms by HA can also reduce the humanitarian supply chain’s total cost.
... Chick et al. [9] formulate a contract between a supplier and the government who aims to minimize the expected social cost under stochastic yield, moral hazard, and adverse selection. Shamsi et al. [10] design an option contract for vaccines needed at the time of emergencies or outbreaks. Mamani et al. [11] study the inefficiencies in the allocation of influenza vaccine through a game-theoretical model. ...
In this paper, we analyze the vaccine supply chain of child immunization program of India under stochastic production yield. We show that the wholesale price contract cannot achieve channel coordination. We propose a subsidy contract to coordinate the vaccine supply chain. A case analysis in the Indian context is presented to illustrate the impact of the proposed subsidy contract.
Disasters affect hundreds of millions of people every year and the response of governments is crucial in alleviating the suffering of those affected. Despite the importance of contracting in response to disasters, research on this topic is conspicuous by its absence. This paper begins to address this gap by investigating the choice of procurement contract type by US federal agencies during disaster management operations. The research relies on 47,560 contracts issued by the US federal government in response to 14 major disasters between 2005 and 2016. We build on agency theory to investigate the choice of the contract type made by federal agencies at the different stages of a relief operation. This research provides empirical evidence of the key factors underpinning the choice of contract in the context of disaster management, namely the amount of spend per contract and the type of acquisition (product or service), and reveals the moderating role of the stage of the relief operation.
Le COVID-19 est une pandémie mondiale qui a bouleversé les modes de gouvernance des organisations. Les chaînes logistiques ont contribué, de plusieurs manières, à faire face et à atténuer les effets de cette épidémie. Néanmoins, ces chaînes ont été confrontées à plusieurs modifications et ont opéré plusieurs changements pour s’adapter avec les nouvelles barrières frontalières et opérationnelles.
L’objet de ce papier de recherche est d’établir une analyse qualitative des effets du COVID-19 sur la logistique et le supply chain. Nous proposons alors une analyse théorique des travaux traitant la gestion des chaînes d’approvisionnement lors des épidémies et spécialement la pandémie du COVID-19. À travers une revue de littérature, nous avons synthétisé plusieurs écrits scientifiques traitant les chaînes d’approvisionnement dans une pandémie. Cet examen nous a permis de dégager les principaux challenges et opportunités des chaînes d’approvisionnement mondiales pendant et après cette épidémie. L’analyse qualitative réalisée montre différents défis et opportunités actuels et futurs des SC.
Mots clefs : Supply chain, pandémie, logistique de pandémie, logistique de service, performance, performance logistique, COVID-19.
Relief activities are complicated when multiple disasters take place simultaneously at different locations. Designing effective relief networks for these instances involves managing the priorities among regions and products, developing the capacity to share limited resources and facilities, and engaging with multiple suppliers over several periods. Unfortunately, even after recent experiences in different countries, the management of simultaneous disasters is still understudied. This article introduces a two-stage dynamic formulation for logistics decisions in instances caused by simultaneous disasters. It guides supplier selection, facility location, stock prepositioning, and resource allocation at the first stage, whereas relief distribution, postdisaster procurement, and inventory management are addressed at the second stage. The model minimizes cost and the maximum shortage. Results of numerical experiments show the way the model considers the characteristics of each situation to dispatch limited shared resources. The experiments show that planning for single disasters has a negative impact on performance when faced with situations caused by simultaneous disasters. That is confirmed by findings from the case study in Mexico, which also highlights the preference for prepositioning stock using a mix of different kind of suppliers, and the importance of developing a reliable network of facilities and suppliers to handle simultaneous disasters effectively.
In preparation for a potential disaster, it is important to have cooperative relationships in place between relief organizations and businesses. Through a suitable framework agreement (FA), relief organizations can reduce a large amount of the inventory costs and decrease the social costs (i.e., the sum of deprivation costs and logistics costs) associated with their humanitarian operations, while businesses can make more profit. Unfortunately, in China, such cooperation between local authorities and business enterprises is still far from developed, due to the lack of high-quality FA contracts. In this paper, we solve the problem by designing a new FA that has an incentive for both relief organizations and businesses to establish the partnership, leading to a win-win situation. Unlike the widely studied contracts that are based on quantity and corresponding pricing strategies for relief items, the FA designed here incentivizes the delivery time, and encourages faster delivery of relief items, which is also important in mitigating human suffering. We consider the uncertainty of disaster timing and the dynamic relationships between delivery lead times and logistics/deprivation costs, and propose a decision-making process for relief organizations and partner businesses to negotiate and sign the new FA. A case study based on real-world data from a field investigation is conducted to prove the feasibility and effectiveness of our new FA.
The extant study aimed to create a kind of coordination in the humanitarian chain by using a quantity flexibility (QF) contract. The QF contract considers a kind of coordination between a relief organization and a producer for inventory management determining order volumes. Due to insufficiency of amenities or time limits during the crisis, an internal producer can outsource a part of its duties to an external producer to produce items and accelerate the relief process. Hence, this study proposed a completely novel bi-objective mathematical model to coordinate relief items' supply and distribution by using QF contracts and buying in the spot market under demand uncertainty conditions to reduce costs and accelerate relief services. The augmented epsilon constraint method was used to solve the small scales of this model and NSGA-II and NRGA algorithms were employed to solve large scales. The results indicated the powerful performance of NRGA in terms of most evaluation indicators.
Purpose
Each individual needs to be vaccinated to control the spread of the COVID-19 pandemic in the shortest possible time. However, the vaccine distribution with an already strained supply chain in low- and middle-income countries (LMICs) will not be effective enough to vaccinate all the population in stipulated time. The purpose of this paper is to show that there is a need to revolutionize the vaccine supply chain (VSC) by overcoming the challenges of sustainable vaccine distribution.
Design/methodology/approach
An integrated lean, agile and green (LAG) framework is proposed to overcome the challenges of the sustainable vaccine supply chain (SVSC). A hybrid best worst method (BWM)–Measurement of Alternatives and Ranking According to COmpromise Solution (MARCOS) methodology is designed to analyze the challenges and solutions.
Findings
The analysis shows that vaccine wastage is the most critical challenge for SVSC, and the coordination among stakeholders is the most significant solution followed by effective management support.
Social implications
The result of the analysis can help the health care organizations (HCOs) to manage the VSC. The effective vaccination in stipulated time will help control the further spread of the virus, which will result in the normalcy of business and availability of livelihood for millions of people.
Originality/value
To the best of the author's knowledge, this is the first study to explore sustainability in VSC by considering the environmental and social impact of vaccination. The LAG-based framework is also a new approach in VSC to find the solution for existing challenges.
Purpose
The already-strained vaccine supply chain (VSC) of the expanded program for immunization (EPI) require a more robust and structured distribution network for pandemic/outbreak vaccination due to huge volume demand and time constraint. In this paper, a lean-agile-green (LAG) practices approach is proposed to improve the operational, economic and environmental efficiency of the VSC.
Design/methodology/approach
A fuzzy decision framework of importance performance analysis (IPA)–analytical hierarchy process (AHP)–technique for order for preference by similarity in ideal solution (TOPSIS) has been presented in this paper to prioritize the LAG practices on the basis of the influence on performance indicators. Sensitivity analysis is carried out to check the robustness of the presented model.
Findings
The derived result indicates that sustainable packaging, coordination among supply chain stakeholders and cold chain technology improvement are among the top practices affecting most of the performance parameters of VSC. The sensitivity analysis reveals that the priority of practices is highly dependent on the weightage of performance indicators.
Practical implications
This study's finding will help policymakers reframe strategies for sustainable VSC (SVSC) by including new management practices that can handle regular immunization programs as well as emergency mass vaccination.
Originality/value
To the best of the authors' knowledge, this is the first study that proposes the LAG framework for SVSC. The IPA–Fuzzy AHP (FAHP)–Fuzyy TOPSIS (FTOPSIS) is also a novel combination in decision-making.
We study risk hedging in the online procurement problem, where one buyer and one seller sign reservation contracts in advance to hedge against the risks from the uncertainties of real demand and spot price. We generalize the traditional two-stage procurement model such that the buyer has the flexibility of signing multiple contracts in the first stage and makes decision on executions in the second stage. A lower bound on the performance of any deterministic algorithms is presented by restricting the possible execution price sequence and real demand in worst case. Then a deterministic online algorithm called Price Look Back (PLB) is designed with a competitive ratio that tends to the lower bound if historical execution prices are less fluctuant. Extensive experiments are conducted on both synthetic and real-life instances to evaluate the practical performance of PLB. The experimental results show that PLB performs significantly better than its (worst-case) theoretical guarantee in most instances. In addition, PLB is robust with respect to inaccurate information learned from the historical data. Specifically, the average extra cost incurred by the inaccurate information can be around 5% in real-life instances.
When disaster relief is executed by a monopolistic emergency management agency, this entity is responsible for the procurement and storage of relief goods in the given area. In the case of extreme disasters, relief goods are generally donated to the affected area from all over the world, but the delivery of these donations normally takes time. To ensure effective disaster relief, the emergency management agency should consider extreme disaster scenarios in the procurement of relief goods. Besides, both the supply and demand of relief goods can be differently affected by the disaster depending on its magnitude. And the management agency aims to minimize costs while accounting for potential shortages. In this study, we propose and develop a combined entrusted reserve and option (CEO) contract for humanitarian relief goods procurement. In our model, both the supply and demand of relief goods are described as functions of disasters intensity. Further, a bi-objective optimization problem is formulated with the model to minimize the management agency's expected cost and conditional value-at-risk (CVaR) based shortage risk. Then, we use the epsilon-constraint method to solve the problem and obtain the optimal CEO contract. We also conduct a case study of disasters occurred in Beijing, China from 2000 to 2014. The CEO contract is shown to alleviate losses related to the disasters and reduce costs of the management agency. Insights to further improve the effectiveness of the CEO contract are also discussed in the paper.
This paper presents a review of the existing research studies on vaccine supply chain (VSC) management. We analyze the current VSC system in India and investigate the research on VSC management specific to India. We focus on the coordination aspect and network design in the literature review. The paper summarizes the challenges in managing the VSC and provides future research directions to improve their performance.
Influenza vaccine supply chains are subject to yield and demand uncertainty, which leads to the mismatch between supply and demand. This paper studies the production and procurement decisions in the influenza vaccine supply chain consisting of a manufacturer facing uncertain production yield and a social planner who faces uncertain demand and is responsible for social infection costs. We develop a novel model framework considering the risks resulting from uncertainties on both supply and demand sides that the manufacturer may delay part of delivery and the social planner may order under or over demand. Based on the framework, we first discuss the production and procurement decision-making problem in a centralized and a decentralized system. By comparing the two systems, we present the existence and extent of the inefficiency in the influenza vaccine supply chain. Further, we propose a procurement strategy that provides the social planner with two ordering opportunities and explore the conditions under which the two members would be willing to accept the strategy. The results show that such a strategy is effective on improving the influenza vaccine supply chain coordination. Additionally, considering large-scale outbreaks of influenza epidemics, we extend the models with a piecewise linear infection probability function to those with a generic one and describe the characteristics of the extended models and their solutions.
Objectives:
The 2014-15 Ebola outbreak in West Africa highlighted the challenges many hospitals face when preparing for the potential emergence of highly contagious diseases. This study examined the experiences of frontline health care professionals in an Australian hospital during the outbreak, with a focus on participant views on information, training and preparedness, to inform future outbreak preparedness planning.
Study design:
Semi-structured interviews were conducted with 21 healthcare professionals involved in Ebola preparedness planning, at a hospital in Australia.
Methods:
The data were systematically coded to discover key themes in participants' accounts of Ebola preparedness.
Results:
Three key themes identified were: 1) the impact of high volumes of-often inconsistent-information, which shaped participants' trust in authority; 2) barriers to engagement in training, including the perceived relative risk Ebola presented; and finally, 3) practical and environmental impediments to preparedness.
Conclusions:
These clinicians' accounts of Ebola preparedness reveal a range of important factors which may influence the relative success of outbreak preparedness and provide guidance for future responses. In particular, they illustrate the critical importance of clear communication and guidelines for staff engagement with, and implementation of training. An important outcome of this study was how individual assessments of risk and trust are produced via, and overlap with, the dynamics of communication, training and environmental logistics. Consideration of the dynamic ways in which these issues intersect is crucial for fostering an environment that is suitable for managing an infectious threat such as Ebola.
As more supply chains are becoming dependent upon suppliers, the need and the value of a backup supply is increasingly evident. The purpose of this paper is to help a buyer determine the order quantity of a make-to-order contract with the backup supplier when the main supplier's recurrent uncertainties and possible disruptions are taken into consideration. We show that (1) if no supply disruption is considered, the buyer would rather order less from the backup supplier than that when the risks are decoupled; (2) bundling and decoupling the risks can result in different optimal solutions, and the properties of supply uncertainties and disruption risks play a vital role in the following two ways: (i) with the increase of the recurrent uncertainty, it is better for the buyer to order less from the backup supplier, which is opposite to the decision suggested by the stand-by contract in the literature; (ii) with the increase of the disruption probability, the buyer should order more from the backup supplier. And (3) under the make-to-order contract, bundling the risks can lead to under utilization of the backup supplier when the disruption probability is small enough, but may result in over utilization of the backup supplier when the probability is large.
In this paper, we address a two-echelon humanitarian logistics network design problem involving multiple central warehouses (CWs) and local distribution centers (LDCs) and develop a novel two-stage scenario-based possibilistic-stochastic programming (SBPSP) approach. The research is motivated by the urgent need for designing a relief network in Tehran in preparation for potential earthquakes to cope with the main logistical problems in pre- and post-disaster phases. During the first stage, the locations for CWs and LDCs are determined along with the prepositioned inventory levels for the relief supplies. In this stage, inherent uncertainties in both supply and demand data as well as the availability level of the transportation network's routes after an earthquake are taken into account. In the second stage, a relief distribution plan is developed based on various disaster scenarios aiming to minimize: total distribution time, the maximum weighted distribution time for the critical items, total cost of unused inventories and weighted shortage cost of unmet demands. A tailored differential evolution (DE) algorithm is developed to find good enough feasible solutions within a reasonable CPU time. Computational results using real data reveal promising performance of the proposed SBPSP model in comparison with the existing relief network in Tehran. The paper contributes to the literature on optimization based design of relief networks under mixed possibilistic-stochastic uncertainty and supports informed decision making by local authorities in increasing resilience of urban areas to natural disasters.
In this paper, we have developed a compartment of epidemic model with vaccination. We have divided the total population into five classes, namely susceptible, exposed, infective, infective in treatment and recovered class. We have discussed about basic properties of the system and found the basic reproduction number (R0) of the system. The stability analysis of the model shows that the system is locally as well as globally asymptotically stable at disease-free equilibrium E0 when R0 < 1. When R0 > 1 endemic equilibrium E1 exists and the system becomes locally asymptotically stable at E1 under some conditions. We have also discussed the epidemic model with two controls, vaccination control and treatment control. An objective functional is considered which is based on a combination of minimizing the number of exposed and infective individuals and the cost of the vaccines and drugs dose. Then an optimal control pair is obtained which minimizes the objective functional. Our numerical findings are illustrated through computer simulations using MATLAB. Epidemiological implications of our analytical findings are addressed critically.
In this paper, using the methodology of system dynamics modeling, we separately build two models for a supply chain under two circumstances of supply disruptions, without backup supplier, and with a contingent supplier. The retailer's total profits are also compared under these two circumstances of supply disruptions to help the decision-makers better understanding the backup purchasing strategy. The supply chain studied only involves one retailer and two independent suppliers that are referred to as major supplier and backup supplier. The paper contributes to the literature by providing a better understanding of the impacts of supply disruptions on the system performance and by shedding insights into the value of a backup supply.
A mathematical model of an SIR epidemic model with constant recruitment and two control variables using control terms and a deterministic system of dierential equation is presented and analyzed mathematically and numerically. We intend to control the susceptible and infected individuals with educational campaign and treatment strategies. We analyzed the model by non-dimensionalizing the system of equations of our SIR epidemic model and derived our basic reproduction number.We aim to minimize the total number of infective individuals and the cost associated with the use of educational campaign and treatment on [0; T ]. We used Pontryagin's maximum principle to characterize the optimal levels of the two controls. The resulting optimality system is solved numerically. The results show that the optimal combination of treatment and educational campaign strategy required to achieve the set objective will depend on the relative cost of each of the control measures. The results from our simulation is discussed. Keywords: Computational simulations, Disease Free Equilibrium, Optimal control, Pontryagin's Maximum Principle, stability theory.
Tuberculosis is a global epidemic disease and almost two billion people across the globe are infected with the tuberculosis bacilli. Many countries like China, Europe and United States has achieved dramatic decrease in TB mortality rate but country like India is still struggling hard to control this epidemic. Jharkhand one of the states of India is highly epidemic toward this disease. We propose a mathematical model to understand the spread of tuberculosis disease in human population for both pulmonary and drug-resistant subjects. A number of new vaccines are currently in development. Keeping in mind, vaccination as one of the treatment for TB patients may be infant or adult in future; an assumption for the transfer of proportion of susceptible population to the vaccination class is considered. Quarantine class is also considered in our epidemic model for multidrug-resistant patients, and it is observed that it may play a vital role for controlling the disease. Threshold and equilibria are obtained and the condition for epidemic under different conditions of threshold is established. Real parametric values of the Jharkhand state are taken into account to simulate the system developed, and the results so obtained validate our analytical results.
The most basic stochastic epidemic models are those involving global transmission, meaning that infection rates depend only on the type and state of the individuals involved, and not on their location in the population. Simple as they are, there are still several open problems for such models. For example, when will such an epidemic go extinct and with what probability (questions depending on the population being fixed, changing or growing)? How can a model be defined explaining the sometimes observed scenario of frequent mid-sized epidemic outbreaks? How can evolution of the infectious agent transmission rates be modelled and fitted to data in a robust way?
Copyright © 2014 The Authors. Published by Elsevier B.V. All rights reserved.
We focus on an epidemic model which incorporates a non-linear force of infection and two controls: an imperfect preventive vaccine given to susceptible individuals and therapeutic treatment given to infectious. We study both the cases of constant and non constant controls. In the case of constant controls we perform a qualitative analysis based on Lyapunov stability which allows to integrate the bifurcation analysis performed in a previous paper. The occurrence of a backward bifurcation is discussed in the perspective of disease control. The case of time-dependent controls is studied by means of the optimal control theory. The strategy is to minimize both the disease burden and the intervention costs. We derive the optimality system and solve it numerically. The characterization of the optimal time profile of the controls, together with the qualitative analysis provides a rather complete picture of the possible outcomes of the model.
We present a review of models of swine flu A H1N1. We discuss how control of epidemic critically depends on the value of the Basic Reproduction Number (R_0). The R_0 for new influenza estimated 1.5. By means of suitable Volterra-type Lyapunov functions, we establish the global stability of the steady state of an disease transmission models with control measures type SIR. We conclude that R_0 plays an important role in the designing disease control strategies.
Tuberculosis is a global epidemic disease and almost two billion people across the globe are infected with the tuberculosis bacilli. Many countries like China, Europe and United States has achieved dramatic decrease in TB mortality rate but country like India is still struggling hard to control this epidemic. Jharkhand one of the states of India is highly epidemic toward this disease. We propose a mathematical model to understand the spread of tuberculosis disease in human population for both pulmonary and drug-resistant subjects. A number of new vaccines are currently in development. Keeping in mind, vaccination as one of the treatment for TB patients may be infant or adult in future; an assumption for the transfer of proportion of susceptible population to the vaccination class is considered. Quarantine class is also considered in our epidemic model for multidrug-resistant patients, and it is observed that it may play a vital role for controlling the disease. Threshold and equilibria are obtained and the condition for epidemic under different conditions of threshold is established. Real parametric values of the Jharkhand state are taken into account to simulate the system developed, and the results so obtained validate our analytical results.
Purpose
– Although noticeable improvements have been made in global health in recent years, the distribution is uneven throughout the world and many developing and low-income countries lack access to required medicine and vaccines. Thus, a model to strategically source vaccines for these nations can contribute a great deal. This paper aims to present an extensive review of strategic sourcing literature, and to identify the criteria and available models in making strategic sourcing decisions. The purpose is to develop a decision making framework for future empirical study of humanitarian aid networks, more specifically, sourcing and distribution of vaccines in developing countries.
Design/methodology/approach
– A thorough review of several purchasing and supply chain management (SCM) journals was conducted to identify the strategic criteria in making sourcing decisions, hence “strategic sourcing”. In line with this, a number of sourcing strategies were reviewed to find the relevant strategic criteria. Secondary data from practice were also investigated for special characteristics of vaccine supply chains in humanitarian aid networks. Articles were then scrutinized and results categorized in order to develop a framework for future empirical studies.
Findings
– The findings show the historical development of strategic sourcing and the criteria in making strategic sourcing decisions. More recent studies, while taking a look back in history, have revealed a mix of strategies for more flexible models. Quality has been noted to be a strategic criterion for sourcing vaccines and this has caused the supply market to be dispersed on a global scale.
Research limitations/implications
– Considering the extensive number of academic publications, due to the focus of this study being sourcing within humanitarian aid networks, a number of academic journals in logistics/SCM/sourcing were reviewed.
Originality/value
– A decision making framework is presented for sourcing vaccines within the humanitarian sector. The criteria in making strategic sourcing decisions are further re-evaluated and a base model proposed. The framework will be used for further research on sourcing in the humanitarian aid sector as well as practical implications.
The recent devastating earthquake of December 26 in Bam, 2003 created various risk factors; caused a sharp increase in incidence of anthroponotic cutaneous leishmaniasis (ACL) cases and reached to an epidemic proportion. The objective of this study was to evaluate the status of ACL cases five years before the earthquake compared to the cases occurred five years after the earthquake (1999-2008).
Status of disease was assessed retrospectively for the five years before the earthquake and prospectively for the five years after the earthquake. Identification was confirmed by smear and polymerase chain reaction (PCR).
The mean annual incidence of ACL for the period from 1999 to 2003 was 1.9 per 1000 comparing to post earthquake period, which was 7.6 per 1000. Most of the infection was in individuals of <20 years, more frequently in females before the earthquake, whilst in contrast, there was a progressive rise in the number of cases, significantly in male individuals of >20 years (P< 0.0001) in post earthquake era. The anatomical distribution of lesions considerably changed during the two periods. Most of the cases were limited to three zones within the city prior to the earthquake, whereas it was spread throughout different zones after the earthquake. PCR indicated that the CL was due to Leishmania tropica in the city.
The results strongly suggest that in natural disasters such as earthquakes various precipitating factors in favor of disease will be created, which in turn provide a suitable condition for propagation of the vector and the transmission of the parasite.
In this paper, a novel multi-objective integrated sustainable-resilient mixed integer linear programming model for designing a pharmaceutical supply chain network under uncertainty is presented. To cope with the uncertainty aspect of the model, a new fuzzy possibilistic-stochastic programming approach is developed. Additionally, due to NP-hard nature of the problem, we propose a novel Pareto-based lower bound method as well as a new meta-heuristic algorithm. Several numerical examples, as well as a case study targeting Truvada© supply chain for the LGBTQ community, as they account for majority of the market for such product, in France is proposed.
Supplier selection is an important strategic decision in the context of supply chain management. Existing literature on the subject of supplier selection is focused on evaluating primary (e.g., cost, quality, lead time) and green (e.g., CO2 emission, environmental practices) criteria. However, the concept of supplier resilience has recently emerged due to advent of competitive and global supply chains (and the operational and disruptive risks to which they are exposed). Several resilience-based supplier selection criteria are developed with respect to absorptive, adaptive, and restorative capacities. This paper further proposes a Bayesian network (BN), a paradigm that effectively models the causal relationships among variables but that has not been used in the context of supplier evaluation and selection, to quantify the appropriateness of suppliers across primary, green, and resilience criteria. Some benefits of the BN paradigm, including an ability to handle expert evidence and to perform sensitivity and propagation analyses, are demonstrated with an initial illustrative example of three suppliers.
There are two broad categories of risk affecting supply chain design and management: (1) risks arising from the problems of coordinating supply and demand, and (2) risks arising from disruptions to normal activities. This paper is concerned with the second category of risks, which may arise from natural disasters, from strikes and economic disruptions, and from acts of purposeful agents, including terrorists. The paper provides a conceptual framework that reflects the joint activities of risk assessment and risk mitigation that are fundamental to disruption risk management in supply chains. We then consider empirical results from a rich data set covering the period 1995-2000 on accidents in the U.S. Chemical Industry. Based on these results and other literature, we discuss the implications for the design of management systems intended to cope with supply chain disruption risks.
This work presents a novel model of emergency medical logistics for quick response to public health emergencies. The proposed methodology consists of two recursive mechanisms: (1) the time-varying forecasting of medical relief demand and (2) relief distribution. The medical demand associated with each epidemic area is forecast according to a modified susceptible-exposed-infected-recovered model. A linear programming approach is then applied to facilitate distribution decision-making. The physical and psychological fragility of affected people are discussed. Numerical studies are conducted. Results show that the consideration of survivor psychology significantly reduces the psychological fragility of affected people, but it barely influences physical fragility.
This work focuses on optimal vaccination policies for an Susceptible - Infected - Recovered (SIR) model; the impact of the disease is minimized with respect to the vaccination strategy. The problem is formulated as an optimal control problem and we show that the value function is the unique viscosity solution of an Hamilton - Jacobi - Bellman (HJB) equation. This allows to find the best vaccination policy. At odds with existing literature, it is seen that the value function is not always smooth (sometimes only Lipschitz) and the optimal vaccination policies are not unique. Moreover we rigorously analyze the situation when vaccination can be modeled as instantaneous (with respect to the time evolution of the epidemic) and identify the global optimum solutions. Numerical applications illustrate the theoretical results. In addition the pertussis vaccination in adults is considered from two perspectives: first the maximization of DALY averted in presence of vaccine side-effects; then the impact of the herd immunity on the cost-effectiveness analysis is discussed on a concrete example.
Copyright © 2015. Published by Elsevier Inc.
A precise definition of the basic reproduction number, R o , is presented for a general compartmental disease transmission model based on a system of ordinary differential equations. It is shown that, if R o < 1, then the disease free equilibrium is locally asymptotically stable; whereas if R o > 1, then it is unstable. Thus, R o is a threshold parameter for the model. An analysis of the local centre manifold yields a simple criterion for the existence and stability of super-and sub-threshold endemic equilibria for R o near one. This criterion, together with the definition of R o , is illustrated by treatment, multigroup, staged progression, multistrain and vector-host models and can be applied to more complex models. The results are significant for disease control.
This paper proposes a novel relief supply collaboration approach to address the issue of post-disaster relief supply–demand imbalance in emergency logistics (EL) operations. This proposed approach involves two levels of recursive functions: (1) a two-stage relief supplier clustering mechanism for time-varying multi-source relief supplier selection and (2) the use of stochastic dynamic programming model to determine a multi-source relief supply that minimises the impact of relief supply–demand imbalance during EL response. The distinctive features of this proposed approach are to identify the potential relief suppliers and to minimise the imbalanced supply–demand impact under relief supply collaboration. Scenario design and model tests are conducted to demonstrate that relief supply collaboration with grouped relief suppliers has a significant benefit of alleviating the impact of imbalanced relief supply–demand, relative to collaboration with ungrouped ones.
This paper is concerned with the long time behavior of a stochastic SIS epidemic model with vaccination. Sufficient conditions for extinction and persistence in mean are obtained. We find a threshold of the stochastic model which determines the outcome of the disease in case the white noises are small. At last, some numerical simulations are carried out to support our results.
This paper investigates the problem of sourcing decisions under stochastic demand considering quantity discounts and suppliers' failure risks. A Mixed Integer Non-Linear Programming (MINLP) model is developed considering different failure probability, capacity, price discounts, compensation potential, and transportation cost under a stochastic demand environment to determine the optimal suppliers' portfolio (i.e. the number of suppliers and order quantity allocation) for a single product in a single period. The model considers that each supplier has different failure probability, capacity, transportation cost, price discounts and compensations potential. The MINLP model is NP-hard in nature and difficult to solve with exact methods; therefore, a Real Coded Genetic Algorithm (RCGA) is employed here to solve it. Further, RCGA performance is benchmarked by comparing its results with the MINLP solver BONMIN (Basic Open-source Mixed Integer Non-Linear Programming). A numerical study is conducted to illustrate the proposed model, a genetic algorithm and BONMIN to find the solution. Finally, different managerial implications have been drawn based on sensitivity analysis.
Vaccination is one of the most promising methods to control the epidemic spread by protecting the most vulnerable population and reducing the number of susceptible population who are exposed to the virus. However, the vaccine doses are usually limited and can only be supplied during the epidemic outbreak. How to distribute the vaccines to different populations to reduce the total number of infectious people is important to the public health. In this paper, a DE algorithm is proposed to solve the problem by searching for the optimal strategy to distribute the limited vaccines to different age groups of population. The performance of the algorithm is compared with three strategies in the literature. The results show that the proposed algorithm can offer more effective vaccine distributions significantly.
In this paper, we discuss the dynamics of a stochastic SIS epidemic
model with vaccination. When the noise is large, the infective decays
exponentially to zero regardless of the magnitude of R0. When
the noise is small, sufficient conditions for extinction exponentially
and persistence in the mean are established. The results are illustrated
by computer simulations.
This paper studies coordination in a three-echelon supply chain and examines the impact of sub-supply chain coordination (sub-coordination). Our analysis is based on the price-only contracts that are commonly used in practice. The model is of the newsvendor type. We consider the following cases: no coordination between any members of the supply chain (decentralized), coordination between only two members (sub-supply chain coordination) and coordination of the whole supply chain as a benchmark. We explicitly analyze the order quantity and contracting decisions for a decentralized three-echelon supply chain. We compare supply chain efficiency when there is upstream coordination and when there is downstream coordination and show that the former is more efficient than or as efficient as the latter. In our setting, the difference between upstream and downstream sub-supply chain coordination is equivalent to the shortage cost transfer. We find that both the supplier and the retailer would prefer to act alone rather than to coordinate with the manufacturer when sub-supply chain coordination is suggested. This contradiction may partly explain the popularity of price-only contracts in practice.
In this paper, we analyze an SIS epidemic model with partially protective vaccination of efficacy e ∈ [0, 1]. The model exhibits backward bifurcation for certain parameter values. The primary aim of this paper is to investigate the possibility of eliminating the infections in static as well as exponentially growing populations with a public health strategy based solely on vaccination. The critical vaccination rate ψ* above which the endemic infection dies out and the conditions on model parameters that ensure its existence are obtained. It has been found that eliminating the infection requires an application of control measures other than vaccination to reduce the basic reproduction number to below the reinfection threshold and then vaccinate susceptible individuals with a rate slightly greater than ψ*. The implication is that, generally, even if all newborns get vaccinated immediately after birth, an effective control is not necessarily assured except if the basic reproduction number is reduced to below the reinfection threshold. We further include the fatality of the infection and investigate its impact on the dynamics. Some numerical simulations are given to illustrate the theoretical analysis.
Relief material management which aims to reduce the impact of disaster and maintain social stability is of great importance for nonprofit organization (NPO) such as government, department of civil affair or Red Cross. However, the research of efficiency and performance on this field has long been ignored. In order to improve the efficiency and performance of the relief material management, we apply the supply chain management method into this field. Considering the relief material management system as a supply chain with one buyer and one supplier, we introduce the option contract mechanism into relief material supply chain management. With reasonable assumptions, we design an option contract with two delivery steps, and build an option pricing model with binominal lattice to estimate the different values of the same option contract for both members of supply chain. Furthermore, we analyze the impacts of the different parameters (such as the ratio of inventory, subjective probability of disaster, etc.), on the supply chain and its members in detail. The numerical example presented at last demonstrates that, with two delivery steps, there is a feasible price range of option contract which makes both members of relief material supply chain profitable and willing to conduct the transaction with option contract.
In this paper, a supplier selection problem is studied under risks of supplier failure due to the catastrophic events disruption. An analytical model is developed to determine the optimal number of suppliers considering different failure probability, capacity, and compensation. An algorithm is designed to find the optimal solution and numerical study is carried out to illustrate the model. Results of numerical study and sensitivity analysis provide useful guidelines for managers to select the optimal number of suppliers under the risks of supply disruption.
This article summarizes the 1988, 1990, 1995, and 2002 Working Groups on California Earthquake Probabilities (WGCEPs). Each of these studies used the best available science to make a time-dependent earthquake forecast. All involved applying elastic-rebound-theory-motivated recurrence models to estimate the probability of rupture on discrete fault segments. The focus was necessarily limited to those faults that had sufficient information to make a time-dependent analysis, although the later studies included probabilities for other events as well. This manuscript does not give a point-by-point critique or review of the previous WGCEPs, both because it would take considerably more text and because such discussions will necessarily be documented by future working groups as they justify changes. One opinion that is emphasized, however, is that future WGCEPs should resist overcomplexity in certain aspects of the model given basic assumptions that have been made and/or limitations in our understanding of the earthquake system. For example, one might argue that the level of sophistication applied by previous WGCEPs with respect to recurrence-interval variability and uncertainty was overkill given their basic assumptions that large earthquakes obey segment boundaries, ruptures never jump from one fault to another, and earthquake-clustering effects can be ignored.
This research examines how to use an option contract to coordinate a retailer-led supply chain where the market information can be updated. Based on Stackelberg game theory, we build a mode with one supplier and one retailer in which the retailer designs contracts to coordinate the supplier's production in a two-mode production environment. This focuses on an option contract that consists of two option prices and one exercise price. By theoretical analysis and numerical example, we find that such a contract can coordinate the supplier and retailer to act in the best interest of the channel. The optimal pricing conditions are given as follows: First, option prices should be negatively correlated to the exercise price and should be in a relevant range. Second, the first-period option price should be no greater than the second-period price and should be linearly correlated to the second-period option price when the latter is beyond some threshold. The results show that such option contracts can arbitrarily allocate the extra system profit between the two parties so that each party is in a win-win situation.
Purpose
This paper aims to provide a tool for decision makers to help them with selection of the appropriate supplier.
Design/methodology/approach
Companies often depend on their suppliers to meet customers' demands. Thus, the key to the success of these companies is selection of the appropriate supplier. A methodology is proposed to address this issue by first identifying the appropriate selection criteria and then developing a mechanism for their inclusion and measurement in the evaluation process. Such an evaluation process requires decision maker's preferences on the importance of these criteria as inputs.
Findings
Human assessments contain some degree of subjectivity that often cannot be expressed in pure numeric scales and requires linguistic expressions. To capture this subjectivity the authors have applied fuzzy logic that allows the decision makers to express their preferences/opinions in linguistic terms. Decision maker's preferences on appropriate criteria as well as his/her perception of the supplier performance with respect to these criteria are elicited. Fuzzy membership functions are used to convert these preferences expressed in linguistic terms into fuzzy numbers. Fuzzy mathematical operators are then applied to determine a fuzzy score for each supplier. These fuzzy scores are in turn translated into crisp scores to allow the ranking of the suppliers. The proposed methodology is multidisciplinary across several diverse disciplines like mathematics, psychology, and operations management.
Practical implications
The procedure proposed here can help companies to identify the best supplier.
Originality/value
The paper describes a decision model that incorporates decision maker's subjective assessments and applies fuzzy arithmetic operators to manipulate and quantify these assessments.
This chapter reviews the supply chain coordination with contracts. Numerous supply chain models are discussed. In each model, the supply chain optimal actions are identified. The chapter extends the newsvendor model by allowing the retailer to choose the retail price in addition to the stocking quantity. Coordination is more complex in this setting because the incentives provided to align one action might cause distortions with the other action. The newsvendor model is also extended by allowing the retailer to exert costly effort to increase demand. Coordination is challenging because the retailer's effort is noncontractible—that is, the firms cannot write contracts based on the effort chosen. The chapter also discusses an infinite horizon stochastic demand model in which the retailer receives replenishments from a supplier after a constant lead time. Coordination requires that the retailer chooses a large basestock level.
The objectives of this paper are to define, compare and contrast the commercial supply chain and the humanitarian relief chain, discuss an approach to performance measurement in the domain of humanitarian relief, and identify the challenges faced by relief chain logisticians in practice and research.
This paper examines optimal policies in a continuous review inventory management system when demand in each time period follows a log-normal distribution. In this scenario, the distribution for demand during the entire lead time period has no known form. The proposed procedure uses the Fenton-Wilkinson method to estimate the parameters for a single log-normal distribution that approximates the probability density function (PDF) for lead time demand, conditional on a specific lead time. Once these parameters are determined, a mixture of truncated exponentials (MTE) function that approximates the lead time demand distribution is constructed. The objective is to include the log-normal distribution in a robust decision support system where the PDF that best fits the historical period demand data is used to construct the lead time demand distribution. Experimental results indicate that when the log-normal distribution is the best fit, the model presented in this paper reduces expected inventory costs by improving optimal policies, as compared to other potential approximations.
In this paper the mathematical SIRC epidemic model is considered. It efficiently describes diseases in which a cross immune class (C) is present, along with the susceptible (S), the infected (I) and the removed (R) ones. Controlling epidemic diseases corresponds to the introduction of vaccination, quarantine and treatment strategies; generally only one of these actions is considered. In this paper the possibility of optimal controls both over the susceptible and the infected subjects is assumed, taking into account also limitations of resources. A suitable cost index is introduced and via the Pontryagin's Minimum Principle the optimal control strategy is determined and the existence of the optimal solution is assessed. Numerical results are developed analyzing the effects of different control strategies.
This article studies two contract mechanisms to share demand and supply risk in a decentralized supply chain. In an option contract, the buyer reserves capacity with a supplier who guarantees delivery up to this limit. This insulates the buyer from any disruption risk, but the supplier faces both demand and supply risk. The second mechanism, the firm order contract, represents a conventional dyadic channel relationship where the buyer places a firm order and the supplier builds capacity but does not guarantee delivery if any disruption occurs. It is shown that the buyer's preference for using the different risk-sharing mechanisms switches back and forth (as the probability of disruption increases). Consequently, a supplier with a higher disruption risk may make higher expected profits compared to one with lower risk. In addition, the buyer may benefit from a higher wholesale price since it provides incentive for the supplier to participate without requiring the buyer to use higher order quantities. Two operational mitigation strategies that can be used by the buyer to hedge against the disruption risk are considered: the use of an alternate reliable supplier during a shortage and use of a direct subsidy for the supplier to improve reliability. It is found that the value of the reliable supplier depends on the type of contract with the unreliable supplier: interestingly, it is in the option contract—where supply is guaranteed—that the buyer almost always uses the reliable supplier as well. Also, it is found that offering a subsidy for reliability improvement acts as a strategic alternative to placing large pre-orders as a way to improve supplier operations.
In this paper, we propose and analyze an epidemic problem which can be controlled by vaccination as well as treatment. In the first part of our analysis we study the dynamical behavior of the system with fixed control for both vaccination and treatment. Basic reproduction number is obtained in all possible cases and it is observed that the simultaneous use of vaccination and treatment control is the most favorable case to prevent the disease from being epidemic. In the second part, we take the controls as time dependent and obtain the optimal control strategy to minimize both the infected populations and the associated costs. All the analytical results are verified by simulation works. Some important conclusions are given at the end of the paper.
The demand for humanitarian aid is extraordinarily large and it is increasing. In contrast, the funding for humanitarian operations does not seem to be increasing at the same rate. Humanitarian logistics has the challenge of allocating scarce resources to complex operations in an efficient way. After acquiring sufficient contextual knowledge, academics can use operations research (OR) to adapt successful supply chain management best practices to humanitarian logistics. We present two cases of OR applications to field vehicle fleet management in humanitarian operations. Our research shows that by using OR to adapt supply chain best practices to humanitarian logistics, significant improvements can be achieved.