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Robust vehicle routing with drones under uncertain demands and truck travel times in humanitarian logistics
Abstract
Resource transport in the aftermath of disasters is critical, yet in the absence of sufficient historical data or accurate forecasting approaches, the development of resource transport strategies often faces the challenge of dealing with uncertainty, especially uncertainties in demand and travel time. In this paper we investigate the vehicle routing problem with drones under uncertain demands and truck travel times. Specifically, there is a set of trucks and drones (each truck is associated with a drone) collaborating to transport relief resources to the affected areas, where a drone can be launched from its associated truck at a node, independently transporting relief resources to one or more of the affected areas, and returning to the truck at another node along the truck route. For this problem, we present a tailored robust optimization model based on the well-known budgeted uncertainty set, and develop an enhanced branch-andprice-and-cut algorithm incorporating a bounded bidirectional labelling algorithm to solve the pricing problem, which can be modelled as a robust resource-constrained vehicle and drone synthetic shortest path problem. To enhance the performance of the algorithm, we employ subset-row inequalities to tighten the lower bound and incorporate some enhancement strategies to quickly solve the pricing problem. We perform extensive numerical studies to assess the performance of the developed algorithm, discuss the benefits of considering uncertainty and robustness, and analyse the impacts of key model parameters on the optimal solution. We also evaluate the benefits of the truck–drone collaborative transport mode over the truck-only transport mode through a real case study of the 2008 earthquake in Wenchuan, China.
... Rabta 2021) also consider a depot where all drones initially take off from; however, the items to be delivered to demand points are not located in this depot but held in intermediary laboratories along the network. Similarly, Lu et al. (2022Lu et al. ( , 2023, Yin et al. (2023), and Zhang et al. (2023b) consider a setting with intermediary replenishment points; however, the drone take-off points are assumed to be the trucks. Kallaj (2023) addresses an inventory routing problem where blood is collected using bloodmobiles and is delivered to final destinations concurrently by both bloodmobiles and drones. ...
... Kallaj (2023) and Shadlou et al. (2023) aim to provide a certain service level by minimizing the maximum arrival times to nodes. Yin et al. (2023) seek to improve the service level by imposing a penalty for late deliveries. Only Different than the information collection problems, in delivery problems, an important limitation of drones is their restricted load capacity. ...
... Martins et al. (2021) consider intermediary units located inside and outside the affected area, and drones pick up the necessary loads to deliver at these points. On the other hand, synchronized delivery trucks are considered to be demand replenishment points for drones by Lu et al. (2022Lu et al. ( , 2023, Yin et al. (2023), and Zhang et al. (2023b). Similarly, Kallaj (2023) introduces a setting where truck-collection and truck-drone delivery are synchronized. ...
The increasing use of drones has led to growing interest in their potential applications in disaster response. In this study, we examine the role of drones in disaster management under three categories of operation types, which are information collection, delivery, and communication network recovery. Focusing on an operations research (OR) perspective, we analyze and summarize the important characteristics of different problem structures and highlight the solution approaches. We also identify gaps and limitations in the current literature and propose future directions for further investigation. Overall, the study provides a comprehensive summary and valuable insights for researchers and practitioners interested in exploring the use of drones for humanitarian purposes and developing OR‐based approaches to support decision‐making.
... Gu, Liu, and Poon [15] proposed a framework combining a Markov decision process and a heuristic algorithm to address the uncertainty of the pick-to-order problem in a dynamic truck-drone routing problem to improve the total profits of the logistics system and the acceptance rate of customer requests. Yin et al. [16] considered the uncertainty of customer demand and travel time, studied a class of collaborative transportation problems between drones and trucks in humanitarian logistics, proposed a framework combining robust optimization and a branch-and-price algorithm to solve the problem, and verified the superiority and practicability of this method through a real case analysis. Zhao et al. [17] proposed a robust multi-drone traveling salesman problem (TSP) to address parcel delivery. ...
... Constraint (6) can be represented by the following deterministic constraint: (16) Expanding (16) yields: ...
... This was evident in the model's emphasis on UAV battery consumption metrics and its aspiration to optimize allocations that would minimize operational costs and expected risks, particularly the risk of UAVs being shot down. Reinforcing this aerial perspective, both References [37,38] underscored the potential of drone technology, implicitly championing its benefits in enhancing the safety and security of humanitarian personnel. ...
... Constraints (37)(38) are optional and should be included in the model if some budgetary restrictions exist (i.e., expenses from fuel or security escorts). Constraint (37) is the period-to-period spending constraint, and Constraint (38) is the overall operating budgetary constraint. ...
In this study, we address a pressing yet underexplored problem in humanitarian logistics (HLs), which is enhancing the safety and security of humanitarian personnel in conflict zones, through the introduction of non-routineness of trips in vehicle routing models. This research is critically justified, as evidenced by the alarming statistics from 2020, where over 100 road ambushes were reported, affecting over 200 humanitarian workers through kidnappings, injuries, and fatalities. Moving beyond traditional approaches that primarily focus on increasing convoy sizes or incorporating ambush probabilities, our research poses a pivotal question: How can existing knowledge from security journals and manuals be effectively leveraged to address this problem? In response, we have developed a groundbreaking vehicle routing model that ensures variability in routes and travel times, significantly reducing the predictability of humanitarian convoys and enhancing their security. Our approach also integrates additional security measures, including avoiding night travel and implementing convoy camping strategies, to further mitigate risks. A central innovation of our study is the creation of a first-of-its-kind index, designed to quantify the routineness of trips – a critical yet previously overlooked metric in HLs. The efficacy of our model is demonstrated through a comprehensive case study in South Sudan, a region afflicted by ongoing civil unrest, underscoring the real-world applicability and urgency of our research. Additionally, we provide an approximate closed-form solution for the aid allocation subproblem, optimizing for both fairness and effectiveness. This research marks a significant leap forward in logistics optimization, especially within HLs in conflict zones, addressing a vital gap in the literature and offering innovative perspectives and practical solutions to complex security problems faced by humanitarian logisticians.
... To extend the flight range of drones, multiple depots or recharging stations might be investigated. The development of drone delivery strategies often faces the challenge of dealing with uncertainty, e.g., uncertain customer demand and travel time [50]. Robust optimization can be explored to address these uncertainty-related constraints. ...
Unmanned aerial vehicles (UAVs), or drones, are recognized for their potential to improve efficiency in last-mile delivery. Unlike the vehicle routing problem, drone route design is challenging due to several operational signatures, such as speed optimization, multi-trip operation, and energy consumption estimation. Drone energy consumption is a nonlinear function of both speed and payload. Moreover, the high speed of drones can significantly curtail the drone range, thereby limiting the efficiency of drone delivery systems. This paper addresses the trade-off between speed and flight range in a multi-trip drone routing problem with variable flight speeds (DRP–VFS). We propose a new model to specifically consider energy constraints using a nonlinear energy consumption model and treat drone speeds as decision variables. The DRP–VFS is initially formulated using mixed-integer linear programming (MILP) to minimize energy consumption. To solve large-scale instances, we propose a three-phase adaptive large neighborhood search (ALNS) algorithm and compare its performance with a commercial MIP solver. The experimental results demonstrate that the proposed method is capable of effectively identifying suboptimal solutions in practical scenarios. Furthermore, results indicate that operating drones at variable speeds leads to about 21% energy savings compared to fixed speeds, with advantages in cost savings and range extension.
... In recent years, drones have seen extensive utilization in various fields, with notable applications in logistic management, particularly in the last-mile delivery (Meng et al., 2023;Zhao et al., 2022a;Wen and Wu, 2022), humanitarian logistics (Yin et al., 2023;Ghelichi et al., 2022a) and detection (Shen et al., 2022). In these studies, the predominant focus lies in addressing the routing problem or optimizing drone network design. ...
A rise in traffic accidents has led to both traffic congestion and subsequent secondary accidents. Effectively addressing this issue requires rapid accident investigation and management. In this paper, we aim to improve the efficiency of traffic accident assessment and investigation with the aid of drone technologies. Our approach involves strategically pre-positioning drones, enabling traffic supervisory agencies to dispatch drones immediately upon receiving an accident report. Methodology-wise, we present a data-driven robust stochastic optimization (RSO) model, which encapsulates the uncertainty of traffic accidents within a scenario-wise Wasserstein ambiguity set. To the best of our knowledge, this is the first study that incorporates covariates, i.e., weather conditions, into the Wasserstein ambiguity set with the CVaR metric. We demonstrate that the proposed RSO model can be reformulated into a mixed-integer programming model, allowing an efficient solution approach. Via a real-world dataset of London traffic accidents, we validate the practical applicability of the RSO model. Across various parameter settings, our RSO model exhibits superior out-of-sample performance compared with various benchmark models. The numerical results yield valuable insights for traffic supervisory agencies.
... Many studies in recent years have addressed the humanitarian relief network design issues spanning location-allocation, locationrouting, and evacuation planning under uncertainties in demand (Kınay et al., 2018;Wang and Chen, 2020;Stienen et al., 2021;Yang et al., 2023), supply (Rahmani et al., 2018;Cheng et al., 2021;Chakravarty, 2014), cost (Condeixa et al., 2017;Torabi et al., 2018), network connectivity (Bastian et al., 2016;Elçi and Noyan, 2018), and traveling time (Caunhye et al., 2016;Li et al., 2020;Yin et al., 2023b), in order to find the optimal relief plan or policy to optimize cost, equity, reliability, and/or response time (Ye et al., 2020;Dönmez et al., 2021). ...
We consider an integrated location-allocation and evacuation planning problem in a disaster context, where the effects of a disaster, including the uncertain capacities of relief facilities (rescue centers and distribution centers), uncertain demands for relief supplies and casualty treatment services, and uncertain availability of transportation links are characterized by a discrete scenario set. Instead of complete failures, we allow the disrupted relief facilities only lose part of their capacity. To deal with the uncertainties, we propose a two-stage recoverable robust optimization model, where the location decision of relief facilities, the allocation decision of delivering relief supplies from relief facilities to affected areas, the transfer decision of transporting casualties from affected areas to rescue centers etc are defined in two stages where the first-stage solution should be robust against the possible effects of a disaster that are revealed in the second stage, and the second-stage solution involves some recovery actions, which we term as multi-mitigation strategies: reopening and re-operation, reallocation , and relief supply sharing, to mitigate the effects. To solve the model to optimality, we develop a nested two-stage decomposition algorithm that iterates between a master problem considering only a subset of disaster scenarios solved by a Benders decomposition algorithm that incorporates some non-trivial acceleration strategies, and an adversarial separation problem that identifies disaster scenarios to enhance the worst-case recovery cost of the master problem. We introduce some warm-start techniques to accelerate the convergence of the solution algorithm. We conduct numerical studies on simulation instances to assess the performance of the solution algorithm, and analyze the robustness and recoverability of the model. We also conduct extensive numerical studies on realistic instances from Ya'an and Ganzi to demonstrate the benefits of accounting for recoverable robustness over a stochastic policy and a robust policy without recovery actions, the benefits of considering integrated optimization over sequential optimization, and the benefits of considering partial capacity loss and multi-mitigation strategies.
... It is very important to deliver resources when disaster strikes. Yin et al. (2023) conducted a routing study to provide this distribution in their study. In the course of the research, there is truck and drone cooperation. ...
Drone-based transportation is emerging as a novel mode in city logistics, featuring first-mile pickup and last-mile instant delivery using drones and truck transshipment. A fundamental challenge involves coordinating merchants, drones, transshipment hubs, trucks, and consumer communities through the hub-and-spoke network (HSN). This study formulated the optimization problem for HSN to minimize logistics costs and loss of orders constrained by service time limits. The ε-constraint model, two evolutionary algorithms based on Non-dominated Sorting Genetic Algorithm II (NSGA-II) using permutation (EAp) and rand key-based (EAr) encoding/decoding schemes were devised to solve the bi-objective mathematical program. Three groups of twelve experiments were conducted using ideal datasets and datasets generated from Shenzhen city to validate the models and algorithms. Relaxing the logistics objective by 10% and subsequently minimizing the loss of orders can significantly reduce average unmet orders by 24.61%; when spokes were beyond 20, the ε-constraint model failed to achieve solutions within an acceptable time. While EAp and EAr demonstrated competence, EAr proved to be more competitive in computation time, hypervolume, spacing metric, and the number of non-dominated solutions on the Pareto fronts. Key parameters influencing the HSN solutions include drone and truck speeds, acceptable delivery times, and the processing and waiting time at hubs.
This paper presents a two-stage hybrid robust programming model that integrates multiple blood products scheduling and multiple casualty types evacuation under facility disruptions risk and casualty number uncertainty. The model seeks to maximize the rescue efficiency and minimize the total operations cost. Under a set of disruption scenarios, we adopt a scenario-based robust method to address disruption risks at temporary medical centres and two robust uncertainty sets to deal with uncertain casualty numbers. We propose a proximal bundle algorithm to solve large-scale instances of the proposed hybrid robust model approximately. Extensive numerical experiments show that: (i) the trade-off between model robustness and solution robustness can help the decision-makers determine an appropriate risk-aversion weight; (ii) compared with the corresponding stochastic and scenario-based robust models, the hybrid robust model can obtain more robust solutions with a slight increase in cost; (iii) the proximal bundle algorithm can produce near-optimal solutions within reasonable computational times; (iv) some model parameters have significant impact on the total cost, which can help decision-makers set the appropriate parameters to achieve the desired outcome. Finally, we also use the real data of the 2008 Wenchuan County Earthquake in Sichuan Province, China, to illustrate the application of the model.
This paper applies the truck and drone cooperative delivery model to humanitarian logistics and proposes a multi-objective humanitarian pickup and delivery vehicle routing problem with drones (m-HPDVRPD) which contains two subproblems: cooperative routing subproblem and relief supplies allocation subproblem. The m-HPDVRPD is formulated as a multi-objective mixed integer linear programming (MILP) model with two objectives, which simultaneously minimizes the maximum cooperative routing time and maximizes the minimum fulfillment rate of demand nodes. We develop a hybrid multi-objective evolutionary algorithm with specialized local search operators (HMOEAS) and a hybrid multi-objective ant colony algorithm (HACO) for the problem. A set of numerical experiments are performed to compare the performance of the two algorithms and their three variants. And the experimental results prove that HMOEAS is more effective than other methods. Taking the Corona Virus Disease 2019 (COVID-19) epidemic in Wuhan as a case, we compare the truck-drone cooperative delivery model with the truck-only delivery and the drone-only delivery models, and find that our model has advantages in the delivery efficiency of anti-epidemic materials. Moreover, based on the real-world case, a sensitivity analysis is conducted to investigate the impact of different drone parameters on the efficiency of truck-drone cooperative delivery.
Recently, there are attempts to utilize drones in the logistic application. We consider the case in which there are multiple drones with different characteristics, such as speed and battery capacity. The truck and drone collaborate the delivery to serve all customers, while the drones are carried by and dispatched from the truck. The multiple drones can be deployed simultaneously; however, the truck must wait until all drones return. Therefore, the goal is to minimize the total sum of truck travel and waiting times for drones to return after deliveries. We call the proposed model a heterogeneous drone-truck routing problem (HDTRP), and a mixed-integer programming formulation for the problem is presented. We develop an exact algorithm based on the logic-based Benders decomposition approach, which outperforms the state-of-the-art solvers.
This paper proposes a scenario-based three-stage hybrid robust and stochastic model that optimally designs the response network and distributes casualties effectively under uncertain combinational scenarios of primary and secondary disasters. Following the stochastic severity of combinational disasters, the robust counterparts are derived against the ambiguous uncertainty of evacuee scales and transportation time, respectively. A customized progressive hedging algorithm based on the augmented Lagrangian relaxation is developed to solve the problem. We decompose the problem based on the scenario and iteratively solve the adaptively penalized sub-problems with decision variables independent of stages. The results of an illustrative example show that incorporating secondary disaster scenarios can contribute to improving relief coverage. The proposed algorithm is competitive with some benchmarks.
The efficient planning of search and rescue (SAR) operations is highly impactful in the disaster response phase, which offers a limited time window with a declining chance for saving trapped people. The present paper introduces a new robust decision support framework for planning SAR resource deployment in post-disaster districts. A two-stage decomposition approach is applied to formulate the problem as iterative interrelated stages of mixed-integer programming (MIP) models. The first stage presents a robust multi-period allocation model for maximizing fair and effective demand coverage in the affected districts during the entire planning horizon. It takes into account the time-sensitiveness of the operations via a time-dependent demand satisfaction measure and incorporates resource transshipment optimization. The second stage optimizes the routing of the resources allocated in the first stage for each district during the upcoming period. It aims to minimize the weighted sum of SAR demand fulfillment times under consideration of secondary destruction risk, resource collaboration, and rest time requirements. At the end of each period, the proposed framework can be re-executed to capture updated resource, demand, and travel time parameters. To tackle the environment’s inherent uncertainty, an interval-based robust optimization approach is adopted. The proposed framework is solved and analyzed for an urban zone in Iran under an earthquake scenario. Results show that the proposed robust models have superior performance compared to a deterministic approach for adaptation to an uncertain disaster environment. More importantly, they prove to be a strong analysis tool for providing helpful managerial insights for the mitigation and preparedness phases.
We focus on rapid needs assessment operations conducted immediately after a disaster to identify the urgent needs of the affected community groups, and address the problem of selecting the sites to be visited by the assessment teams during a fixed assessment period and constructing assessment routes under travel time uncertainty. Due to significant uncertainties in post-disaster transportation network conditions, only rough information on travel times may be available during rapid needs assessment planning. We represent uncertain travel times simply by specifying a range of values, and implement robust optimization methods to ensure that each constructed route is feasible for all realizations of the uncertain parameters that lie in a predetermined uncertainty set. We present a tractable robust optimization formulation with a coaxial box uncertainty set due to its advantages in handling uncertainty in our selective assessment routing problem, in which the dimension of the uncertainty (number of arcs traversed) is implicitly determined. To solve the proposed model efficiently, we develop a practical method for evaluating route feasibility with respect to the robust route duration constraints, and embed this feasibility check procedure in a tabu search heuristic. We present computational results to evaluate the effectiveness of our solution method, and illustrate our approach on a case study based on a real-world post-disaster network.
The purpose of this manuscript is to explore methodologies for conducting comprehensive literature review. The manuscript objectives are twofold: one is to identify a suitable methodology for conducting comprehensive literature review and two is to enable the identification of main research themes and clusters obtained from the literature. The domain of humanitarian operations, logistics and supply chain performance is selected as the review context. The main strength of a systematic literature review from other styles of literature review is that it provides a much higher level of methodology to the process. It further provides a rapid comprehensive identification of main research themes and clusters as illustrated from the humanitarian operations and logistics performance domain.
In this paper, we consider the vehicle routing problem with load-dependent drones (VRPLD),
in which the energy consumption of drones is load-dependent and represented by a nonlinear
function. To strengthen the collaboration between trucks and drones, a kind of facility called
the docking hub is introduced to extend the service coverage of drones. When a truck visits
the hub, a part number of parcels are transferred to the drones departing from the hub
to serve the designated customers. We propose a mixed-integer model for the problem,
which is nonlinear due to the load-dependent energy consumption. To solve the model,
we develop a branch-and-price-and-cut algorithm based on the Danzig-Wolfe decomposition
framework, and propose a series of acceleration strategies, including two valid inequalities,
to expedite the convergence of the exact algorithm. Computational results on a set of
randomly generated instances reflect that the proposed algorithm outperforms Gurobi in
terms of both efficiency and effectiveness. Compared with VRPLD, the vehicle routing
problem with drones (VRPD) which ignores the load-dependent constraints underestimates
the total travel cost by 6.83%. Another drawback of VRPD is that some results may
become infeasible when considering the load-dependent energy consumption. The results
under VRPLD further reveal that a more accurate description of the energy consumption
makes the drones rely more on services from auxiliary facilities. We also conduct sensitivity analysis to draw some managerial insights that setting the hub at a reasonable location can
significantly reduce the delivery cost and improve truck and drone cooperation efficiency.
Increasing e-commerce activities poses a tough challenge for logistics distribution. With the development of new technology, firms attempt to leverage drones for parcel delivery to improve delivery efficiency and reduce overall costs. We consider the truck-based drone delivery routing problem with time win- dows. In our setting, a set of trucks and drones (each truck is associated with a drone) collaborate to serve customers, where a drone can take offfrom its associated truck at a node, independently serve one or more customers within the time windows, and return to the truck at another node along the truck route. To solve the problem, we develop an enhanced branch-and-price-and-cut algorithm incorpo- rating a bounded bidirectional labelling algorithm to solve the challenging pricing problem. To improve the algorithm, we use the subset-row inequalities to tighten the lower bound and apply enhancement strategies, which solve the pricing problem efficiency. We perform extensive numerical studies to evalu- ate the performance of the developed algorithm, assess the gain of the truck-based drone delivery over the truck-only delivery, and provide some managerial insights.
Humanitarian logistics often faces the challenge of dealing with uncertainties when developing a rescue strategy in response to the occurrence of a disaster. We develop a distributionally robust model (DRM) for the multi-period location-allocation problem with multiple resources and capacity levels under uncertain emergency demand and resource fulfilment time with only limited distributional information being available in humanitarian logistics. We show that the model can be equivalently reformulated as a mixed-integer linear program, and develop a tailored branch-and-Benders-cut algorithm to solve it. To enhance the efficiency of the algorithm, we propose some improvement strategies, including in-out Benders cut generation, dual lifting, and normalization of the dual variables. We perform extensive numerical studies to verify the performance of the developed algorithm, assess the value of the DRM over the corresponding deterministic and stochastic models, and discuss the impacts of key model parameters to gain managerial insights, particularly for the decision-maker planning on allocating resources based on tradeoff among the operating cost, equity and efficiency. We also demonstrate how our model performs had it been used in the actual earthquake that occurred in Jiuzhaigou, China.
This work focuses on a broad class of facility location problems in the context of adaptive robust stochastic optimization under the state-dependent demand uncertainty. The demand is assumed to be significantly affected by related state information, such as the seasonal or socio-economic information. In particular, a state-wise ambiguity set is adopted for modeling the distributional uncertainty associated with the demand in different states. The conditional distributional characteristics in each state are described by a support, as well as by mean and dispersion measures, which are assumed to be conic representable. A robust sensitivity analysis is performed, in which, on the one hand, we analyze the impact of the change in ambiguity-set parameters (e.g., state probabilities, mean value abounds, and dispersion bounds in different states) onto the optimal worst-case expected total cost using the ambiguity dual variables. On the other hand, we analyze the impact of the change in location design onto the worst-case expected second-stage cost and show that the sensitivity bounds are fully described as the worst-case expected shadow-capacity cost. As for the solution approach, we propose a nested Benders decomposition algorithm for solving the model exactly, which leverages the subgradients of the worst-case expected second-stage cost at the location decisions formed insightfully by the associated worst-case distributions. The nested Benders decomposition approach ensures a finite-step convergence, which can also be regarded as an extension of the classic L-shaped algorithm for two-stage stochastic programming to our state-wise, robust stochastic facility location problem with conic representable ambiguity. Finally, the results of a series of numerical experiments are presented that justify the value of the state-wise distributional information incorporated in our robust stochastic facility location model, the robustness of the model, and the performance of the exact solution approach.
The truck and drone-based cooperative model of delivery can improve the efficiency of last mile delivery, and has thus increasingly attracted attention in academia and from practitioners. In this study, we examine a vehicle routing problem and apply a cooperative form of delivery involving trucks and drones. We propose a mixed-integer programming model and a branch-price-and-cut-based exact algorithm to address this problem. To reduce the computation time, we design several acceleration strategies, including a combination of dynamic programming and calculus-based approximation for the pricing problem, and various effective inequalities for the restricted master problem. Numerical experiments are conducted to validate the effectiveness and efficiency of the proposed solution.
In this paper, we introduce the multiple Traveling Salesman Problem with Drone Stations (mTSP-DS), which is an extension to the classical multiple Traveling Salesman Problem (mTSP). In the mTSP-DS, we have a depot, a set of trucks, and some packet stations that host a given number of autonomous vehicles (drones or robots). The trucks start their mission from the depot and can supply some packet stations, which can then launch and operate drones/robots to serve customers. The goal is to serve all customers either by truck or by drones/robots while minimizing the makespan. We formulate the mTSP-DS as a mixed integer linear programming (MILP) model to solve small instances. To address larger instances, we first introduce two variants of a decomposition-based matheuristic. Afterwards, we suggest a third approach that is based on populating a solution pool with several restarts of an iterated local search metaheuristic, which is followed by determining the best combination of tours using a set-partitioning model. To verify the performance of our algorithms, we conducted extensive computational experiments. According to the numerical results, we observe that the use of drone stations leads to considerable savings in delivery time compared to traditional mTSP solutions. Furthermore, we investigated the energy consumption of trucks and drones. Indeed, depending on the energy consumption coefficients of trucks and drones as well as on the distance covered by drones, the mTSP-DS can also achieve energy savings in comparison to mTSP solutions.
Humanitarian aid in disasters is critical to saving lives and alleviating human suffering. This paper presents a novel scenario-based robust bi-objective optimization model that integrates medical facility location, casualty transportation, and relief commodity allocation considering triage. The proposed model aims to minimize the total deprivation cost of casualties due to the delayed access to medical services and the total operation cost. Following a set of disruption scenarios, the scenario-based robust approach is applied to protect solutions against the risk of disruptions in temporary medical centers. Considering the uncertain number of casualties under each scenario, the robust method which denotes the uncertainty as interval data is adopted. We utilize the ε-constraint method to deal with the bi-objective model. Additionally, we consider real case studies of the Wenchuan Earthquake to validate the proposed model. Several numerical experiments are conducted to examine the effects of uncertainties and capacities of medical facilities on the main objective value. The performance of considering the uncertainty and facility disruption is also discussed.
The increasing number and severity of natural and man-made disasters worldwide has led to calls for more precise and effective humanitarian responses, and the use of humanitarian relief network assessment to reduce disaster uncertainty can play a vital role in the delivery of precise humanitarian operations. In this study, a collaborative truck-and-drone system was developed as a post-disaster assessment tool for use by humanitarian relief networks. The proposed system comprises a drone equipped with a camera that can launch from a truck to collect information from both nodes and links of a post-disaster transportation network. Following drone operation, the truck is used to retrieve and recharge the drone’s battery. To optimize this collaborative truck-and-drone system, we focused on the routing problem with the objective of maximizing the value of information collected from nodes and links within a predefined time limit, a problem made challenging by the need to determine the routes of the truck and drone in an integrated manner. To the best of our knowledge, this study was the first to consider the problem of collaborative truck-and-drone routing optimization with the goal of profit maximization. After formulating the proposed problem as a mixed-integer linear programming (MILP) model, we decomposed the problem structure into a path-based master problem and two sub-problems to allow the use of a column generation (CG) framework to tackle the problem. Numerical experiments were conducted to examine the proposed model and algorithm at various instance sizes that were generated by modifying an existing benchmark, with the results indicating that the proposed algorithm can obtain high-quality solutions with optimality gaps of less than 10% for all terminated instances within predefined time limit. A real-world instance—the Kartal district of Istanbul—was then used to demonstrate the practicality of the proposed model. Finally, the results of the numerical analysis were used to develop managerial insights for application by humanitarian relief agencies.
Column generation (CG) is widely used for solving large-scale optimization problems. This article presents a new approach based on a machine learning (ML) technique to accelerate CG. This approach, called column selection, applies a learned model to select a subset of the variables (columns) generated at each iteration of CG. The goal is to reduce the computing time spent reoptimizing the restricted master problem at each iteration by selecting the most promising columns. The effectiveness of the approach is demonstrated on two problems: the vehicle and crew scheduling problem and the vehicle routing problem with time windows. The ML model was able to generalize to instances of different sizes, yielding a gain in computing time of up to 30%.
Increasing online purchases and higher customer requirements in terms of speed, flexibility, and costs of home deliveries are challenges to every company involved in last mile delivery. Technological advances have paved the way for last mile deliveries by unmanned aerial vehicles (UAV). Yet, the limited range and capacity of UAVs remain a challenge. This makes the possibility of pairing drones with well-established means of transportation highly attractive. However, the optimization problem arising in joint delivery by truck and drone has only recently been considered in the literature.
We develop a new mixed integer linear programming (MILP) model for the vehicle routing problem with drones (VRPD) with two different time-oriented objective functions. Additionally, we introduce new valid inequalities based on problem properties to strengthen the linear relaxation. One type of valid inequalities is an extension of the well known subtour elimination constraints. As the number of these constraints grows exponentially with instance size, we provide a separation routine that identifies violated cuts in relaxed solutions to add them efficiently. We therefore derive the first branch-and-cut algorithm for the VRPD. Extensive numerical experiments are performed to demonstrate the competitiveness of our MILP formulation and to show the impact of different combinations of valid inequalities. We optimally solve instances with unrestricted drone ranges with up to 20 nodes and instances with range-limited drones with up to 30 nodes. These are significantly larger instance sizes than the previously known exact approaches are able to handle. In addition, we introduce a relaxation of the VRPD that provides good lower bounds in notable reduced run times. To provide managerial insights, we show that integrating truck-drone tandems into transportation systems can not only lead to improvements regarding the speed of deliveries, but can also be used to reduce the fleet size without slowing down the delivery process and increasing the workload of truck drivers.
Purpose
This study aims to minimize the expected arrival time of relief vehicles to the affected areas, considering the destruction of potential routes and disruptions due to disasters. In relief operations, required relief items in each affected area and disrupted routes are considered as uncertain parameters. Additionally, for a more realistic consideration of the situations, it is assumed that the demand of each affected area could be met by multiple vehicles and distribution centers (DCs) and vehicles have limited capacity.
Design/methodology/approach
The current study developed a two-stage stochastic programming model for the distribution of relief items from DCs to the affected areas. Locating the DCs was the first-stage decisions in the introduced model. The second-stage decisions consisted of routing and scheduling of the vehicles to reach the affected areas.
Findings
In this paper, 7th district of Tehran was selected as a case study to assess the applicability of the model, and related results and different sensitivity analyses were presented as well. By carrying out a simultaneous sensitivity analysis on the capacity of vehicles and the maximum number of DCs that can be opened, optimal values for these parameters were determined, that would help making optimal decisions upon the occurrence of a disaster to decrease total relief time and to maximize the exploitation of available facilities.
Originality/value
The contributions of this paper are as below: presenting an integrated model for the distribution of relief items among affected areas in the response phase of a disaster, using a two-stage stochastic programming approach to cope with route disruptions and uncertain demands for relief items, determining location of the DCs and routing and scheduling of vehicles to relief operations and considering a heterogeneous fleet of capacitated relief vehicles and DCs with limited capacity and fulfilling the demand of each affected area by more than one vehicle to represent more realistic situations.
The interest in using drones in various applications has grown significantly in recent years. The reasons are related to the continuous advances in technology, especially the advent of fast microprocessors, which support intelligent autonomous control of several systems. Photography, construction, and monitoring and surveillance are only some of the areas in which the use of drones is becoming common. Among these, last-mile delivery is one of the most promising areas. In this work we focus on routing problems with drones, mostly in the context of parcel delivery. We survey and classify the existing works and we provide perspectives for future research.
Disasters such as fires, earthquakes, and floods cause severe casualties and enormous economic losses. One effective method to reduce these losses is to construct a disaster relief network to deliver disaster supplies as quickly as possible. This method requires solutions to the following problems. 1) Given the established distribution centers, which center(s) should be open after a disaster? 2) Given a set of vehicles, how should these vehicles be assigned to each open distribution center? 3) How can the vehicles be routed from the open distribution center(s) to demand points as efficiently as possible? 4) How many supplies can be delivered to each demand point on the condition that the relief allocation plan is made a priority before the actual demands are realized? This study proposes a model for risk-averse optimization of disaster relief facility location and vehicle routing under stochastic demand that solves the four problems simultaneously.
The novel contribution of this study is its presentation of a new model that includes conditional value at risk with regret (CVaR-R)—defined as the expected regret of worst-case scenarios—as a risk measure that considers both the reliability and unreliability aspects of demand variability in the disaster relief facility location and vehicle routing problem. Two objectives are proposed: the CVaR-R of the waiting time and the CVaR-R of the system cost. Due to the nonlinear capacity constraints for vehicles and distribution centers, the proposed problem is formulated as a bi-objective mixed-integer nonlinear programming model and is solved with a hybrid genetic algorithm that integrates a genetic algorithm to determine the satisfactory solution for each demand scenario and a non-dominated sorting genetic algorithm II (NSGA-II) to obtain the non-dominated Pareto solution that considers all demand scenarios. Moreover, the Nash bargaining solution is introduced to capture the decision-maker’s interests of the two objectives. Numerical examples demonstrate the trade-off between the waiting time and system cost and the effects of various parameters, including the confidence level and distance parameter, on the solution. It is found that the Pareto solutions are distributed unevenly on the Pareto frontier due to the difference in the number of the distribution centers opened. The Pareto frontier and Nash bargaining solution change along with the confidence level and distance parameter, respectively.
With growing consumer demand and expectations, companies are attempting to achieve cost-efficient and faster delivery operations. The integration of autonomous vehicles, such as drones, in the last-mile network design can curtail many operational challenges and provide a competitive advantage. This paper deals with the problem of delivering orders to a set of customer locations using multiple drones that operate in conjunction with a single truck. To take advantage of the drone fleet, the delivery tasks are parallelized by concurrently dispatching the drones from a truck parked at a focal point (ideal drone launch location) to the nearby customer locations. Hence, the key decisions to be optimized are the partitioning of delivery locations into small clusters, identifying a focal point per cluster, and routing the truck through all focal points such that the customer orders in each cluster are fulfilled either by a drone or truck. In contrast to prior studies that tackle this problem using multi-phase sequential procedures, this paper presents mathematical programming models to jointly optimize all the decisions involved. We also consider two polices for choosing a cluster focal point - (i) restricting it to one of the customer locations, and (ii) allowing it to be anywhere in the delivery area (i.e., a customer or non-customer location). Since the models considering unrestricted focal points are computationally expensive, an unsupervised machine learning-based heuristic algorithm is proposed to accelerate the solution time. Initially, we treat the problem as a single objective by independently minimizing either the total cost or delivery completion time. Subsequently, the two conflicting objectives are considered together for obtaining the set of best trade-off solutions. An extensive computational study is conducted to investigate the impacts of restricting the focal points, and the influence of adopting a joint optimization method instead of a sequential approach. Finally, several key insights are obtained to aid the logistics practitioners in decision making.
In recent years, drone routing and scheduling has become a highly active area of research. This research introduces a new routing model that considers a synchronized truck-drone operation by allowing multiple drones to fly from a truck, serve one or multiple customers, and return to the same truck for a battery swap and package retrieval. The model addresses two levels (echelons) of delivery: primary truck routing from the main depot to serve assigned customers and secondary drone routing from the truck, which behaves like a moveable intermediate depot to serve other sets of customers. The model takes into account both trucks' and drones’ capacities with the objective of finding optimal routes of both trucks and drones that minimizes the total arrival time of both trucks and drones at the depot after completing the deliveries. The problem can be solved by formulated mixed integer programming (MIP) for the small-size problem, and two efficient heuristic algorithms are designed to solve the large-size problems: Drone Truck Route Construction (DTRC) and Large Neighborhood Search (LNS). Numeric results from the experiment compare the performance of both heuristics against the MIP method in small/medium-size instances from the literature. A sensitivity analysis is conducted to show the delivery time improvement of the proposed model over the previous truck-drone routing models.
Vehicle routing problems (VRPs) are among the most studied problems in operations research. Nowadays, the leading exact algorithms for solving many classes of VRPs are branch-price-and-cut algorithms. In this survey paper, we highlight the main methodological and modeling contributions made over the years on branch-and-price (branch-price-and-cut) algorithms for VRPs, whether they are generic or specific to a VRP variant. We focus on problems related to the classical VRP—that is, problems in which customers must be served by several capacitated trucks and which are not combinations of a VRP and another optimization problem.
We address the robust vehicle routing problem with time windows (RVRPTW) under customer demand and travel time uncertainties. As presented thus far in the literature, robust counterparts of standard formulations have challenged general-purpose optimization solvers and specialized branch-and-cut methods. Hence, optimal solutions have been reported for small-scale instances only. Additionally, although the most successful methods for solving many variants of vehicle routing problems are based on the column generation technique, the RVRPTW has never been addressed by this type of method. In this paper, we introduce a novel robust counterpart model based on the well-known budgeted uncertainty set, which has advantageous features in comparison with other formulations and presents better overall performance when solved by commercial solvers. This model results from incorporating dynamic programming recursive equations into a standard deterministic formulation and does not require the classical dualization scheme typically used in robust optimization. In addition, we propose a branch-price-and-cut method based on a set partitioning formulation of the problem, which relies on a robust resource-constrained elementary shortest path problem to generate routes that are robust regarding both vehicle capacity and customer time windows. Computational experiments using Solomon’s instances show that the proposed approach is effective and able to obtain robust solutions within a reasonable running time. The results of an extensive Monte Carlo simulation indicate the relevance of obtaining robust routes for a more reliable decision-making process in real-life settings.
The deployment of drones to support the last-mile delivery has been initially attempted by several companies such as Amazon and Alibaba. The complementary capabilities of the drone and the truck pose an innovative delivery mode. The relevant optimisation problem associated with this new mode, known as the travelling salesman problem with drone (TSP-D), aims to find the coordinated routes of a drone and a truck to serve a list of customers. In practice, managers sometimes intend to attain a compromise between operational cost and completion time. Therefore, this article addresses a bi-objective TSP-D considering both objectives. An improved non-dominated sorting genetic algorithm (INSGA-II) is proposed to solve the problem. Specifically, the label algorithm-based decoding method, the fast non-dominated sorting approach, the crowding-distance computation procedure, and the local search component are devised to accommodate the features of the problem. Furthermore, the first Pareto front obtained by the INSGA-II is improved by a post-optimisation component. Computational results validate the competitive performance of the proposed algorithm. Meanwhile, the trade-off analysis demonstrates the relationship between operational cost and completion time and provides managerial insights for managers designing reasonable compromise routes.
Traffic congestion is one key factor that delays emergency supply logistics after disasters, but it is seldom explicitly considered in previous emergency supply planning models. To fill the gap, we incorporate traffic congestion effects and propose a two-stage location-allocation model that facilitates the planning of emergency supplies pre-positioning and post-disaster transportation. The formulated mixed-integer nonlinear programming model is solved by applying the generalized Benders decomposition algorithm, and the suggested approach outperforms the direct solving strategy. With a case study on a hurricane threat in the southeastern U.S., we illustrate that our traffic congestion incorporated model is a meaningful generalization of a previous emergency supply planning model in the literature. Finally, managerial insights about the supplies pre-positioning plan and traffic control policy are discussed.
In this paper, we consider a variant of a truckload open vehicle routing problem with time windows, which is suitable for modeling vehicle routing operations during a humanitarian crisis. We present two integer linear programming models to formulate the problem. The first one is an arc-based mixed integer linear programming model that can be solved using a general purpose solver. For the second formulation, we first devise a task adjacency graph, that we use to develop a path-based integer linear program. We then propose a column generation framework to solve large-scale instances. Finally, we perform numerical experiments to compare the performance of the two models. Our computational results show that the path-based formulation solved using our proposed column generation framework outperforms the arc-based mixed integer linear program in solution time, without sacrificing solution quality.
E-commerce and retail companies are seeking ways to cut delivery times and costs by exploring opportunities to use drones for making last mile delivery deliveries. This paper addresses the delivery concept of a truck-drone combination along with the idea of allowing autonomous drones to fly from delivery trucks, make deliveries, and fly to any available delivery truck nearby. We present a mixed integer programming (MIP) formulation that captures this scenario with the objective of minimizing the arrival time of both trucks and drones at the depot after completing the deliveries. A new algorithm based on insertion heuristics is also developed to solve large sized problems containing up to a hundred locations. Experiments are conducted to compare the MIP solutions with those obtained from different models with single truck, multiple truck and a single truck and drone system, as well as test the performance of the proposed algorithm. The numerical results demonstrate the potential operational gain when implementing the proposed drone delivery system compared to the conventional truck alone or single truck/drone delivery system.
The importance of drone delivery services is increasing. However, the operational aspects of drone delivery services have not been studied extensively. Specifically, with respect to truck-drone systems, researchers have not given sufficient attention to drone facilities because of the limited drone flight range around a distribution center. In this paper, we propose a truck-drone system to overcome the flight-range limitation. We define a drone station as the facility where drones and charging devices are stored, usually far away from the package distribution center. The traveling salesman problem with a drone station (TSP-DS) is developed based on mixed integer programming. Fundamental features of the TSP-DS are analyzed and route distortion is defined. We show that the model can be divided into independent traveling salesman and parallel identical machine scheduling problems for which we derive two solution approaches. Computational experiments with randomly generated instances show the characteristics of the TSP-DS and suggest that our decomposition approaches effectively deal with TSP-DS complexity problems.
Last mile deliveries with unmanned aerial vehicles (also denoted as drones) are seen as one promising idea to reduce excessive road traffic. To overcome the difficulties caused by the comparatively short operating ranges of drones, an innovative concept suggests to apply trucks as mobile landing and take‐off platforms. In this context, the paper on hand schedules the delivery to customers by drones for given truck routes. Given a fixed sequence of stops constituting a truck route and a set of customers to be supplied, we aim at a drone schedule (i.e., a set of trips each defining a drone's take‐off and landing stop and the customer serviced), such that all customers are supplied and the total duration of the delivery tour is minimized. We differentiate whether multiple drones or just a single one are placed on a truck and whether or not take‐off and landing stops have to be identical. We provide an analysis of computational complexity for each resulting subproblem, introduce efficient mixed‐integer programs, and compare all cases with regard to their potential of reducing the delivery effort on the last mile.
Emergency distribution is an important aspect of disaster response. However, when planning such activities, decision makers should consider not only uncertain and dynamic input data such as supply and demand, but also the real-time adjustment requirements of the existing distribution plans that account for the deviation between the predicted and actual (or observed) values of the input data. Consequently, we present a multi-commodity, multi-period distribution model that considers both relief commodities and injured people to minimize the total weighted unmet demand throughout the planning horizon. Furthermore, we propose a rolling horizon-based framework, based on the robust model predictive control (RMPC) approach, to obtain robust relief distribution plans and adjust them in accordance with updated real-time information. We then use a numerical example based on the Great Wenchuan Earthquake that occurred on May 12, 2008, in Sichuan Province, China, to investigate the application of our proposed model and framework, and we perform a detailed analysis of the influence of the settings of robust optimization parameters.
Researchers have proposed the use of unmanned aerial vehicles (UAVs) in humanitarian relief to search for victims in disaster‐affected areas. Once UAVs must search through the entire affected area to find victims, the path‐planning operation becomes equivalent to an area coverage problem. In this study, we propose an innovative method for solving such problem based on a Partially Observable Markov Decision Process (POMDP), which considers the observations made from UAVs. The formulation of the UAV path planning is based on the idea of assigning higher priorities to the areas that are more likely to have victims. We applied the method to three illustrative cases, considering different types of disasters: a tornado in Brazil, a refugee camp in South Sudan and a nuclear accident in Fukushima, Japan. The results demonstrated that the POMDP solution achieves full coverage of disaster‐affected areas within a reasonable time span. We evaluate the traveled distance and the operation duration (which were quite stable), as well as the time required to find groups of victims by a detailed multivariate sensitivity analysis. The comparisons with a Greedy Algorithm showed that the POMDP finds victims more quickly, which is the priority in humanitarian relief, whereas the performance of the Greedy focuses on minimizing the traveled distance. We also discuss the ethical, legal and social acceptance issues that can influence the application of the proposed methodology in practice.
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This study investigates a new delivery problem that has emerged after the attempts of several ecommerce and logistics firms to deploy drones in their operations to increase efficiency and reduce delivery times. In this problem, a delivery truck that carries a drone on its roof serves customers in coordination with a drone. The drone is considered to complement the truck due to its cost-efficiency and ability to access difficult terrains and to travel without exposure to congestion. This study presents an iterative algorithm that is based on a decomposition approach to minimize delivery completion time. In the first stage of the proposed methodology, the truck route and the customers assigned to the drone are determined. In the second stage, a mixedinteger linear programming model is solved to optimize the drone route by fixing the routing and the assignment decisions that are made in the first stage. Beginning with the shortest truck route, the assignment and the routing decisions are iteratively improved. The solution times of our algorithm are compared with the solution times of the state-of-the-art formulations that are solved by CPLEX. The results demonstrate that our algorithm yields shorter solution times for the instances that we generated with the specified parameters. An optimization-based heuristic algorithm, which obtains solutions for medium-sized instances, is developed by reducing the feasible search area.
The fast and cost-efficient home delivery of goods ordered online is logistically challenging. Many companies are looking for new ways to cross the last mile to their customers. One technology-enabled opportunity that recently has received much attention is the use of drones to support deliveries. An innovative last-mile delivery concept in which a truck collaborates with a drone to make deliveries gives rise to a new variant of the traveling salesman problem (TSP) that we call the TSP with drone. In this paper, we model this problem as an integer program and develop several fast route-first, cluster-second heuristics based on local search and dynamic programming. We prove worst-case approximation ratios for the heuristics and test their performance by comparing the solutions to the optimal solutions for small instances. In addition, we apply our heuristics to several artificial instances with different characteristics and sizes. Our experiments show that substantial savings are possible with this concept compared to truck-only delivery.
The online appendix is available at https://doi.org/10.1287/trsc.2017.0791 .
This paper addresses the capacitated vehicle routing problem (CVRP) and the split delivery vehicle routing problem (SDVRP) with uncertain travel times and demands when planning vehicle routes for delivering critical supplies to the affected population in need after a disaster. A robust optimization approach is used for CVRP and SDVRP considering the five objective functions: minimization of the total number of vehicles deployed (minV), the total travel time/travel cost (minT), the summation of arrival times (minS), the summation of demand-weighted arrival times (minD), and the latest arrival time (minL), out of which we claim that minS, minD, and minL are critical for deliveries to be fast and fair for relief efforts while minV and minT are common cost-based objective functions in the traditional VRP. A new two-stage heuristic method that combines the extended insertion algorithm and tabu search is proposed to solve the VRP models for large-scale problems. The solutions of CVRP and SDVRP are compared for different examples using five different metrics in which we show that the latter is not only capable of accommodating the demand greater than the vehicle capacity but also is quite effective to mitigate demand and travel time uncertainty, thereby outperforms CVRP in the disaster relief routing perspective.
Emergency logistics is an essential component of post-disaster relief campaigns. However, there are always various uncertainties when making decisions related to planning and implementing post-disaster relief logistics. Considering the particular environmental conditions during post-disaster relief after a catastrophic earthquake in a mountainous area, this paper proposes a stochastic model for post-disaster relief logistics to guide the tactical design for mobilizing relief supply levels, planning initial helicopter deployments, and creating transportation plans within the disaster region, given the uncertainties in demand and transportation time. We then introduce a robust optimization approach to cope with these uncertainties and deduce the robust counterpart of the proposed stochastic model. A numerical example based on disaster logistics during the Great Sichuan Earthquake demonstrates that the model can help post-disaster managers to determine the initial deployments of emergency resources. Sensitivity analyses explore the trade-off between optimization and robustness by varying the robust optimization parameter values.
This study proposes a stochastic modeling approach as an evacuation decision support system to determine the required vehicles, scheduling and routes under uncertainties in evacuee population, time windows and bushfire propagation. The proposed model also considers road availability and disruptions. A greedy solution method is developed to cope with the complex nature of vehicle routing problem. Furthermore, the effectiveness of the proposed solution is evaluated by comparison with a designed genetic algorithm on sets of various numerical examples. The model is then applied on the real case study of the 2009 Black Saturday bushfires in Victoria, Australia. Several plausible evacuation scenarios are generated, utilizing the historical data of Black Saturday. The results are analyzed using the frequency approach to determine the optimal evacuation plan. The results show that it would have been possible to evacuate the late evacuees on Black Saturday, even within hard time windows and a maximum population.
Studies show that by the course of time, the number of natural disasters such as earthquakes is increasing. Therefore, developing a model for locating distribution centers and relief goods distribution systems in disaster times, along with appropriately locating health centers with the ease of access for transferring the casualties and saving their lives, is among the most essential concerns in relief logistics. Considering these two subjects, simultaneously, results in an increase in the quality of service in disaster zones. In this study, a multi-objective programming model is developed for locating relief goods distribution centers and health centers along with distributing relief goods and transferring the casualties to health centers, with pre/post-disaster budget constraints for goods and casualties logistics. For a better modelling of the reality, the uncertainties in demand, supply, and cost parameters are included in the model. Also, facility failure (e.g. relief distribution centers, health centers, hospitals and supply points failure) due to earthquakes is considered. The proposed model maximizes the response level to medical needs of the casualties, while targeting the justly distribution of relief goods and minimizing the total costs of preparedness and response phases. In order to handle the uncertainties, the robust optimization approach is utilized. The model is solved with – constraint method. For the large sized form, the MOGASA algorithm is proposed, and the results are compared to those of the NSGAII algorithm. Then the validity and efficiency of the proposed algorithm is explored based on the results of both the proposed and exact methods.
The fast and cost-efficient home delivery of goods ordered online is logistically challenging. Many companies are looking for new ways to cross the last-mile to their customers. One technology-enabled opportunity that recently has received much at- tention is the use of a drone to support deliveries. An innovative last-mile delivery concept in which a truck collaborates with a drone to make deliveries gives rise to a new variant of the traveling salesman problem (TSP) that we call the TSP with drone. In this paper, we model this problem as an IP and develop several fast route first-cluster second heuristics based on local search and dynamic programming. We prove worst-case approximation ratios for the heuristics and test their performance by comparing the solutions to the optimal solutions for small instances. In addition, we apply our heuristics to several artificial instances with different characteristics and sizes. Our experiments show that substantial savings are possible with this concept in comparison to truck-only delivery.
In this paper we consider uncertain scalar optimization problems with infinite scenario sets. We apply methods from vector optimization in general spaces, set-valued optimization and scalarization techniques to develop a unified characterization of different concepts of robust optimization and stochastic programming. These methods provide new insights on the interrelation between different concepts for handling uncertainties and naturally lead to new concepts of robustness.
This paper presents a rolling horizon-based framework for real-time relief distribution in the aftermath of disasters. This framework consists of two modules. One is a state estimation and prediction module, which predicts relief demands and delivery times. The other is a relief distribution module, which solves for optimal relief distribution flows. The goal is to minimize the total time to deliver relief goods to satisfy the demand, considering uncertain data and of the risk-averse attitude of the decision-maker. A numerical example based on the large-scale earthquake that occurred on September 21, 1999 in Taiwan is presented to demonstrate the system.
Over the past few years, unmanned aerial vehicles (UAV), also known as drones, have been adopted as part of a new logistic method in the commercial sector called "last-mile delivery". In this novel approach, they are deployed alongside trucks to deliver goods to customers to improve the quality of service and reduce the transportation cost. This approach gives rise to a new variant of the traveling salesman problem (TSP), called TSP with drone (TSP-D). A variant of this problem that aims to minimize the time at which truck and drone finish the service (or, in other words, to maximize the quality of service) was studied in the work of Murray and Chu (2015). In contrast, this paper considers a new variant of TSP-D in which the objective is to minimize operational costs including total transportation cost and one created by waste time a vehicle has to wait for the other. The problem is first formulated mathematically. Then, two algorithms are proposed for the solution. The first algorithm (TSP-LS) was adapted from the approach proposed by Murray and Chu (2015), in which an optimal TSP solution is converted to a feasible TSP-D solution by local searches. The second algorithm, a Greedy Randomized Adaptive Search Procedure (GRASP), is based on a new split procedure that optimally splits any TSP tour into a TSP-D solution. After a TSP-D solution has been generated, it is then improved through local search operators. Numerical results obtained on various instances of both objective functions with different sizes and characteristics are presented. The results show that GRASP outperforms TSP-LS in terms of solution quality under an acceptable running time.
Theng-path relaxation was introduced by Baldacci, Mingozzi, and Roberti [Baldacci R, Mingozzi A, Roberti R (2011) New route relaxation and pricing strategies for the vehicle routing problem. Oper. Res. 59(5): 1269-1283] for computing tight lower bounds to vehicle routing problems by solving a relaxation of the set-partitioning formulation, where routes are not necessarily elementary and can contain predefined subtours. The strength of the achieved lower bounds depends on the subtours that routes can perform. In this paper, we introduce a new general bounding procedure called dynamic ng-path relaxation that enhances the one of Baldacci, Mingozzi, and Roberti (2011) by iteratively redefining the subtours that routes can perform. We apply the bounding procedure on the well-known delivery man problem, which is a generalization of the traveling salesman problem where costs for traversing arcs depend on their positions along the tour. The proposed bounding procedure is based on column generation and computes a sequence of nondecreasing lower bounds to the problem. The final lower bound is used to solve the problem to optimality with a simple dynamic programming recursion. An extensive computational analysis on benchmark instances from the TSPLIB shows that the new bounding procedure yields better lower bounds than those provided by the method of Baldacci, Mingozzi, and Roberti (2011). Furthermore, the proposed exact method outperforms other exact methods recently presented in the literature and is able to close five open instances with up to 150 vertices.
Once limited to the military domain, unmanned aerial vehicles are now poised to gain widespread adoption in the commercial sector. One such application is to deploy these aircraft, also known as drones, for last-mile delivery in logistics operations. While significant research efforts are underway to improve the technology required to enable delivery by drone, less attention has been focused on the operational challenges associated with leveraging this technology. This paper provides two mathematical programming models aimed at optimal routing and scheduling of unmanned aircraft, and delivery trucks, in this new paradigm of parcel delivery. In particular, a unique variant of the classical vehicle routing problem is introduced, motivated by a scenario in which an unmanned aerial vehicle works in collaboration with a traditional delivery truck to distribute parcels. We present mixed integer linear programming formulations for two delivery-by-drone problems, along with two simple, yet effective, heuristic solution approaches to solve problems of practical size. Solutions to these problems will facilitate the adoption of unmanned aircraft for last-mile delivery. Such a delivery system is expected to provide faster receipt of customer orders at less cost to the distributor and with reduced environmental impacts. A numerical analysis demonstrates the effectiveness of the heuristics and investigates the tradeoffs between using drones with faster flight speeds versus longer endurance.
We propose a multi-depot location-routing model considering network failure, multiple uses of vehicles, and standard relief time. The model determines the locations of local depots and routing for last mile distribution after an earthquake. The model is extended to a two-stage stochastic program with random travel time to ascertain the locations of distribution centers. Small instances have been solved to optimality in GAMS. A variable neighborhood search algorithm is devised to solve the deterministic model. Computational results of our case study show that the unsatisfied demands can be significantly reduced at the cost of higher number of local depots and vehicles.
The effective distribution of critical relief in post disaster plays a crucial role in post-earthquake rescue operations. The location of distribution centers and vehicle routing in the available transportation network are two of the most challenging issues in emergency logistics. This paper constructs a nonlinear integer open location-routing model for relief distribution problem considering travel time, the total cost, and reliability with split delivery. It proposes the non-dominated sorting genetic algorithm and non-dominated sorting differential evolution algorithm to solve the proposed model. A case study on the Great Sichuan Earthquake in China expounds the application of the proposed models and algorithms in practice.
Purpose
– The purpose of this paper is to present a literature review of humanitarian logistics (HL) that aims to identify trends and suggest some directions for future research.
Design/methodology/approach
– This conceptual paper develops a research framework for literature review through qualitative and quantitative content analysis. First, previous literature reviews in HL are updated and detailed. Then, seven classification criteria are added to earlier ones in order to advance the literature analysis.
Findings
– The conclusions identify some literature gaps and research opportunities. The main conclusions are the need for more studies into the disaster recovery phase and the need for closer relationships between academia and humanitarian organizations to increase the number of applied research.
Research limitations/implications
– The literature is limited to academic peer-reviewed journals because of their academic relevance, accessibility, and ease of searching.
Practical implications
– Help potential researchers to set up a research agenda for future work.
Social implications
– Reinforce earlier calls to increase truly applied research and improve social impact of the field.
Originality/value
– In total, 228 papers that were published in the HL area are reviewed, giving rise to the most extensive literature review in this area. New dimensions for literature review in HL are proposed, which give some new insights into potential research directions.