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In this paper, we present a mathematical model which integrates tactical-operational production and distribution decisions in a shared resources environment. More precisely, we integrate lot sizing production and distribution decisions with vehicle routing decisions. We obtain a global multi-period multi-item multi-vehicle model where a capacity co...
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This paper proposes a mixed integer programming formulation for modeling the capacitated multi-level lot sizing problem with both backlogging and setup carryover. Based on the model formulation, a progressive time-oriented decomposition heuristic framework is then proposed, where improvement and construction heuristics are effectively combined, the...
This paper considers the lot-sizing problem i n multi-stage production settings with capacity-constrained resources. This problem deals with the determination o f a production plan for the end item and its components in order to meet the forecast demand in each period of a planning horizon. The production plan should minimize the sum of production,...
This paper proposes a mixed integer programming formulation for modeling the capacitated multi-level lot sizing problem with both backlogging and linked lot sizes. Based on the model formulation, a progressive time-oriented decomposition heuristic framework is then proposed, where improvement and construction heuristics are effectively combined, th...
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... Most of the applications emerge in maritime logistics: Bertazzi and Speranza (2002), Grønhaug et al. (2010), Christiansen et al. (2011), andStålhane et al. (2012). Non-maritime cases include, for example, the delivery of perishable goods (Hssini, Meskens, and Riane 2016;Dehghani, Abbasi, and Oliveira 2021), the transportation of gas by tanker trucks (Bell et al. 1983), the production and the distribution planning in the gas filling industry (Strack et al. 2011), and the vehicle parts industry (Alegre, Laguna, and Pacheco 2007). ...
In this paper, we investigate a two-level supply chain consisting of a company which manufactures a set of products and distributes them via its central warehouse to a set of customers. The problem is modelled as a dynamic and stochastic inventory routing problem (DSIRP) that considers two flexible instruments of transshipment and substitution to mitigate shortages at the customer level. A new resolution approach, based on the hybridisation of mathematical modelling, Genetic Algorithm and Deep Reinforcement Learning is proposed to handle the combinatorial complexity of the problem at hand. Tested on the 150 most commonly used benchmark instances for single-vehicle-product DSIRP, results show that the proposed algorithm outperforms the current best results in the literature for medium and large instances. Moreover, 450 additional instances for multi-products DSIRP are generated. Different demand distributions are examined in these experiments, namely, Normal distribution, Poisson distribution for demand occurrence, combined with demands of constant size; Stuttering Poisson distribution and Negative Binomial distribution. In terms of managerial insights, results show the advantages of promoting inventory sharing and substitutions on the overall supply chain performance.
... De manera particular, en las empresas que manufacturan y distribuyen sus productos es importante que las áreas de producción y de logística de distribución trabajen de manera sincronizada para garantizar que las estrategias de nivel de servicio, eficiencia y costo puedan conducir a un mejor desempeño global. De hecho, muchos autores han reconocido la importancia de la coordinación de las dos áreas; pueden verse, por ejemplo, los trabajos de [1], [2], [3], [4], [5], entre otros. ...
... En la revisión realizada se encontró que de los artículos que estudian la modelación integrada de producción y logística, ninguno considera de manera explícita el manejo de las discrepancias entre los tamaños de lote de producción y logística. Véase, por ejemplo, también los trabajos de [1], [12], [13], [14], [15], [16], [17], entre otros. La estrategia principal de dichos trabajos es plantear una estructura jerárquica de análisis en la que en un primer nivel de jerarquía está logística, el cual encuentra el lote óptimo de acuerdo con sus restricciones; información que alimenta en una segunda fase a un subproblema de producción al cual se le exige cumplir con el lote solicitado por logística. ...
Discrepancies that may occur between the production lot size and the production lot preliminarily requested by the area of logistics and the impact that these differences may have on the level of customer service are studied in this paper. We used mixed integer programming as our methodological approach and we found that although lot sizing disa-greements may cause a negative impact on customer service, it should not always be associated with worsening in the service level. We found that even in scenarios of high shortage cost, with high level of service, beneficial discrepancies could appear, generating cost reductions with a constant service level. It was concluded that the concept of integration between production and distribution do not necessarily imply that any area should always do what the other define. Rather, the integration must be posed better in terms of the benefit in the global system, under which the discrepancy may have some important role.
E-commerce has been continuously growing in the last years to a primary retail market. Recently in France, the threshold of 1 billion of online transactions was overcome. Due to a high demand fluctuation of e-commerce, the workforce sizing for the logistic chain is a challenging problem. Companies have to develop good strategies to have a sustainable workforce size while guaranteeing a high-level service. In this paper, we consider the management of the workforce for a warehouse of an e-commerce company. Specifically, we address issues as i) How the workforce at the warehouse can be determined; ii) What is the daily operational production planning; iii) How the demand peaks can be smoothed, and the production maintained ideally constant over the time horizon. To provide answers to these issues, we introduce the Packaging and Shipping Problem (PSP). The PSP looks for a solution approach that jointly determines the workforce over a multi-period horizon and daily operational plans while minimizing the total logistics cost. We consider two strategies that aim to enhance the flexibility of the process and the efficiency of resources use: reassignment and postponement. To tackle the Packaging and Shipping Problem we propose a model, and a three-phase matheuristic. This heuristic is proved to be competitive with respect to the direct solution of the model with a commercial solver on real-life based instances.
We develop an aggregated model to study rational environmental adaptation policies that compensate negative consequences of climate change. The model distinguishes three categories of adaptation measures that (a) compensate the decrease of environmental amenity value, (b) compensate the decrease of total productivity, (c) develop and introduce new hazard-protected capital and technology. We analyze the optimal balance among consumption, capital investment, and different categories of adaptation investments under exogenous climate change. It appears that the climate change damage and subsequent adaptation do not lead to a higher level of capital modernization in the long run as compared to the benchmark case with no climate change. A synergism between productivity-related and amenity-related adaptation activities arises because the productivity-related adaptation positively impacts the economy and creates better possibilities for the amenity adaptation.
This paper shows how the role of the market, the state and the family in providing financial support at old age has evolved over time with changes in factors such as the reliability and the effectiveness of family support, the rate of interest, the cost of public funds and earning inequality. We model a society in which agents with different productivity are asked to vote over the existence of a Beveridgian pension system. We show that when children assistance is certain and large, agents may rely exclusively on family to finance old-age consumption and prefer to vote for a zero tax rate. Only if income inequalities are very large, a majority will be in favor of a pension system. However, when the size and the likelihood of family generosity decreases, a pension system is more likely to emerge. In that case, agents supplement children assistance with pension benefits. A pension system is also more likely to emerge when the cost of public fund is small and the return from private savings is high.
The paper is not intended for game theorists - unless they are interested in learning how their theories, and the theory of environmental games as developed in a forthcoming book, are being used for studying the current problem of climate change. Similarly for economists. In general, the presentation is addressed to those who have an interest in seeing how theory can shape policy in the area of climate change. After a summary presentation of the relevant features of the Protocol, followed by the sketching out of an economic model serving as support for the theoretical construct, we consider a series of aspects of it - such as reference emissions, efficiency and stability, competitive trading, desirability of free trade in emissions and the clean development mechanism -, not to defend it and independently of the subsequent developments, but rather as a benchmark for understanding the various issues concerning the climate change problem in general. Then, we extend this exercise to an appraisal of the situation of the world climate regime that is currently prevailing, after the Protocol has entered into force. Finally, we discuss four aspects of the world climate regime that is likely to prevail after the expiry of the Kyoto commitment period 2008-2012. Our message is a non-conventional one, compared with the common wisdom of commentaries of the Kyoto Protocol and of its follow-ups. It is inspired by research on the foundations of international cooperation in general and on climate change in particular.
The focus of this paper is on the trade-off between cost efficiency and access in the choice of the optimal mix of public and private provision in universal health systems. We model a simple health care market in which the regulator acts as a third payer. Patients need one unit of medical service and differ in the severity of illness. A private and a public hospital are available. The private manager internalizes profits, and has an incentive both to refuse to treat costly patients and to exert effort in cost reduction. The public manager does not internalize profits, and has no incentive to reduce costs or to dump costly patients. We show that, when a relatively efficient effort in cost reduction is available, it is optimal to buy part of the services from the private hospital. This may be the case for procedures that are easier to standardize, such as elective surgery. Since the regulator acts as an insurer for the whole population, a public hospital has to be used as a last resort facility. Imposing a no-dumping constraint on the private hospital is not always optimal since eliciting effort and truthful revelation of costs may become more difficult.
This paper proposes a real option capacity expansion model for power generation with several technologies that differ in operation and investment costs. The economy is assumed perfectly competitive and the instantaneous payoff accruing from the generation system is the instantaneous welfare defined as the usual sum of consumer and producer surplus. The computation of this welfare requires the solution of a multi- technology optimization problem and the obtained optimal function value is not additively separable in generation capacities, contrary to what is generally assumed in multi asset real option models to prove the optimality of a myopic behavior. Using the geometric Brownian motion as uncertainty driver we propose two regression models to approximate the instantaneous welfare. A first, additively separable approximation implies the optimality of myopia. The second approximation is non separable and hence forces to take myopic behavior as an assumption. Using myopia as an assumption, we propose a semi-analytic method which combines Monte Carlo simulations (used to compute the value of the marginal capacity) and analytical treatment (to solve an optimal stopping problem on a regression scheme).
This paper considers the general problem of optimal timing of the exchange of the sum of n Ito-diffusions for the sum of m others (e.g., the optimal time to exchange a geometric Brownian motion for a geometric mean reverting process). We first contribute to the literature by providing analytical sufficient conditions and necessary conditions for optimal stopping (i.e. sub- and super- sets of the stopping region) for some sub-cases of the general problem. We then exhibit a connection between the problem of finding sufficient conditions for optimal stopping and linear programming. This connection provides a unified approach which does not only allow to recover previous analytically determinable subsets of the stopping region, but also allows to characterize (more complex) subsets of the stopping region that do not have an analytical expression. In the particular case where all assets are geometric Brownian motions, this connection gives us new insights. In particular, it simplifies the expression of the subset of the stopping region identified by Nishide and Rogers (2011). Our numerical examples finally confirms the good behavior of the candidate investment rule introduced by Gahungu and Smeers (2011) for this particular case, which seems to comfort a conjecture that their rule might be optimal.
This paper considers the problem of the optimal timing of the exchange of the sum of n geometric Brownian motions for the sum of m others. We propose a closed form determinable stopping time based on the heuristic principle of smooth fit. We cannot prove that this stopping time is optimal. However, we show numerically on examples that it is a potentially useful candidate: letting S^Ø denote the stopping region induced by our stopping time we show that (i) S^- c S^Ø c S^+ where S^- and S^+ are well-known subset and superset of the optimal stopping region; (ii) stopping at the first entry time of S^Ø offers a better payoff than stopping at the first entry time of S^- or S^+, especially when assets are correlated.
