Mathematics in the Supply Chain

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Modeling Industrial Lot Sizing Problems: A Review

In this paper we give an overview of recent developments in the field of modeling single-level dynamic lot sizing problems. The focus of this paper is on the modeling various industrial extensions and not on the solution approaches. The timeliness of such a review stems from the growing industry need to solve more realistic and comprehensive production planning problems. First, several different basic lot sizing problems are defined. Many extensions of these problems have been proposed and the research basically expands in two opposite directions. The first line of research focuses on modeling the operational aspects in more detail. The discussion is organized around five aspects: the set ups, the characteristics of the production process, the inventory, demand side and rolling horizon. The second direction is towards more tactical and strategic models in which the lot sizing problem is a core substructure, such as integrated production-distribution planning or supplier selection. Recent advances in both directions are discussed. Finally, we give some concluding remarks and point out interesting areas for future research

An inventory model of purchase quantity for fully-loaded vehicles with maximum trips in consecutive transport time

Products made overseas but sold in Taiwan are very common. Regarding the cross-border or interregional production and marketing of goods, inventory decision-makers often have to think about how to determine the amount of purchases per cycle, the number of transport vehicles, the working hours of each transport vehicle, and the delivery by ground or air transport to sales offices in order to minimize the total cost of the inventory in unit time. This model assumes that the amount of purchases for each order cycle should allow all rented vehicles to be fully loaded and the transport times to reach the upper limit within the time period. The main research findings of this study included the search for the optimal solution of the integer planning of the model and the results of sensitivity analysis

Order release strategies to control outsourced operations in a supply chain

In this paper, we propose and compare three different order release strategies to plan and control outsourced operations in a supply chian where the contract manfacturer is producing different variants of a certain product

Applying Operations Research techniques to planning of train shunting

In this paper, we discuss a model-based algorithmic approach for supporting planners in the creation of shunt plans for passenger trains. The approach provides an example of a mathematical model and a corresponding solution approach for model based support. We introduce a four-step solution approach and we discuss how the planners are supported by this approach. Finally, we present computational results for these steps and give some suggestions for further research.A* search;railway optimization;real world application;routing

Capacity reservation and utilization for a manufacturer with uncertain capacity and demand

We consider an OEM (Original Equipment Manufacturer) that has outsourced the production activities to a CM (Contract Manufacturer). The CM produces on a non-dedicated capacitated production line, i.e., the CM produces for multiple OEMs on the same production line. The CM requires that all OEMs reserve capacity slots before ordering and responds to these reservations by acceptance or partial rejection, based on allocation rules that are unknown to the OEM. Therefore, the allocated capacity for the OEM is not known in advance, also because the OEM has no information about the reservations of the other OEMs. We study this problem from the OEM's perspective who faces stochastic demand and stochastic capacity allocation from the contract manufacturer. A single-item periodic review inventory system is considered and we assume linear inventory holding, backorder, and reservation costs. We develop a stochastic dynamic programming model for this problem and characterize the optimal policy. We conduct a numerical study where we also consider the case that the capacity allocation is dependent on the demand distribution. For this case, we show the structure of the optimal policy based on a numerical study. Further, the numerical results reveal several interesting managerial insights, such as the optimal reservation policy is being little sensitive to the uncertainty of capacity allocation. In that case, the optimal reservation quantities hardly increase, but the optimal policy suggests increasing the utilization of the allocated capacity. Moreover, we show that for the contract manufacturer, to achieve the desired behavior, charging small reservation costs is sufficient

PLANIFICATION DES LIVRAISON JOINTES DE DIFFERENTS PRODUITS A DIFFERENTS SITES

Colloque avec actes et comité de lecture. internationale.International audienceLe problème de livraisons jointes de produits (JDP) consiste à planifier les livraisons de différents produits à différents sites de consommation ou de distribution en traitant les problèmes de groupement, de livraison et de stockage. Il s’agit de construire des tournées de livraison sur un horizon de planification, en satisfaisant les demandes et en minimisant le coût total de commande, de livraison et de stockage. Les coûts fixes de commande portent d’une part sur le lancement d’une tournée, d’autre part sur chaque couple (produit, site) présent ou non dans la tournée. Les taux de demandes étant supposées fixes et connus, le problème en horizon infini admet une solution périodique, le plan de livraison optimal sur une période-type pouvant se répéter indéfiniment. Dans notre approche, le problème est formulé en temps discret et nous choisissons comme période-type commune de cyclicité un multiple de la période élémentaire, et cette période-type sert d’horizon de planification. Ainsi, les livraisons restent périodiques à travers la répétition de l’horizon de planification, mais les livraisons pendant l’horizon de planification ne sont pas contraintes à être périodiques. Les résultats numériques montrent en particulier la supériorité de cette approche sur une solution cyclique pour chaque couple (produit, site)