Algorithms for unbounded and varied capacitated lot-sizing problems with outsourcing

Lot-sizing problems have been extensively researched for more than half century．There are relative small number of papers on lot-sizing models with outsourcing, despite its important applications in operations research. Recently several papers related to out-sourcing models are published．When there is no bound on production capacity, linear algorithm（ totally square） is possible. Period varying capacitated lot-sizing model is known as NP-hard even outsourcing is not allowed. In this manuscript, we treat these two extreme cases, we give a efficient algorithm for former case, and propose a pseudo-polynomial scheme for period varying production capacities

Lot-Sizing Problem for a Multi-Item Multi-level Capacitated Batch Production System with Setup Carryover, Emission Control and Backlogging using a Dynamic Program and Decomposition Heuristic

Wagner and Whitin (1958) develop an algorithm to solve the dynamic Economic Lot-Sizing Problem (ELSP), which is widely applied in inventory control, production planning, and capacity planning. The original algorithm runs in O(T^2) time, where T is the number of periods of the problem instance. Afterward few linear-time algorithms have been developed to solve the Wagner-Whitin (WW) lot-sizing problem; examples include the ELSP and equivalent Single Machine Batch-Sizing Problem (SMBSP). This dissertation revisits the algorithms for ELSPs and SMBSPs under WW cost structure, presents a new efficient linear-time algorithm, and compares the developed algorithm against comparable ones in the literature. The developed algorithm employs both lists and stacks data structure, which is completely a different approach than the rest of the algorithms for ELSPs and SMBSPs. Analysis of the developed algorithm shows that it executes fewer number of basic actions throughout the algorithm and hence it improves the CPU time by a maximum of 51.40% for ELSPs and 29.03% for SMBSPs. It can be concluded that the new algorithm is faster than existing algorithms for both ELSPs and SMBSPs. Lot-sizing decisions are crucial because these decisions help the manufacturer determine the quantity and time to produce an item with a minimum cost. The efficiency and productivity of a system is completely dependent upon the right choice of lot-sizes. Therefore, developing and improving solution procedures for lot-sizing problems is key. This dissertation addresses the classical Multi-Level Capacitated Lot-Sizing Problem (MLCLSP) and an extension of the MLCLSP with a Setup Carryover, Backlogging and Emission control. An item Dantzig Wolfe (DW) decomposition technique with an embedded Column Generation (CG) procedure is used to solve the problem. The original problem is decomposed into a master problem and a number of subproblems, which are solved using dynamic programming approach. Since the subproblems are solved independently, the solution of the subproblems often becomes infeasible for the master problem. A multi-step iterative Capacity Allocation (CA) heuristic is used to tackle this infeasibility. A Linear Programming (LP) based improvement procedure is used to refine the solutions obtained from the heuristic method. A comparative study of the proposed heuristic for the first problem (MLCLSP) is conducted and the results demonstrate that the proposed heuristic provide less optimality gap in comparison with that obtained in the literature. The Setup Carryover Assignment Problem (SCAP), which consists of determining the setup carryover plan of multiple items for a given lot-size over a finite planning horizon is modelled as a problem of finding Maximum Weighted Independent Set (MWIS) in a chain of cliques. The SCAP is formulated using a clique constraint and it is proved that the incidence matrix of the SCAP has totally unimodular structure and the LP relaxation of the proposed SCAP formulation always provides integer optimum solution. Moreover, an alternative proof that the relaxed ILP guarantees integer solution is presented in this dissertation. Thus, the SCAP and the special case of the MWIS in a chain of cliques are solvable in polynomial time

Evaluation et gestion de la flexibilité dans les chaînes logistiques : nouveau cadre général et applications

This thesis focuses on flexibility issues in supply chain. These issues are becoming more and more important for firms because of the increasingly changing business environment and customer behaviors. Although some of these issues have been tackled in academic research in recent years, but studies have mainly concentrated in conceptual levels and there is little consensus even on the definition of flexibility. This thesis aims at defining a new framework for the supply chain flexibility, proposing quantitative measures of the flexibility and optimizing the use of flexibility, especially in an integrated production and transportation planning context. The new framework of supply chain flexibility is based on classification of different flexibility aspects in a supply chain into three main categories - manufacturing flexibility,logistic chain flexibility and system flexibility. These flexibility types are further distinguished into major flexibility dimension and other flexibility dimension.In order to measure supply chain flexibility from a quantitative point of view, Mechanical Analogy method is particularly discussed. A procedure is established to enlarge and carry out this method in supply chain, provided with a case study to evaluate the flexibility of Louis Vuitton stores.One of the most important issues is to optimally make use of the available flexibility. We investigate an Integrated Production and Transportation Planning problem with given flexibility tolerances, where the production and transportation activities are intimately linked to each other and must be scheduled in a synchronized way. Particularly, heterogeneous vehicles are taken into account. Two mixed integer linear programming models are constructed.Three algorithms are developed and compared with linear relaxation bounds for large sized real life instances and with optimal solutions for small sized instances. These comparisons show the effectiveness of our heuristics in solving real life problemsCette thèse étudie la problématique de la flexibilité dans les chaînes logistiques. La recherche académique a commencé à s’intéresser à cette problématique depuis quelques années, mais les études existantes restent pour la plupart au niveau conceptuel et il y a peu de consensus sur la définition même de la flexibilité. Cette thèse a pour ambition de définir un nouveau cadre pour la flexibilité dans les chaînes logistiques, proposer des mesures quantitatives pour la flexibilité et enfin optimiser l’utilisation de la flexibilité, en particulier dans un contexte de planification intégrée de la production et du transport.Ce travail de thèse vise tout d’abord à établir un nouveau cadre pour la flexibilité de la chaîne logistique, où les différents aspects de la flexibilité sont classifiés en trois catégories principales: flexibilité de la production, flexibilité de la chaîne logistique et flexibilité du système. Dans chacune de ces catégories, on peut trouver des dimensions primordiales et des dimensions moins importantes.Afin d’évaluer la flexibilité de manière quantitative, nous faisons appel à la méthode Analogie Mécanique. Cette méthode propose une analogie entre un système mécanique vibratoire et une chaîne logistique. Dans ce contexte, nous avons développé une étude de cas pour Louis Vuitton afin d’évaluer la flexibilité de leurs magasins, et nous avons établi une procédure pour implémenter cette méthode.Une autre problématique importante est l’utilisation optimale de la flexibilité existante.Nous nous sommes particulièrement intéressés à la planification intégrée de la production et du transport avec des flexibilités sur la capacité de transport, où la production et le transport sont intimement liés du fait du manque de capacité de stockage et doivent être planifiées conjointement. Particulièrement, les véhicules hétérogènes sont pris en compte.Nous avons construit deux modèles de programmation linéaire en nombres mixtes et développé trois algorithmes qui ont été comparées par rapport à la relaxation linéaire pour les instances de grande taille et aux solutions optimales pour des instances de petite taille. Ces comparaisons montrent que les heuristiques proposées sont efficaces pour résoudre des problèmes réels, aussi bien en termes de qualité de solution qu’en termes de temps de calcul