Please read the abstract in the section 00front of this document. / Thesis (PhD)--University of Pretoria, 2010. / Industrial and Systems Engineering / unrestricted

Coordinated lot sizing problems, which assume a joint setup is shared by a product family, are commonly encountered in supply chain contexts. Total system costs include a joint set-up charge each time period any item in the product family is replenished, an item set-up cost for each item replenished in each time period, and inventory holding costs. Silver (1979) and subsequent researchers note the occurrence of coordinated replenishment problems within manufacturing, procurement, and transportation contexts. Due to their mathematical complexity and importance in industry, coordinated lot-size problems are frequently studied in the operations management literature. In this research, we address both uncapacitated and capacitated variants of the problem. For each variant we propose new problem formulations, one or more construction heuristics, and a simulated annealing metaheuristic (SAM). We first propose new tight mathematical formulations for the uncapacitated problem and document their improved computational efficiency over earlier models. We then develop two forward-pass heuristics, a two-phase heuristic, and SAM to solve the uncapacitated version of the problem. The two-phase and SAM find solutions with an average optimality gap of 0.56% and 0.2% respectively. The corresponding average computational requirements are less than 0.05 and 0.18 CPU seconds. Next, we propose tight mathematical formulations for the capacitated problem and evaluate their performance against existing approaches. We then extend the two-phase heuristic to solve this more general capacitated version. We further embed the six-phase heuristic in a SAM framework, which improves heuristic performance at minimal additional computational expense. The metaheuristic finds solutions with an average optimality gap of 0.43% and within an average time of 0.25 CPU seconds. This represents an improvement over those reported in the literature. Overall the heuristics provide a general approach to the dynamic demand lot-size problem that is capable of being applied as a stand-alone solver, an algorithm embedded with supply chain planning software, or as an upper-bounding procedure within an optimization based algorithm. Finally, this research investigates the performance of alternative coordinated lotsizing procedures when implemented in a rolling schedule environment. We find the perturbation metaheuristic to be the most suitable heuristic for implementation in rolling schedules.

This study is about an integrated procurement and transportation planning system for purchased components of a consumer-durables manufacturer. Due to transportation cost structures and demand characteristics our problem can be classified as a variant of the dynamic-demand joint replenishment problem. The problem is to determine the replenishment policy using the advantages of coordinated transportation of items that will minimize the sum of total inventory holding and tranportation costs over a finite planning horizon. A mathematical model is formulated for purchasing and transportation decisions for the purchased items using the advantage of joint transportation costs. A two-phased solution method is proposed in order to obtain a &ldquo / good solution&rdquo / for the problem. The proposed solution method is compared with the current practice for different problem instances using retrospective data and created data. As a result it is shown that proposed method decrease the total inventory and transportation cost of the system even though the first aggregate problem can not be solved to optimality.

À l'ère de la mondialisation, l’environnement industriel et économique a subi plusieurs changements majeurs. Les chaînes logistiques sont en train de devenir de plus en plus de complexes réseaux composés de nombreux acteurs qui sont tantôt en concurrence et tantôt coopèrent pour répondre aux incessantes exigences des consommateurs. Dans un tel contexte, les entreprises se sont rapidement rendu compte de la limite du modèle complètement décentralisé où chacune d’entre elles optimise sa propre chaîne logistique indépendamment des autres acteurs. Afin de trouver de nouvelles sources de compétitivité et de faire face à la perpétuelle complexité de l’environnement économique, les entreprises tentent de dépasser la frontière des actions individuelles favorisant les actions coordonnées et centralisées. Désormais, la coopération entre les diverses chaînes logistiques et la formation d’alliances se trouvent au coeur des préoccupations des entreprises. En effet, en mutualisant les moyens logistiques, la coopération permet une meilleure exploitation des ressources et par le biais des actions collectives, elle permet de mieux bénéficier des économies d’échelles conduisant à réduire significativement les coûts et à générer des bénéfices considérables. Toutefois, dans de tels systèmes coopératifs, les acteurs sont indépendants et par ailleurs toujours intéressés en priorité par leurs profits individuels. De ce fait, la coopération soulève deux enjeux essentiels : (1) Quelles sont les alliances qui sont susceptibles de se former ? Et (2), comment partager les bénéfices réalisés sur les différents acteurs coopérants ? Dans cette thèse, nous nous intéressons au phénomène de la coopération dans les chaînes logistiques. Particulièrement, nous posons les précédentes questions dans des chaînes logistiques ou plusieurs firmes peuvent réduire leurs coûts logistiques en optant pour une gestion collective des stocks. Les principaux résultats de cette thèse portent sur l’utilisation des principes de la théorie des jeux coopératifs pour déterminer les alliances les plus profitables ainsi que la portion de profit que chaque firme doit recevoir afin de garder la stabilité des alliances formées. / In the age of outsourcing and globalization, the economic and industrial landscape has seen many radical changes. In such context, supply chains are becoming complex networks of a large number of entities that sometimes compete and sometimes cooperate to fulfill customers’ needs. Standalone supply chains, where each entity makes its decisions so as to maximize its own profits according to its own objectives, often lead to a loss of efficiency and fail to face the complexity of the economic environment they are facing with. Cooperative structures, however, where resources/service facilities are shared and decisions are made to maximize the global profit, prove to be more beneficial and efficient. Consequentially, many companies are fundamentally changing their way of doing business by exceeding the border of standalone and individual actions toward collective actions and cooperative strategies. Therefore, building alliances appears as a successful strategy in modern supply chain networks. In general, cooperation enables a better exploitation of the system’s resources and offers the opportunity to get benefit from large economies of scope, which in turn reduces the total cost/increases the total savings. However, it raises two natural questions that need to be addressed: (1) Which coalitions can be expected to be formed? And, (2) How will the cooperating actors share their total profit? In this Ph.D. dissertation, we tempt to address these questions in retail supply chains where independent retailers coordinate their replenishment from a supplier in order to save on delivery costs. Considering various joint replenishment environments, our principal contribution is to use principles from cooperative game theory to identify the most profitable alliances and to determine the portion of profit that would be allocated to each actor in order to guarantee the stability of the formed alliances.

In this study, the design of a three-level distribution system is considered in which a single supplier ships a number of items to the retailers via a set of distribution centers (DC) and stochastic demand is observed at the retailers. The problem is to specify the number and location of the DCs, and the assignment of the retailers to the DCs in such a way that total facility, transportation, safety stock, and joint ordering and average inventory costs are minimized, and customer service requirements are satisfied. Single source constraints are imposed on the assignment of the retailers to the DCs. The integrated location/inventory model incorporates the inventory management decisions into the strategic location/allocation decisions by considering the benefits of risk pooling and the savings that result in the joint replenishment of a group of items. We develop two heuristic methods to solve the non-linear integer-programming model in an integrated way: (1) Improvement type heuristic, (2) Constructive type heuristic. The heuristic algorithms are tested on a number of problem instances with 81 demand points (retailers) and 4 different types of items. Both of the heuristics are able to generate solutions in very reasonable times. The results are compared to the results of the p-median problem and found that the total cost and the number of DCs can be lowered using our integrated model instead of the p-median problem. Finally, sensitivity analysis is performed with respect to the changes in inventory, transportation, and ordering cost parameters, and variability of the demand.

Le problème d’approvisionnement conjoint (JDP) proposé est un problème de planification des tournées de livraisons sur un horizon de temps décomposé en périodes élémentaires, l’horizon de temps étant la période commune de livraison de tous les produits,. La donnée de ces paramètres permet d’obtenir une formulation linéaire du problème, avec des variables de décision binaires. Le modèle intègre aussi des contraintes de satisfaction de la demande à partir des stocks et des quantités livrées, des contraintes sur les capacités de stockage et de transport.Afin de résoudre aussi le problème de choix des tournées de livraison, il est nécessaire d'introduire dans le modèle des contraintes et des variables liées aux sites visités au cours de chaque tour. Il est proposé de résoudre le problème en deux étapes. La première étape est le calcul hors ligne du coût minimal de la tournée associé à chaque sous-ensemble de sites. On peut observer que pour tout sous-ensemble donné de sites, le cycle hamiltonien optimal reliant ces sites à l'entrepôt peut être calculé à l'avance par un algorithme du problème du voyageur de commerce (TSP). Le but ici n'est pas d'analyser pleinement le TSP, mais plutôt d'intégrer sa solution dans la formulation de JRP. .Dans la deuxième étape, des variables binaires sont associées à chaque tour et à chaque période pour déterminer le sous-ensemble de sites choisi à chaque période et son coût fixe associé. / The proposed joint delivery problem (JDP) is a delivery tour planning problem on a time horizon decomposed into elementary periods or rounds, the time horizon being the common delivery period for all products. The data of these parameters provides a linear formulation of the problem, with binary decision variables. The model also incorporates the constraints of meeting demand from stock and the quantities supplied, storage and transport capacity constraints.In order to also solve the problem of choice of delivery rounds, it is necessary to introduce in the model several constraints and variables related to the sites visited during each round. It is proposed to solve the problem in two steps. The first step is the calculation of the minimum off-line cost of the tour associated with each subset of sites. One can observe that for any given subset of sites, the optimal Hamiltonian cycle linking those sites to the warehouse can be calculated in advance by a traveling salesman problem algorithm (TSP). The goal here is not to fully analyze the TSP, but rather to integrate its solution in the formulation of the JRP. In the second stage, binary variables are associated with each subset and each period to determine the selected subset of sites in each period and its associated fixed cost.