On the equivalence of strong formulations for capacitated multi-level lot sizing problems with setup times

Several mixed integer programming formulations have been proposed for modeling capacitated multi-level lot sizing problems with setup times. These formulations include the so-called facility location formulation, the shortest route formulation, and the inventory and lot sizing formulation with (l,S) inequalities. In this paper, we demonstrate the equivalence of these formulations when the integrality requirement is relaxed for any subset of binary setup decision variables. This equivalence has significant implications for decomposition-based methods since same optimal solution values are obtained no matter which formulation is used. In particular, we discuss the relax-and-fix method, a decomposition-based heuristic used for the efficient solution of hard lot sizing problems. Computational tests allow us to compare the effectiveness of different formulations using benchmark problems. The choice of formulation directly affects the required computational effort, and our results therefore provide guidelines on choosing an effective formulation during the development of heuristic-based solution procedures

Supplier-Buyer Negotiation Games: Equilibrium Conditions and Supply Chain Efficiency

In a decentralized supply chain, supplier–buyer negotiations have a dynamic aspect that requires both players to consider the impact of their decisions on future decisions made by their counterpart. The interaction generally couples strongly the price decision of the supplier and the quantity decision of the buyer. We propose a basic model for a repeated supplier–buyer interaction, during several rounds. In each round, the supplier first quotes a price, and the buyer places an order at that price. We find conditions for existence and uniqueness of a well-behaved subgame-perfect equilibrium in the dynamic game. When costs are stationary and there are no holding costs, we identify some demand distributions for which these conditions are met, examine the efficiency of the equilibrium, and show that, as the number of rounds increases, the profits of the supply chain increase towards the supply chain optimum. In contrast, when costs vary over time or holding costs are present, the benefit from multi-period interactions is reduced and after a finite number of time periods, supply chain profits stay constant even when the number of rounds increases

Mixed integer programming in production planning with backlogging and setup carryover : modeling and algorithms

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, therefore efficiently avoiding the weaknesses associated with the one-time decisions made by other classical time-oriented decomposition algorithms. Computational results show that the proposed optimization framework provides competitive solutions within a reasonable time

A computational analysis of lower bounds for big bucket production planning problems

In this paper, we analyze a variety of approaches to obtain lower bounds for multi-level production planning problems with big bucket capacities, i.e., problems in which multiple items compete for the same resources. We give an extensive survey of both known and new methods, and also establish relationships between some of these methods that, to our knowledge, have not been presented before. As will be highlighted, understanding the substructures of difficult problems provide crucial insights on why these problems are hard to solve, and this is addressed by a thorough analysis in the paper. We conclude with computational results on a variety of widely used test sets, and a discussion of future research

Supply-chain research opportunities with the poor as suppliers or distributors in developing countries

Many social enterprises and some companies have developed supply chains with the poor as suppliers or distributors to alleviate poverty and to create revenues for themselves. Such supply chains have created new research opportunities because they raise issues fundamentally different from those examined in the existing operations management literature. We report this phenomenon of supply chains with the poor as suppliers or distributors in developing countries and identify operations management (OM) research opportunities. We also provide some stylized models to serve as potential seeds for modeling-based research in this area

Solving a Discrete Lot Sizing and Scheduling Problem with Unrelated Parallel Machines and Sequence Dependent Setup Using a Generic Decision Support Tool

In any manufacturing systems, planning and scheduling are not intuitive. Some dedicate tools may exist to help some specific companies to daily plan and assign their activities. Our purpose is to develop a generic decision support tool to solve any planning or scheduling problems. To do so, we use a hybridization between a metaheuristic and a list algorithm. The metaheuristic is generic to any studied problems. The list algorithm needs to be specific to the considered problem. The use of our tool needs a minimum work development. In this paper, our proposal is illustrated by the case study of a textile company which intends to schedule its production, by assigning it resources and dates. This problem can be seen as a Discrete Lot Sizing and scheduling Problem (DLSP)

A priori reformulations for joint rolling-horizon scheduling of materials processing and lot-sizing problem

In many production processes, a key material is prepared and then transformed into different final products. The lot sizing decisions concern not only the production of final products, but also that of material preparation in order to take account of their sequence-dependent setup costs and times. The amount of research in recent years indicates the relevance of this problem in various industrial settings. In this paper, facility location reformulation and strengthening constraints are newly applied to a previous lot-sizing model in order to improve solution quality and computing time. Three alternative metaheuristics are used to fix the setup variables, resulting in much improved performance over previous research, especially regarding the use of the metaheuristics for larger instances