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This paper treats a two-echelon inventory system. The higher echelon is a single location reffered to as the depot, which places orders for supply of a single com modity. The lower echelon consists of several points, called the retailers, which are supplied by shipments from the depot, and at which random demands for the item occur. Stocks are reviewed and decisions are made periodically. Orders and/or shipments may each require a fixed lead time before reaching their respective desti nations. Section II gives a short literature review of distribution research. Section III introduces the multi-echelon distribution system together with the underlying as sumptions and gives a description of how this problem can be viewed as a Markovian Decision Process. Section IV discusses the concept of cost modifications in a distribution context. Section V presents the test-examples together with their optimal solutions and also gives the characteristic properties of these optimal solutions. These properties then will be used in section VI to give adapted ver sions of various heuristics which were used in assembly experiments previously and which will be tested against the test-examples.
The multi-stage production system is viewed as a production process in which component parts have to be obtained by manufacturing or by purchasing then assembled into subassemblies, assemblies, and finally into the finished good. At the aggregate level a new formulation for the aggregate planning model is given, in order to bring computational feasibility to situations in which older formulations went beyond the capabilities of current linear programming codes. The resulting aggregate model is a large scale system that lends itself to solution by column generation. A dynamic programming algorithm for the generation of columns is developed. Next, at the disaggregation level, the problem of computing optimal lot sizes in multi-stage systems is addressed and solved. Since exact solution procedures are found to be either very expensive or computationally infeasible, a heuristic approach is adopted and results are reported. For more complex situations, in which parts are common to several end products or where there is independent demand for parts, even the heuristics become infeasible; therefore it is suggested that myopic lot sizing policies be used.
​Due to a varying product demand (changing product mix) and different production speeds, bottlenecks may shift between the stages. In that case, a simultaneous lot-sizing and scheduling of these stages is recommendable. Hence, an improved version of the General Lot-Sizing and Scheduling Problem for Multiple production Stages (GLSPMS) was developed. Moreover, several reformulation techniques were applied to this model to solve it exactly. Besides, a new meta-heuristic which combines the principles of Variable Neighborhood Decomposition Search (VNDS) and Exchange was implemented to find good solutions, even for a real-world problem case. Finally, further model extensions, e.g., for scarce setup resources, were proposed.
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