Abstimmungsmechanismen zwischen Programmplanung und Mengenplanung in der mehrstufigen Produktionsplanung
This paper discusses several approaches to solve production planning problems especially in the area of Master Planning and Lot Sizing. Most modern Production Planning Concepts inherit a hierarchical planning approach. The splitting of a simultaneous production planning approach leads to the reduction of complexity and allows the consideration of organizational structures within the system. The most popular and widely used paradigm for Hierarchical Production Planning is Manufacturing Resource Planning (MRP II). It consists of 4 different levels. The highest level is called Master Production Scheduling or Program Planning. It determines a Master Schedule using aggregate capacity limits and demand forecasts. Mathematical Models for Master Planning try to coordinate the use of inventory and overtime. The next level in the hierarchy has to deal mainly with Lot Sizing Problems. These models have to combine orders for the same product into lots that are produced without interruption. The objective is to minimize the sum of setup and holding costs that have to be paid for inventory that is used to serve orders that are due during the production cycle of a different product or in a period with insufficient production capacity. The following two levels are Capacity Planning and Production Scheduling which are not going to be analysed here. The use of mathematical models for Production Planning is limited by the complexity of the models that have to be solved. Problems are especially caused by binary and mixed integer restrictions like in a setup constraint of a Lot Sizing Problem. Because of these problems hierarchical planning approaches are used to approximate the optimal solution of a model that These steps in Production Planning are frequently used, but up till now almost no scientific simulations have shown how to use information or results from one level in the other in order to find a better global solution of the planning process. The main focus of this paper is to show under which circumstances a MIP Solver like ILOG CPLEX can be used to solve the total model in one step, and which mechanisms can be used to coordinate the results of different levels of a hierarchical planning approach, and how they have to be adjusted such that the result of the hierarchical planning process comes closest to the result of the optimal solution of the total model. For this purpose a system of models, including mechanisms for their coordination, is developed and the performance of the system as well as the quality of the results provided by the system are evaluated by simulations. The simulation results show, that ILOG CPLEX is able to find good solutions in a reasonable time if parameters are adjusted properly. Since the runtime is rising exponentially with the size of the problem the use of a heuristic which was developed here should be considered. This heuristic is able to find solutions of almost the same quality but in much less runtime. The simulations of the hierarchical approach showed that in order to achieve good coordination between the two levels, a mixed integer model which is able to anticipate the setup decisions of the base level has to be used in the top level.
copy citation link