In this work a continuous lot sizing and sequencing model is developed. The model deals with a single-machine, multi-item production system. In a finite planning horizon the dynamic demand is fixed for each product type. Start and finishing times for production are determined so that certain restrictions are fulfilled and the resulting holding and setup costs are minimised. Setup times are included, at any one time only one type of activity (setup or production) can be performed, the pro-duction rate has an upper bound for each product type and backlog is not allowed. First a literature review of the most important lot sizing and sequencing models is given. Optimal control theory is taken as the mathematical basis. The fundamental theorem of optimal control – the maximum principle – is formulated and fully proved. If the sequence of production lots is fixed, the structure of an optimal solution can be characterised with the help of the maximum principle for problems with state constraints. For a known structure, a standard solver (optimization toolbox of MATLAB) is capable of finding the optimal start and finishing times for all production lots. A start algorithm, which finds an admissible solution for numerous problems, is devel-oped. Based on this start solution, the sequence of the production lots can be improved with heuristic search procedures such as Best First Search and Tabu Search. The work concludes with the results of some test instances. The results of the presented solution approach are compared to another approach – the IZKS model – which was devel-oped within a research project at the University of Applied Sciences in Steyr. In large parts the presented algorithm yields better solutions concerning the objective function but the calculation times of examples with numerous production lots is a good deal bigger.
|Translated title of the contribution||Optimal control of setup and production processes|
|Publication status||Published - 2007|