Robust optimization models for MRP ? a comparison to stochastic programming approaches and a decomposition based solution method
Sprache des Vortragstitels:
International Conference on Operations Research
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This paper investigates robust optimization models for Material Requirements Planning (MRP). The addressed optimization problem is the multi-item multi-echelon capacitated lot-sizing problem with constant lead times under uncertain demand. The presence of stochasticity in the demand for end items in a production system can have significant influence on optimal production quantities and the resulting inventory- and backlog levels. Neglecting this uncertainty within the optimization model by solving a deterministic version of the problem with uncertain parameters replaced by their averages, results in suboptimal production plans. While tackling this issue by using scenario-based stochastic optimization assumes knowledge of probability distributions, robust optimization serves as a worst-case approach and comes with great potential in reducing computational complexity. Especially for large scale problems with complex manufacturing structures efficient modelling and solution methods are desirable. This paper compares solutions obtained by two-stage stochastic programming techniques to robust solutions concerning two characteristics. On the one hand computational complexities of both approaches are compared, while on the other hand the structures and qualities of the obtained solutions are analysed. A simulation framework is used to evaluate the performance of the different resulting production plans in an uncertain environment. Since solving stochastic programs with a large number of scenarios is computationally challenging, this paper also introduces a solution method based on Benders Decomposition tailored to the observed production planning problem, in order to obtain results for the comparison of both frameworks in reasonable time.