A Multi-level multi-item capacitated lot sizing problem (MLCLSP) model

Abstract

This research was motivated by problems arising from manufacturing of end product from various raw materials. The firm also needs to take into account of other factors, for example: workstation capacity changes over time period; warehouse capacity; raw materials are affected by either availability or price and etc. The purchasing and production planning in multi-item multi-period multi-workstation capacitated lot size situation is discussed and formulated as a Mixed Integer Programming model (MIP) and can be called as a Multi-item Multi-level capacitated lot size with multi-workstation problem (MLCLSP-M). With too complexity of the solving large problem, three heuristic methods are developed, tested and compared based on standard library, illustrating the solution quality and computational time. The proposed heuristics are Assignment-Lot size heuristic (A-LS), Partial Assignment – Lot size (PA-LS), and Max Cover Period – Lot size (MCP-LS). These methods are based on the decomposition of the MLCLSP-M into two phases consisting of an assignment with given lot size phase and a lot size with given assignment phase. Each iteration, the sub problem mathematical models are solved with AMPL/CPLEX 8.0.0 solver. Computational test results are analyzed and discussed on performance and running time. On comparing with the original mathematical model solving, the results indicate that the A-LS heuristic gives a satisfactory solution with very fast solving time, the PA-LS heuristic gives a closely optimal solution with very long solving time, and the MCP-LS gives a good solution with medium solving time.