A genetic algorithm for multi-level, multi-machine lot sizing and scheduling

Abstract

This contribution introduces a mixed-integer programming formulation for the multi-level, multi-machine proportional lot sizing and scheduling problem. It also presents a genetic algorithm to solve that problem. The efficiency of that algorithm is due to an encoding of solutions which uses a two-dimensional matrix representation with non-binary entries rather than a simple bitstring. A computational study reveals that the proposed procedure works amazingly fast and competes with a tabu search approach that has recently been published. Scope and purpose The logic of Manufacturing Resource Planning (MRP II) is implemented in most production planning software packages. In the short-term scope, where lot sizing and scheduling has to be done, MRP II systems basically pass three phases: First, lot sizes are computed while disregarding capacity constraints. Multi-level product structures are taken into account in a level-by-level manner starting with end items. Second, lot sizes are adapted to meet capacity restrictions. This time, precedence relations among items are not taken into account. Finally, sequence decisions are made. Following this strategy is reported to result in high work-in-process and long lead times. To cure these shortcomings, an approach for simultaneous lot sizing and scheduling is required where multi-level product structures and several scarce capacities are taken into account. Unfortunately, such methods have not been presented yet. To close this gap is our aim.