LOT‐SIZING IN CAPACITATED MULTI‐STAGE SERIAL SYSTEMS

Abstract

The lot‐sizing problem in capacitated multi‐stage systems with a serial product structure is addressed. This is a complex optimization problem that is part of the decision set in material requirements planning (MRP) systems. The mathematical model that describes the problem uses the concept of echelon stock and includes lead times. Setup times are taken into account, which implies that the problem of finding a feasible solution is NP‐Complete. This paper proposes a heuristic method that provides a production plan in order to minimize inventory, production, and setup costs. The heuristic starts from a solution for the uncapacitated problem, which is given by the sequential application of the Wagner‐Whitin algorithm. Feasibility is then attempted by shifting production amounts between periods. Computational tests conducted in 1,800 instances with up to 40 components and 18 periods have shown that feasible solutions were obtained in 83.7% of the instances. For the infeasible instances, on average, the heuristic is able to find solutions with very low capacity excess. The solutions' quality is evaluated through a lower bound provided by Lagrangean relaxation and on average the gap is less than 10%.