Stochastic economic lot sizing and scheduling problem with pitch interval, reorder points and flexible sequence

Abstract

This paper presents a solution for a class of the stochastic economic lot sizing scheduling problem that is typical of the replenishment pull system proposed by the lean manufacturing approach. In this class, lots of any product are produced in fixed intervals called pitch. The proposed solution uses flexible production sequences and reorder points that are compatible with the concepts of supermarket and level production. It adopts the queuing discipline obtained from a fluid model that approximates the stochastic process of arrival and production orders. Given the queuing discipline, an iterative algorithm returns a near-optimal solution for the system. The proposed approach allows us possible to differentiate inventory cost and service levels by product, and the stock required is lower than that required by the discipline ‘first stock out, first out’. The algorithm is fast and stable, allowing its frequent use in real-world instances.