Order planning with an outsourcing strategy for a make-to-order/make-to-stock production system using particle swarm optimization with a self-adaptive genetic operator

Abstract

This paper proposes an order planning method for an MTO-MTS (make-to-order/make-to-stock) production system, where semi-finished products are produced in advance to shorten the fulfillment lead time for customer orders. The semi-finished products can be either produced in-house or outsourced from an outside supplier. To minimize the outsourcing cost and the total penalty cost for the order planning, we build an integer programming model to jointly optimize the inventory matching, multi-process production, and outsourcing for both finished and semi-finished product orders. Because the problem is NP-hard, we propose a heuristic algorithm, APSO-SGO, that combines particle swarm optimization (PSO) and a self-adaptive genetic operator (SGO) based on measuring the swarm’s degree of aggregation (“A”) to solve it. Specifically, we first define four metrics to calculate the swarm’s degree of aggregation and determine whether the PSO is trapped in a local optimum. Self-adaptive crossover and mutation operations are then applied to improve the algorithm’s global search based on the current state of the PSO and the particles’ quality. To assess the method, we conduct numerical experiments using multiple datasets from a steel factory. The results demonstrate the effectiveness of our model and algorithm. We also provide some management recommendations for relevant industries.