Bi-objective optimization for a multistate job-shop production network using NSGA-II and TOPSIS

A job-shop production system (JPS) is a manufacturing system wherein each workstation configures multiple types of machines to produce small batches of a variety of products. In each workstation of a JPS, the number of machines that operate normally exhibits multiple levels of capacity owing to failures, partial failures, and maintenance. That is, the number of normal machines in each workstation is stochastic (i.e., multistate). To analyze such a JPS, the JPS is transformed into a multistate job-shop production network (MJPN) using a network topology. For the MJPN, a critical issue is to maximize the network reliability and to minimize the purchase cost when setting up the JPS. To achieve such bi-objective optimization, a machine vector (MV) representing the current number of normal machines in each workstation is introduced to evaluate network reliability. An algorithm based on a depth-first search (DFS) with an expanding technique is proposed to search all MVs for satisfying demand. Subsequently, to obtain a machine configuration (MF) simultaneously having the maximal network reliability and the minimal purchase cost, a two-stage approach is developed based on the non-dominated sorting genetic algorithm II (NSGA-II) and the technique for order of preference by similarity to ideal solution (TOPSIS). A real case of t-shirt production is utilized to illustrate the proposed method.