An efficient hybrid self-learning method for stochastic cellular manufacturing problem: A queuing-based analysis

This paper addresses a new version of Stochastic Mixed-Integer model to design cellular manufacturing systems (CMSs) under random parameters described by continues distributions. In an uncertain environment processing time, part demand, product mix, inter-arrival time and etc. may change over the period of time. Thus, during planning horizon since any of the parameters of the problem may vary widely, design decisions may be in effect. So, in this research to overcome such drawback, it’s assumed that processing time for parts on machines and arrival time for parts to cells are stochastic and described by continues distribution which yields more flexibility to analyze manufacturing framework. In such case, there are some approaches such as stochastic programming (SP), robust optimization (RO) and queuing theory which can formulate and analyze this problem. In this paper, it’s assumed that each machine works as a server and each part is a customer where servers should service to customers. Therefore, formed cells define a queue system which can be optimized by queuing theory. In this way, by optimizing a desired queue system measurement such as maximizing the probability that a server is busy, the optimal cells and part families will be formed. To solve such a stochastic and non-linear model, an efficient hybrid method based on new combination of genetic algorithm (GA) and simulated annealing (SA) algorithm will be proposed where SA is a sub-ordinate part of GA under a self-learning rule (SLR) criterion. This integrative combination algorithm is compared against global solutions obtained from branch-and-bound algorithm and a benchmark heuristic algorithm existing in the literature. Also, sensitivity analysis will be performed to illustrate behavior of the model.