Cell formation in a cellular manufacturing system under uncertain demand and processing times: a stochastic genetic algorithm approach

This paper addresses the stochastic cell formation problem with a newly proposed stochastic genetic algorithm (SGA) approach considering stochastic demand and processing times, thus capacity requirements. A stochastic nonlinear mathematical model [SNMM, proposed by Egilmez et al. (2012)] and the newly proposed SGA approaches are compared based on the solution quality and execution times on 10, 20 and 30-product problems. SGA approach is used to experiment with various GA parameters including number of generation, population size, probability and type of crossover and mutation, which resulted in 456 combinations with 10-replications each. The results of the proposed SGA model indicated that the optimal solution is guaranteed with the 10 product problem and average gaps of 1.75% and 3.70% were obtained from 20 and 30-product problems, respectively. The execution times were significantly reduced by the proposed SGA model, where reductions of 87.2%, 98.3% and 99.5% were achieved in computation times.