Fuzzy Gilmore and Gomory Algorithm: Application in Robotic Flow Shops with the Effects of Job-dependent Transportation and Set-ups

This paper addresses the scheduling of robotic cells with job-dependent transportation and set-up effects with fuzzy methodology. Since transportation and set-up times are a large portion of the production time in a flexible manufacturing cell, ignoring these parameters may cause significant errors in determining the optimal makespan. Furthermore, determining the exact values of these time parameters is a challenging task. To overcome this problem, we represent these parameters using fuzzy L-R numbers. Using the capability of fuzzy numbers to model approximate values, we can represent these parameters without losing valuable information. For generating the optimal part sequencing in the cells, the Gilmore and Gomory algorithm is modified, and instead, a fuzzy Gilmore and Gomory algorithm is developed. We compare the results of the proposed fuzzy method with those of crisp ones. The results indicate the superiority of the proposed algorithm in terms of robustness, flexibility, and reduction of makespan.