The three problems of cell formation (CF), cellular scheduling, and cellular layout are closely interrelated in the design of cellular manufacturing systems (CMSs) and should, therefore, be considered in an integrated structure. This paper presents a mixed-integer programming (MIP) model to examine such concurrent design by considering many design attributes, such as the machine duplication, alternative processing routes, reentrant parts, and variable cell size. In the presented model, decisions including machine grouping, processing route selection, operation sequencing, and cell assignment into candidate locations are taken such that the total completion time is minimized. Since the problem in hand belongs to the NP-hard class, a vibration damping optimization (VDO) algorithm is proposed to solve large-sized problems. In order to verify the efficiency of the proposed algorithm comparing to the CPLEX solver of the GAMS software and two other metaheuristic algorithms, namely a genetic algorithm (GA) and an ant lion optimizer (ALO) algorithm, several sample problems with different sizes and settings are implemented. The results demonstrate that the proposed algorithm can obtain better solutions in less computational time.
