P-Median Approach for the Large-Size Multi-Objective Generalized Cell Formation

Abstract

The p-median model is known as an effective mathematical model for small- to intermediate-size single- objective cell formation (SOCF) problem in the design of cellular manufacturing system. This paper shows that a sequential approach adopting the p-median model can be a very effective alternative for large-size multi-objective generalized cell formation (MOGCF). Our sequential approach proceeds through two-phase procedures. Phase 1 uses a comprehensive generalized part-machine incidence matrix (PMIM) incorporating realistic manufacturing factors such as alternative process plans and duplicate machines as well as processing times, operation sequences, nonconsecutive multiple visits to the same machines, and production volumes of parts. Based on a new generalized similarity coefficient, a 0-1 linear p-median model is formulated to form independent and compact machine cells. Phase 2 uses a systematic part assignment procedure based on a new classification scheme of part types with alternative process plans in pursuit of balanced workload among cells and high machine utilization. Phase 1 implemented using LINGO 16.0 reaches the global optimum within two seconds even on a large problem containing 1,600 binary variables and phase 2 completes speedy assignment of parts within two seconds with high-quality solutions.