Flexible PMP Approach for Large-Size Cell Formation

Abstract

Lately, the problem of cell formation (CF) has gained a lot of attention in the industrial engineering literature. Since it was formulated (more than 50 years ago), the problem has incorporated additional industrial factors and constraints while its solution methods have been constantly improving in terms of the solution quality and CPU times. However, despite all the efforts made, the available solution methods (including those for a popular model based on the p-median problem, PMP) are prone to two major types of errors. The first error (the modeling one) occurs when the intended objective function of the CF (as a rule, verbally formulated) is substituted by the objective function of the PMP. The second error (the algorithmic one) occurs as a direct result of applying a heuristic for solving the PMP. In this paper we show that for instances that make sense in practice, the modeling error induced by the PMP is negligible. We exclude the algorithmic error completely by solving the adjusted pseudo-Boolean formulation of the PMP exactly, which takes less than one second on a general-purpose PC and software. Our experimental study shows that the PMP-based model produces high-quality cells and in most cases outperforms several contemporary approaches. Subject classifications: cell formation; p-median problem; pseudo-Boolean polynomial; group technology. Area of review: Optimization.

Heuristic for Maximizing Grouping Efficiency in the Cell Formation Problem

“…We have found better solutions unknown before for 23 instances of the 24 considered. For CFP instance 6 we have found the same optimal solution with 100% of grouping efficiency as in Goldengorin et al (2012). For CFP instance 1 the solution of Goldengorin et al (2012) has some mistake.…”

“…For CFP instance 6 we have found the same optimal solution with 100% of grouping efficiency as in Goldengorin et al (2012). For CFP instance 1 the solution of Goldengorin et al (2012) has some mistake. For this instance having a small size of 10x20 it can be proved that our solution is the global optimum applying an exact approach (Elbenani & Ferland, 2012) for the grouping efficiency objective and all the possible number of cells from 1 to 10.…”

“…In this paper we use the grouping efficiency measure and compare our computational results with the results of Yang & Yang (2008) and Goldengorin et al (2012). The mathematical programming model of the CFP with the grouping efficiency objective function can be described using boolean variables x ik and y jk .…”

“…Since the objective function of the CFP is rather complicated from the mathematical programming point of view most of the researchers use some approximation model which is then solved exactly for small instances and heuristically for large. Kusiak (1987) formulated CFP via p-median model and solved several small-size CFP instances, Shtub (1989) used Generalized Assignment Problem as an approximation model, Won & Lee (2004) proposed a simplified p-median model for solving large CFP instances, applied minimum k-cut problem to the CFP, Goldengorin et al (2012) used p-median approximation model and solved it exactly by means of their pseudo-boolean approach including large CFP instances up to 50x150 instance. A number of meta-heuristics have been applied recently to the CFP.…”

A Metaheuristic algorithm for the manufacturing cell formation problem based on grouping efficacy

“…The author's investigation with the most popular set of 35 benchmark instances showed that the proposed heuristic returns either the best-known or improved solutions to the MPCF. The most recent examples of exact algorithms are presented in Krushinsky and Goldengorin [30] for solving the MPCF by means of MINpCUT model and Goldengorin et al [22] by means of the p median model. Elbenani et al [19] presented a local search procedure for the manufacturing cell formation problem which applies sequentially an intensification strategy to improve locally a current solution and a diversification strategy destroying more extensively a current solution to recover a new one.…”