Mixed integer linear programming model for integrating cell formation, group layout and group scheduling

Abstract

Cellular manufacturing systems (CMS) are production systems that typically comprise a number of manufacturing cells served by a centralized material handling system. Designing such systems includes three major decisions; cell formation (CF), group layout (GL), and group scheduling (GS). Traditionally, these three decisions have been dealt with separately, which has usually lead to less than optimal system performance. In this paper, a new mixed integer linear programming (MILP) model is proposed for the integrated CF, GL and GS problem, to efficiently design and operate CMSs. The model solves the integrated problem, taking into consideration intercellular and intracellular transportation times to determine the optimal cell formation, layout of machines and schedule of parts on the machines, simultaneously. Sequence-dependent set up times are also considered in the model. The performance of the model is tested by solving problems previously introduced in the literature considering two objectives; minimizing the makespan or minimizing the mean flow time in the system. The results show that the proposed model is efficient in solving small to medium-sized problems.

Making an integrated decision in a three-stage supply chain along with cellular manufacturing under uncertain environments: A queueing-based analysis

“…The objective function minimizes the penalty cost, i.e., due dates have not been met. Fahmy [43] presented a mixed-integer linear programming model to integrate CF, group layout, and group scheduling decision problem to design a CM system. The model considered intercellular and intracellular transportation time and sequence-dependent setup time to determine optimal CF, candidate locations for machines within cells, the distances between these locations and between cells to obtain the optimal group layout, and the schedule of parts on machines concurrently.…”

A two-stage stochastic supply chain scheduling problem with production in cellular manufacturing environment: A case study

“…Objective function minimizes the penalty cost, when due dates have not met. Fahmy [52] presents a mixed integer linear programming model to formulate and solve combined CF, group layout, and group scheduling decision problem to design the CM system. Model takes into account intercellular and intracellular transportation time and sequence-dependent setup time to determine the optimal CF, candidate positions for machines within cells, distances between these positions and between cells to obtain the optimal group layout, and schedule of parts on machines, simultaneously.…”

Multi-Objective Bi-Level Programming for the Energy-Aware Integration of Flexible Job Shop Scheduling and Multi-Row Layout

“…In the simultaneous method, the layout model is simply appended to the scheduling model as constraints [10,[15][16][17], which leads to the layout scheme lacking autonomy. Without its own objectives, the layout model is optimized to purse the objectives of the scheduling model.…”

“…Equations (14) and (15) calculate the horizontal coordinate and vertical coordinate of each machine in the workshop, respectively. Equation (16) calculates the distance between machine l and machine k. Equation (17) guarantees that the machines do not overlap in the horizontal direction. Equation (18) ensures that the vertical coordinates of the machines are identical in the same row.…”

“…Besides this, in the field of cellular manufacturing, Wu et al [15], Arkat et al [16], and Fahmy et al [17] studied the integrated cell formation, group layout, and group scheduling, and applied GA to solve the problem for minimizing makespan. Arkat et al [18] adopted the multi-objective genetic algorithm (MOGA) for the cell formation problem considering cellular layout and operation scheduling to minimize makespan and transportation cost.…”