A mixed integer linear programming formulation of closed loop layout with exact distances

Abstract

In the layout problem of manufacturing cells, rectangular cells are to be positioned without overlapping. The objective is to minimize the total transportation cost, i.e. the sum of distances of all pairs of cells weighted by their flow values. The types of layouts are categorized according to the shape of the transportation system's track. In the case of a closed loop layout, the track has a rectangular shape. A common difficulty of all layout problems is the manner in which distances are measured. A frequently used approximation is the Manhattan distance. However, it is significantly shorter than the exact distance in many cases. Both the metaheuristics and exact models suggested by earlier studies use the Manhattan distance. In this paper, a new mathematical model is suggested for the closed loop layout with exact distances. Many feasible solutions are generated for benchmark problems that are competitive with the solutions provided by metaheuristics.