Computers ind. Engng Vol. 19, Nos 1-4, pp. 294-298, 1990 0360-8352/90 $3.00 + 0.00 Printed in Great Britain. All rights reserved Copyright © 1990 Pergamon Press pie MODELING THE MACHINE LAYOUT PROBLEM Sunderesh Heragu Department of Management and Marketing School of Business and Economics State University of New York Plattsburgh, NY 12901 ABSTRACT using a modified penalty algorithm. The In this paper, a mathematical model for the algorithm produced solutions of high quality machine layout problem is presented. The and requires low computation time. In this objective function of the model minimizes the paper, a new model for the machine layout total cost involved in transporting material problem is presented. The model is an between each pair of machines. The extension of the one presented in Heragu constraints ensure that: (i) the pickup and (1988). To solve the model presented, a drop-off points of a machine fall within the simulated annealing algorithm is also boundaries of the machine~ (ii) no two presented. machines in the layout overlap; and (iii) the machines are located inside the building. A In the next section, some of the models simulated annealing algorithm for solving the developed for the facillty/machine layout model is also presented. The solution problem are listed. In section 3, models for provided by the algorithm indicates the MHS the single-row and multl-row machine layout paths, the relative positioning of each problem are presented. A simulated annealing machine, the pick-up and drop-off points for algorithm for solving the layout problem is each machine, and clearance between machines, also presented. Concluding remarks and some llmltations of the simulated anneallng algorithm are provided in section 4. INTRODUCTION The objective of developing machine layout in LITERATURE REVIEW an automated manufacturing system is to minimize the total time required by the Traditionally, the layout problem has been material handling systems to transport modeled as a QAP. Given that: material between the machines. Two patterns n total number of machines or locations of machine layout frequently occur in fik number of trips to be made between practice (Heragu and Kusiak, 1990): machines i and k - slngle-row machine layout Cjl cost per trip between locations j and 1 - multi-row machine layout, xij is I if plant i is at location j; 0 otherwise The single-row and multi-row layout problems have also been referred to as one- the QAP can be stated as (Koopmans and dimensional and two-dimensional space Beckman, 1957): allocation problems (Simmons, 1969). The single-row (multi-row) layout problem n n involves problems in which the machines are Min ~ ~ flkCjlXijXkl (I) arranged linearly along one row (two or more i-I j=l rows). Heragu and Kusiak (1990) identify a number of applications of the single-row and n multi-row layout problems, s.t. ~ xij - l, i=l,...,n (2) J=l In this paper, the development of machine layout in a manufacturing system is n discussed. Traditionally, the layout problem ~ xij - i, j-l,...,n (3) has been modeled as a quadratic assignment i-I problem (QAP). It is well-known that the QAP is NP-complete and cannot be used to solve x~j - 0 or l, i,j-I .... ,n (4) large scale layout problems, for example, problems in which there are fifteen or more A number of other models have also been machines. Heragu (1988) has presented a new developed for the layout problem. For model with absolute values in the objective example, Bazaraa (1975) presented the function and constraints and solved the model Quadratic Set Covering model~ Love and Wont 294