Backtracking and its Amoebic Properties in One-dimensional Machine Location Problems

• Published in: The Journal of the Operational Research Society Vol. 45; no. 9; pp. 1024 - 1039
• Main Authors: Sarker, Bhaba R., Wilhelm, Wilber E., Hogg, Gary L.
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 01-09-1994; Macmillan Press; Pergamon Press; Taylor & Francis Ltd
• Subjects: amoebic properties; Assembly lines; backtracking; Heuristics; Integers; Location analysis; machine locations; Machinery; Materials handling; Mathematical vectors; Matrices; Operations research; Production planning; Property lines; quadratic assignment problem; Studies; Theoretical Papers; Zero
• ISSN: 0160-5682; 1476-9360
• DOI: 10.1057/jors.1994.168

This paper studies the assignment of M unique machines to M equally spaced locations along a linear material handling track with the objective of minimizing the cost of (jobs) backtracking (i.e. moving upstream). Because of the arrangement of machines and restrictions imposed by the sequence of operations for each job, some jobs may have to backtrack to complete required processing on different machines. This problem is formulated as a quadratic assignment problem. An optimal solution to a problem with large M is computationally intractable. The backtracking distance matrix in problems involving equally-spaced machine locations in one dimension is seen to possess some unique characteristics called amoebic properties. Ten amoebic properties have been identified and exploited to devise a heuristic and a lower bound on the optimal solution. Results which describe the performance of the heuristic and the lower bound are presented.