Time–cost trade-off in a multi-choice assignment problem

Abstract

ABSTRACT The conventional assignment problem is unable to handle scenarios that may arise due to different working modes of machines leading to multiple cost and time entries corresponding to a job–machine pair. The present article deals with this problem and models it as a multi-choice bi-objective assignment problem, the two objectives being assignment cost and bottleneck time. Two different solution procedures are presented based on the Decision-Maker's (DM's) preference structure. First, when the DM provides his/her preference structure as goals, a solution methodology is proposed using goal programming and its different multi-choice variants. In the second case, when no preference is provided by the DM, a two-step approach is presented that iteratively solves a multi-choice cost-minimizing assignment problem to obtain all Pareto-optimal time–cost pairs and finally, based on the Technique for Order Preference by Similarity to the Ideal Solution (TOPSIS), a single efficient pair is obtained. The algorithm is successfully implemented using the CPLEX ® optimization package and tested on various test problems.