Developing a Technique for a Bi-objective Scheduling Model with Rejection by Simulated Annealing

We consider the general problem of scheduling a set of jobs on a single machine where we may choose not to schedule certain jobs, potentially exceed machine’s capacity, and thereby incur a penalty for each rejected job. More specifically, we focus on choosing a set of jobs to reject and constructing a schedule for the remaining jobs so as to optimize two objective functions simultaneously: the sum of weighted completion times of the jobs scheduled and the sum of the penalties of the jobs rejected. We believe that this is the first time that this kind of problem, where rejection is permitted, is treated as a bi-objective problem. In this paper, we solve this problem by Multi-Objective Simulated annealing Algorithm and as there is no benchmark, the non-dominated set obtained by the proposed algorithm, is compared with the set of exact Pareto-optimal solutions obtained from complete enumeration. We show that the results are reasonably good by comparing to the solutions we get from complete enumeration for small size while the proposed algorithm requires less computational effort.