Novel Heuristic Approach for Solving Multi-objective Scheduling Problems

Abstract

In this paper, we studied the scheduling of jobs on a single machine. Each of n jobs is to be processed without interruption and becomes available for processing at time zero. The objective is to find a processing order of the jobs, minimizing the sum of maximum earliness and maximum tardiness. This problem is to minimize the earliness and tardiness values, so this model is equivalent to the just-in-time production system. Our lower bound depended on the decomposition of the problem into two subprograms. We presented a novel heuristic approach to find a near-optimal solution for the problem. This approach depends on finding efficient solutions for two problems. The first problem is minimizing total completion time and maximum tardiness. The second is minimizing total completion time and maximum earliness. We used these efficient solutions to find a near-optimal solution for another problem which is a sum of maximum earliness and maximum tardiness. This means we eliminate the total completion time from the two problems. The algorithm was tested on a set of problems of different n. Computational results demonstrate the efficiency of the proposed method.

Solving the Multi-Criteria Problem: Total Completion Time, Total Late Work, Total Earliness Time, Maximum Earliness, and Maximum Tardine

“…Nagar et al [2] presented a survey of multiple and binary problems in scheduling. In general, there are two structures for dealing with conflicting criteria, namely hierarchical minification and concurrent minification [3]. The first one is the primary criterion, and the other is the secondary criterion.…”

“…Given the schedule ( ( ) ( ) ( )), then for each job , we calculate the completion time by and for . The earliness of the job is defined by , the two problems 1// , 1// , and 1// are NP-hard [6], [3], [7], [8], [9], [10]. Any problem including cost functions as sub-problems is NP-hard.…”