Novel Heuristic Approach for Solving Multi-objective Scheduling Problems

Begard A Amin,Ayad M Ramadan

doi:10.30526/34.3.2677

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.

Highlights

Since 1954, scheduling problems have received much attention in the literature
The objective function is to minimize the sum of maximum earliness and maximum tardiness ETmax
We present a novel heuristic method to find a best solution depending on a new idea that is inserting an objective function to our problem, and find efficient solutions for the two problems

Summary

Introduction

Since 1954, scheduling problems have received much attention in the literature. At first, the researchers considered only one objective function. The efficient solutions (Pareto set) will be generated, and the decision-maker the one with the best composite objective function [4]. The objective function is to minimize the sum of maximum earliness and maximum tardiness ETmax This problem was first introduced by Amin-Nayeri and Moslehi [6]. Mahnam and Moslehi presented an efficient branch-and-bound algorithm to minimize the problem on a single machine with unequal release times and no unforced idle time [14]. Et al, showed that the problem is irregular; so many properties of regular will be missed for the present objective function They presented a heuristic method using a novel branch-and-bound algorithm to minimize the sum of maximum earliness and tardiness on a single-machine scheduling problem where the due dates were distinct [15]

Algorithms for Solving Multi-objective Problems

Schedules

Conclusions and Future Works