Local Search Methods for Solving Total Completion Times, Range of Lateness and Maximum Tardiness Problem

Abstract

In this paper, we introduce one of the multi-criteria objectives function in machine scheduling problem (MSP). Our problem is minimizing three functions: Total Completion Times, Range of Lateness and Maximum Tardiness ( $\sum {C_{j}}, {R_{L}}, {T_{max}}$ ) simultaneously. We prove that some rules give efficient solutions for our problem. Since our problem is NP-hard problem we introduced and proved some special cases which find some efficient solutions suitable for the discussed problem and to find good or optimal solution for the total of the three objective functions $\left(\sum {C_{j}}+{R_{L}}+{T_{max}}\right)$ . Lastly, we solve the two suggested problems using two local search methods (Bees Algorithm and Particle Swarm Optimization).