A Heuristic Algorithm to Minimize Mean Squared Deviation of Completion Times

This paper addresses the problem of minimizing the mean squared deviation(MSD) of completion times from a common due date in unconstrained case. The unconstrained MSD is known to be NP-complete and a heuristic algorithm which consists of two phases(schedule construction and improvement) is proposed. In the schedule construction phase, by using the simulated annealing technique and balanced V-shape schedule, good initial solutions are constructed. Then, the improvement phase enhances the quality of solution based on the concepts of both better dual and better pair. The developed two phases are serially employed to obtain the schedule of minimizing MSD problem. The first phase focuses on the finding of good initial solution and the second phase stresses on the improvement of solution quality. For the unconstrained MSD problem, the best known heuristic the algorithm is in Ventura and Weng(1995) and the algorithm in Gupta et al.(1990) finds fairly good solutions with much less computational time than one in Ventura and Weng(1995). The proposed heuristic finds all optimal solutions of the test problems in Eilon and Chowdhury(1977) and Gupta et al.(1990) with much less computational time compared with the heuristic in Ventura and Weng(1995). In order to show the performance of proposed heuristic in detail when job sizes are large, several test problems are generated. The computational results show that it provides better or same solutions for almost all test problems than the heuristic in Gupta et al.(1990).