Experimental-based simulated annealing for job shop scheduling problems with stochastic processing times

Abstract

Job shop scheduling problem is widely known as one of the most difficult NP-Hard problems to solve and present efforts to solve the problems are mostly expressed in the form of heuristics. This thesis investigates the application of simulated annealing algorithm for solving job shop scheduling problem with stochastic processing times. Schedule quality is assessed based on the distribution of the schedule makespan, which is the maximum completion time of all jobs. The main idea is the integration of simulation into the simulated annealing algorithm. As such, variants of simulated annealing procedure for deterministic problems are first analyzed which are then extended to stochastic versions by incorporating simulation to evaluate schedules generated by the algorithms. Experimental results show that the stochastic variants provide an efficient tool in incorporating all the available distributional information on the processing times into the scheduling procedure. In addition, incorporating statistical tools such as the sampling methods enhance to certain extend the quality as well as the efficiency of the solutions. The performance of the simulated annealing variants is further investigated when three different temperature functions are proposed. The extensive computational tests and analysis on selected problem instances show the superiority of the proposed algorithms compared to some typical dispatching algorithms in high variability levels. Finally, the correlations between the expected makespan and the a-quantile of makespan are examined. The solutions obtained for low variability levels indicate that the two measures are perfectly correlated, and makespan distributions mostly follow the normal distributions, with few cases where they fail the normality tests. Although only stochastic processing times are considered in this thesis, the formulations and methodology can be extended to handle different objective functions as well as other kinds of uncertainties, such as uncertain arrival times, due dates and the handling of unpredictable machine breakdown and incorporation of new activities.