Determination of due dates in job shop scheduling by simulated annealing

Abstract

The scheduling of n jobs to m machines in a job shop is considered. A predefined due date, a release time and the minimization of the maximal job's lateness is the objective assigned to each job. A search space consisting of triads (job, operation, machine) is formulated, and an iterrative improvement approach, the simulated annealing method, is then used to obtain feasible and global optimal solution. The simulated annealing method is applied to two alternative energy functions to model the maximum lateness. For calculation of the first energy function at each step, complete schedules are created and the lateness of each job is derived by abstracting the job's completion time from the corresponding due date. The second energy function is calculated on the basis of partial estimates often used by pairwise interchange techniques. The convergence of the algorithm in relation to the initial temperature, temperature iterrations and temperature cycles has been verified in various case studies. Specific characteristics of the scheduling, such as its dimensionality and the deviation of the total processing time from the due dates, were considered. Common characteristics derived were subsequently used for the definition of an efficient annealing schedule.