Integrated Due Date Setting and Scheduling on a Single Machine Considering an Unexpected Unavailability

Abstract

In this paper, an integrated machine scheduling withits due date setting problem has been considered. It is assumed that the machine is subject to some kind of random unavailability. Due dates should be set in an attractive and reliable manner, implying that they should be short and possible to be met. To this end, first, long due dates are penalized in the objective function. Then, for each customer order, the probability of meeting his/her promised due dateis forced to be at least as large as his/her required service level. To handle this integrated problem, first, the optimal due date formulafor any arbitrary sequence is derived. By using this formula, the mathematical programming formulation of the problem,including a nonlinear non-convex expression, is developed. By defining a piecewise linear under-estimator, the solutions of the resultantmixed integer linear programming formulation have become the lower bounds of the problem. Dynasearch is a very efficient heuristic utilizing the dynamic programming approach to search exponential neighborhoods in the polynomial time. Aniterated dynasearch heuristic is developed for the sequencing part of the problem. Each generated sequence is evaluated by computing its optimal due datesusing the above-mentioned formula. Numerical results confirmed the high quality of the solutions found by this algorithm, as compared with the lower bound.