SINGLE MACHINE SCHEDULING WITH LINEAR DETERIORATING JOBS UNDER PREDICTIVE DISRUPTION

Abstract

This paper considers single machine scheduling problems with linear deteriorating jobs under predictive disruption. In this model, the actual processing time of a job is a increasing linear function of its starting time; and machine is subject to an availability constraint. We assume that an optimal schedule can be obtained by using some algorithms if machine is available at all time. Because of the machine disruption, the original schedule may become infeasible or too far from optimal. We want to create the new schedule that takes into account both the original objective function and a measure of deviation from the original schedule. We consider two versions of the problem. In the first one, the objective is weighted sum of total completion time and total tardiness while in the second one, the objective is weighted sum of total completion time and total earliness. We first prove some properties of the optimal schedule then dynamic programming algorithms are proposed, respectively.