Single-Machine Scheduling for Minimizing the Expected Total Cost Subject to Machine Breakdowns

Abstract

A single-machine scheduling model is proposed for minimizing the expected total cost consisting of flowtime cost and asymmetric penalty cost of earliness-tardiness subject to machine breakdowns. All jobs have a common due date and an identical piecewise linear cost function. Since it is difficult to calculate the exact value of expected total cost, an approximate function of expected total cost is introduced to simplify the scheduling model. Dominance conditions necessary for an optimal schedule are derived for this scheduling problem. Efficient methods exploiting these conditions are proposed for obtaining an optimal schedule minimizing the modified expected total cost. Numerical examples are demonstrated to show the effectiveness of the proposed methods.