Optimal Stochastic Scheduling pp 95-140 | Cite as

# Irregular Performance Measures

## Abstract

This Chapter covers stochastic scheduling problems with irregular performance measures. Section 3.1 is focused on models where both the earliness and tardiness costs are functions of the completion time deviations from the due date. In Section 3.2, we consider the problem where the tardiness cost is a fixed charge once a job is late, whereas the earliness cost depends on the amount of completion time deviation from the due date. Section 3.3 addresses the completion time variance problem, a model that has been studied in the scheduling field for decades. We will show that, a common structure of the optimal schedule for an E/T problem appears as a V-shape around a due date. We will derive such properties for each model, characterize the analytic optimal solutions when possible, and develop solution algorithms based on the optimality properties. We will show that dynamic programming algorithms can usually be established based on V-shape properties.

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