Minimizing weighted waiting time variance on a single processor

Abstract

This paper considers the problem of scheduling n non-preemptive jobs on a single processor. Each job may have different size and weight. The objective is to minimize the weighted waiting time variance (WWTV). It is shown that the proof of one previous established optimality property in the literature, called “agreeably weighted property”, is wrong and the corrected proof is presented. Additional optimality properties are proved for the cases where job sizes are directly or inversely proportional to their weights, respectively. In addition, we show that the objective function of the problem can be expressed as a function of positional weights and processing times. With this new functional form, the proofs of several previously established optimality properties in the literature become rather straightforward.