A Functional Equation and its Application to Resource Allocation and Sequencing Problems

Abstract

A functional equation, similar to that formulated for the knapsack problem, is applied to the solution of a problem of resource allocation in critical path scheduling, and to a variety of single-machine sequencing problems with deadlines and loss functions. Among these are: minimization of the weighted number of tardy jobs, maximization of weighted earliness, minimization of tardiness with respect to common relative and absolute deadlines, and minimization of weighted tardiness with respect to a common deadline. Extensions to multiple-machine sequencing problems are discussed, and the sequencing of two machines in series is treated in detail.