Metrics in scheduling problems

Abstract

An important problem of mathematical scheduling theory is constructing metrics which can be used for designing exact and approximate solution algorithms. The introduction of metric spaces in solving NPhard problems of scheduling theory makes it possible to apply general mathematical approaches to construct approximate solutions with a guaranteed absolute error. The application of metrics in solution spaces (spaces of permutation schedules) to some problems of scheduling theory was considered in, e.g., (1, 2). Earlier, for NPhard problems with the minimiza� tion criterion {P, R, Q}|prec, r j |{L max , C max } for the maximal lateness, a metric on the instance space (of the initial parameters of the problem) was con� structed; on the basis of this metric, a general scheme for finding approximate solutions was developed (3). In this paper, we propose an approach to constructing metrics on the instance space for problems with the sum criteria , Tj, Cj, and Uj. Consider a problem of scheduling theory with