Stability polyhedra of optimal permutation of jobs servicing

Abstract

Consideration was given to minimization of the sum of weighted instants of completing servicing of n customers by a single server, provided that the duration of jobs servicing may assume any real value from a given numerical interval. An algorithm of complexity O(n) was developed to construct a polyhedron (parallelepiped) of the optimality of permutation of servicing of n jobs that is contained in the domain of stability of the same permutation and comprises the polyhedron of its stability.