Decomposition of Production Scheduling in Production Systems with Switched Over Continuous Technological Processes

Abstract

Production system SP consisting of M interconnected production sections ZP is under consideration. In k-th production section (k ∈ 1,M) M continuous technological processes could be performed. In each production section in each instant only one technological process can be performed. The aim of production scheduling problem is to optimize: 1) instants of switching over of each technological process at each ZP, 2) loadings of each ZP at each instant. Decomposition method of solving such a problem for the class of SP in which mathematical models of particular technological processes as well as objective functional have a linear form is shown. It is proven that the roduction scheduling problem could be decomposed in two subproblems: Subproblem k of optimization of loadings of individual ZP, subproblem or optimization of instants of switching over of each technological process at each ZP. The possibilities of further decomposition of subproblem B is shown. The considerations are illustrated on the example of a petroleum refinery.