Solution of the Machine Loading Problem with Binary Variables

Abstract

In this paper the machine loading problem, i.e. the problem of the optimal assignment of n jobs to m machines of limited capacities, is considered with the further constraint that each job has to be performed using one machine only. The problem may be formulated as an integer 0,1 LP problem, for which an implicit enumeration method of solution is suggested. This method draws advantage from: i) a proposed heuristic solution, to have a good initial “ceiling” (often the optimal solution itself!), ii) an “a priori” criterium to widely reduce the set of solutions to be inspected, iii) a special method to get bounding functions and branching criteria. A wide computational experience allows a good insight into the method.