Multi-machine scheduling with setup times

Abstract

In this paper we are considering the problem of tasks scheduling executed simultaneously on multiple identical machines with a costcriterion, which is the product of the tasks execution time and the number of used machines. Moreover, it is assumed that between the tasks performed sequentially there must be setup of the machines performed. Solution to the problem comes down to a generalization of a two-dimensional packing problem. The paper presents simulated annealing algorithm with different variants of packing strategy. The conducted computational experiments proved that designated solution differs little from some lower bounds for the constraints of the objective function.