An ant colony optimization approach for the parallel machine scheduling problem with outsourcing allowed

Several manufacturing environments can be represented as a set of identical parallel machines. Moreover, some industries uses third-part manufacturing to increase the production capacity for short periods. This paper proposes, implements and evaluates an ACO algorithm to solve the parallel machine scheduling problem with outsourcing allowed. The goal is to minimize the sum of outsource and delay costs (since, in many practical situations, the delay generates fine). To the best of our knowledge, this work is the first to address this problem. In order to evaluate the algorithm proposed, a mathematical programming model of the problem is also presented and implemented. The ACO algorithm proposed is composed of three sequential transition rules, each one responsible for one different decision: the first one decides the next job to be scheduled; the second decides the machine to schedule a job and the third decides if the job must be outsourced or not. Computational results show that this algorithm, for instances of size larger or equal to 20 jobs, could reach better solutions than the ones found using the mathematical programming method when the commercial solver used has its running time limited by 1 h. Moreover, the times required to reach a solution were significantly smaller when the ACO is executed.