MIC 2011: The IX Metaheuristics International Conference S1-09 Udine, Italy, July 25–28, 2011 Resource constrained scheduling in permutation flowshop problems Michele Ciavotta, Rubén Ruiz Grupo de Sistemas de Optimización Aplicada, Instituto Tecnológico de Informática, Universidad Politécnica de Valencia. Camino de Vera s/n Edif. 8G Acc. B- 46022 Valencia, Spain mciavotta@iti.upv.es, rruiz@eio.upv.es Abstract This short paper gathers the initial results obtained after including the consideration of addi- tional resources, like for example, tools, fixings or man power, into flowshop scheduling problems. The literature on scheduling assumes that the only limiting resource is the machines. However, in real life, personnel operating the plant could be scarcer than the machines themselves. More in de- tails, we consider a single resource with a non-negative and integer consumption from all the tasks in a flowshop. The optimization criterion is the minimization of the maximum completion time or makespan. An important consideration is that resource constrained flowshop problems can be easi- ly transformed into the well-known resource constrained project scheduling problem or RCPSP. Therefore, a natural question is to see how good metaheuristics for the RCPSP behave for the con- sidered resource constrained scheduling setting studied in this paper. Initial results show that sim- ple adaptations of existing metaheuristics for the regular flowshop with the consideration of addi- tional resources behave much better than RCPSP metaheuristics. 1 Introduction The flowshop problem (FSP) is a typical production configuration where there is a set N of n inde- pendent jobs that have to be processed with a fixed, known in advance processing time pij on a set M of m machines. Each job j, j = 1,…,n has to be processed by all the m machines in a fixed sequence. The machine route is the same for all jobs and each machine processes the same sequence of jobs. Furthermore, no machine can process more than one job at the same time and once the processing of a job by a given machine has started, it has to continue until completion. The FSP has been often criticized for being too theoretical as most real industry settings seldom fit into this model. Actually, there is a so-called “scheduling gap” between the cases studied in the litera- ture and the manufacturing problems arising in real-life. In order to partially fulfill this gap, we study in this short paper the flowshop problem with the additional consideration of renewable resources that the processing of jobs needs, apart from machines. In this scenario, we also model, for example, com- plex fixtures, tooling or manpower needed to operate machines and/or jobs. Although the first works on the topic of scheduling with limited resources have been published more than forty years ago, those studies were seldom directed to the flowshop problem. Indeed the parallel machines and jobshop problems are far more popular [7][11][17]. Moreover, the majority of papers that can be retrieved from the literature are concerned to very theoretical and simplified cases as 0-1 resource consumption, for example, or processing times depending on the quantity of the resources assigned. Blazewicz et al. (1983) [3] proposed a classification scheme for resource constraints and in- vestigated the computational complexity of parallel machines, flowshop and openshop with unit pro- cessing time jobs, precedence constraints and maximum completion time. Janiak in [9] and [10] stud- ied an extension of the two-machine flowshop problem to the case with task processing times being inversely proportional to or linearly compressible by the used amounts of continuously divisible re- sources. He studied the complexity, some efficiently solvable cases and proposed a heuristic procedure to tackle that problem. Huq et al. (2004) [8] described the development of a mixed integer linear pro- gramming model for a flowshop with multi-processor workstations and workers to assign to the ma- chines. More recently, Ruiz-Torres and Centeno (2008) [14] consider a permutation flowshop problem