Scheduling Interfering Job Sets on Parallel Machines Hari Balasubramanian 1 , John Fowler 2 , Ahmet Keha 2 , and Michele Pfund 3 1: Department of Mechanical and Industrial Engineering, University of Massachusetts, Amherst, MA 2: Department of Industrial Engineering, Arizona State University, Tempe, AZ 3: Department of Supply Chain Management, Arizona State University, Tempe, AZ hbalasubraman@ecs.umass.edu, john.fowler@asu.edu, ahmet.keha@asu.edu, michele.pfund@asu.edu Abstract We consider bicriteria scheduling on identical parallel machines in a nontraditional context: jobs belong to two disjoint sets, and each set has a different criterion to be minimized. The jobs are all available at time zero and have to be scheduled (non-preemptively) on m parallel machines. The goal is to generate the set of all non-dominated solutions, so the decision maker can evaluate the tradeoffs and choose the schedule to be implemented. We consider the case where, for one of the two sets, the criterion to be minimized is makespan while for the other the total completion time needs to be minimized. Given that the problem is NP-hard, we propose an iterative SPT-LPT-SPT heuristic and a bicriteria genetic algorithm for the problem. Both approaches are designed to exploit the problem structure and generate a set of non-dominated solutions. In the genetic algorithm we use a special encoding scheme and also a unique strategy - based on the properties of a non-dominated solution - to ensure that all parts of the non- dominated front are explored. The heuristic and the genetic algorithm are compared with a time-indexed integer programming formulation for small and large instances. Results indicate that the both the heuristic and the genetic algorithm provide high solution quality and are computationally efficient. The heuristics proposed also have the potential to be generalized for the problem of interfering job sets involving other bicriteria pairs. Keywords: interfering job sets, parallel machines, bicriteria scheduling. 1 Introduction Traditionally, multicriteria scheduling problems have been considered with the objective of mini- mizing criteria that apply to each of the jobs being scheduled. While motivation for such problems can frequently be found in practice, it is also possible to have situations in which jobs belong to disjoint classes or sets, with a criterion associated with each set. The job sets in such a situation are said to compete or interfere with each other for the same resources. Research in the area of interfering job sets is limited. In Hoogeveen [2005]’s review of multicriteria scheduling problems, he mentions the scheduling of interfering job sets as one of the new developments in the area. The work of Peha [1995] is the earliest reference on the topic. He considers the lexicographic opti- mization of the weighted number of tardy jobs for one set and the total weighted completion time for the other under the assumption of unit processing times, integer release dates and identical parallel machines. Peha [1995]’s research is motivated by real time systems and integrated-services 1