Scheduling interfering job sets on parallel machines

• Published in: European journal of operational research Vol. 199; no. 1; pp. 55 - 67
• Main Authors: Balasubramanian, Hari, Fowler, John, Keha, Ahmet, Pfund, Michele
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 16-11-2009; Elsevier; Elsevier Sequoia S.A
• Series: European Journal of Operational Research
• Subjects: Applied sciences; Bicriteria scheduling; Decision theory. Utility theory; Exact sciences and technology; Genetic algorithms; Heuristic; Integer programming; Interfering job sets; Interfering job sets Parallel machines Bicriteria scheduling; Inventory control, production control. Distribution; Operational research and scientific management; Operational research. Management science; Optimization; Parallel machines; Production scheduling; Studies; Parallel machines; Interfering job sets; Bicriteria scheduling; Decision making; Task scheduling; Iterative method; Scheduling; Makespan; Workload; Integer programming; Genetic algorithm; Coding; Heuristic method; NP hard problem
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2008.10.038

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.