88 European Journal of Operational Research 81 (1995) 88-104 North-Holland Theory and Methodology Multiple and bicriteria scheduling: A literature survey Amit Nagar, Jorge Haddock and Sunderesh Heragu Department of Decision Sciences and Engineering Systems, Rensselaer Polytechnic Institute, Troy, N Y 12180-3590, USA Received September 1992; revised March 1993 Abstract: Real life scheduling problems require the decision maker to consider a number of criteria before arriving at any decision. A solution which is optimal with respect to a given criterion might be a poor candidate for some other. The trade-offs involved in considering several different criteria provide useful insights to the decision maker. Thus considering problems with more than one criterion is more relevant in the context of real life scheduling problems. Surprisingly, research in this important field has been scarce when compared to research in single criterion scheduling. In this paper, we provide a detailed literature survey of multiple and bicriteria problems in scheduling. We also provide a broad classification scheme for scheduling problems. Keywords: Scheduling; Survey 1. Introduction Scheduling is an important aspect of opera- tional level shop floor decisions. Its importance and relevance to industry has prompted re- searchers to study it from different perspectives over the past three decades. Scheduling literature ranges from deterministic case to the stochastic case, from single machine problem to the multi- ple machine problem and from static to dynamic problem. Research on multiple and bicriteria scheduling has been scarce, especially when com- pared to research in single criterion scheduling. Dileepan and Sen (1988) list only sixteen papers in their survey paper on bicriteria scheduling. A Correspondence to: Prof. S. Heragu, Department of Decision Sciences and Engineering Systems, Rensselaer Polytechnic Institute, Troy, NY 12180-3590, USA. similar study undertaken by Fry et al. (1989) for multi-objective single machine scheduling yielded thirty-two papers. The thrust of research on scheduling has been on a single criterion prob- lems; the complexity of scheduling problems pro- vides a possible explanation for the lack of pub- lished research in problems involving multiple criteria. It is well known that optimal solutions can be found for only relatively small single crite- rion problems. In fact, only two algorithms (poly- nomial or pseudo-polynomial) have been re- ported for the single machine bicriteria problem - the pseudo-polynomial algorithm was devel- oped by Van Wassenhove and Gelders (1980) and the polynomial algorithm was developed by Cheun and Bulfin (1990). Both of these algorithms gen- erate a set of efficient solutions for the bicriteria problem. Van Wassenhove and Gelders' ap- proach is shown to solve problems with up to 50 0377-2217/95/$09.50 © 1995 - Elsevier Science B.V. All rights reserved SSDI 0377-2217(93)E0140-S