230 Journal of the Chinese Institute of Industrial Engineers, Vol. 21, No. 3, pp. 230-241 (2004) A SURVEY OF ALGORITHMS FOR SINGLE AND MULTI-OBJECTIVE UNRELATED PARALLEL-MACHINE DETERMINISTIC SCHEDULING PROBLEMS Michele Pfund Department of Industrial Engineering John W. Fowler * Department of Industrial Engineering Arizona State University, PO Box 875906, Tempe, AZ 85287-5906, USA Jatinder N. D. Gupta Department of Accounting and Information System The University of Alabama in Huntsville ABSTRACT This paper surveys the literature related to solving traditional unrelated parallel-machine scheduling problems. It compiles algorithms for the makespan, total weighted sum of completion times, maximum tardiness, total tardiness, total earliness and tardiness, and multiple criteria performance measures. The review of the existing algorithms is restricted to the deterministic problems without setups, preemptions, or side conditions on the problem. Even for such traditional problems, this survey reveals that while makespan minimization has been fairly widely studied, problems that include processing characteristics such as release times, sequence dependent setups, and preemptions remain largely unstudied. Research in solving unrelated parallel-machine scheduling problems involving the minimization of the number of tardy jobs, weighted number of tardy jobs, total tardiness, and total weighted tardiness is quite limited. Keywords: scheduling; parallel machines; multi-objective scheduling * Corresponding author: John.Fowler@asu.edu 1. INTRODUCTION Within many manufacturing environments, there are often groups of similar workstations that have a wide variety of similar equipment with differing performance characteristics because they have been either purchased for slightly differing products or at differing technology levels. Consequently, there are often banks of parallel-machines that may or may not be identical to each other. When machines are not identical to one another and cannot be completely correlated by simple rate adjustments, they are said to be unrelated parallel-machines [33]. Often, the machines can be so unrelated as that certain jobs can only be processed on a small subset of machines. This environment can also be classified as an unrelated parallel-machine environment with class scheduling [21]. This type of situation commonly occurs in the drilling operations of PWB Manufacturing [44] machine shops [40], and many other operating centers. While uniform parallel-machine scheduling problems have been well studied ([33] and [9]), many of them are NP-hard [20]. Using the complexity hierarchy of deterministic scheduling, unrelated parallel-machines are some of the most difficult problems to solve. This paper outlines many of the recent advances in unrelated parallel-machine scheduling for deterministic single objective and deterministic multi-objective environments. In addition, it concludes with a brief discussion of directions for future research. 2. BACKGROUND & NOTATION An unrelated parallel-machine environment occurs when the processing time for job j on machine i is not solely dependent on the machine speed for i. Thus, the ratio of processing times for jobs across different machines is not a constant (i.e. the times are