STUDIES IN MULTICRITERIA SCHEDULING PROBLEMS (SEQUENCING, MULTIOBJECTIVE, SINGLE MACHINE)

THURUTHICKARA CHANDY JOHN, Purdue University

Abstract

Scheduling problems traditionally have been studied as single-objective optimization problems. However, in almost all real world applications, an acceptable schedule is a compromise between a number of conflicting objectives. Surveys conducted in industries reveal that any practical solution to a scheduling problem should include a tardiness measure and a flowtime measure. The research reported here is a step toward enriching scheduling models with conflicting objectives. In solving the general, multi-objective problem, one seeks to obtain the preferred solution for a decision maker from the set of all nondominated solutions. In this research efficient algorithms have been developed for a number of single stage scheduling problems with two objectives. The following two problems are extensively studied and elegant solution methods have been developed; I. Scheduling for (i) minimizing the maximum penalty cost and (ii) minimizing the mean flowtime. II. Scheduling for (i) minimizing the number of tardy jobs and (ii) minimizing the total work content in the tardy jobs. The emphasis of research is on developing algorithms that run in polynomial or pseudopolynomial time per solution in the nondominated set. The number of nondominated solutions for a problem could be quite large, not polynomially bounded, in which case no efficient algorithm is possible to generate all of them. The above characteristic should be considered as an inherent difficulty in the problem. Such problems could be solved in an interactive mode or with a priori bounds on the objectives for exploring specific regions of the efficient frontier. A number of related problems are shown to be solvable by simple extensions to the results from this research. These include (1) the single resource scheduling to minimize the total tardiness and total flowtime with a minimum number of tardy jobs, (2) the parallel two-processor scheduling to minimize makespan with minimum mean flowtime, and (3) the single stage scheduling to minimize the weighted number of tardy jobs. Problems have been studied under (1) the hierarchical criteria formulation and (2) the general independent criteria formulation. Illustrative examples are provided for the main algorithms and algorithmic complexity is analysed.

Degree

Ph.D.

Subject Area

Operations research

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