| Over the last forty years, scheduling of production systems has been studied extensively with considerable amount of fruitful results emerged in the field of Deterministic Scheduling. The basic assumption of deterministic scheduling is that the parameters of problems are fixed and crisp numbers, whose values should be known exactly. However, production environments are subject to many sources of uncertainty and thus the assumption of having only deterministic parameters could not be applied. The uncertainty could be due to randomness or imprecision (or vagueness), which should be more appropriately represented as random or fuzzy variables, respectively.; Application of probabilistic models in modelling the randomness of parameters has flourished the development of Stochastic Scheduling since 1970s. Satisfactory and interesting results have been obtained in stochastic scheduling. Recently, we have witnessed the growth of a new branch of scheduling, Fuzzy Scheduling, in which the parameters of scheduling problems are fuzzy numbers. Although the number of publications in this area is increasing dramatically, many of them only consider new problems where the criteria being optimized are new. Few papers have investigated the classical scheduling problems with fuzzy parameters. How to model and solve these problems in fuzzy environments is a new area of interest.; This thesis introduces a general framework for studying the classical scheduling problems in fuzzy environments. We propose a fuzzy tardy function, a fuzzy distance function, and a fuzzy ranking function, which are fundamental to the extension of the deterministic scheduling models to fuzzy environments. The fuzzy tardy function is derived from the well-known extension principle. It can be used to evaluate the degree of timeliness of the job completion against its fuzzy due date. The fuzzy distance function is for approximating the expected fuzzy distance between two fuzzy numbers. It can be used to measure the deviations of job completions from the fuzzy due date. The fuzzy ranking function compares and orders fuzzy numbers by their expected values. It can be used to formulate any scheduling problems with fuzzy parameters.; We have successfully applied the functions to model and solve classical single machine scheduling problems with fuzzy parameters and the following objective functions: (1) the number of tardy jobs with fuzzy due dates, (2) the weighted earliness and tardiness with a common fuzzy due date or job dependent fuzzy due dates, (3) the maximum lateness with fuzzy due dates and non-decreasing lateness functions, (4) the maximum tardiness with fuzzy due dates, (5) the total tardiness with fuzzy due dates, and (6) the weighted completion time with fuzzy processing times and fuzzy weights.; Efficient algorithms are proposed for the problems and evaluated by using the technique of Fuzzy Numerical Simulation. We have compared the schedules obtained by the algorithms with the alternatives generated by approximating the fuzzy parameters by crisp numbers, which can then be solved as deterministic scheduling problems. The results clearly indicate that a better solution can be obtained by considering the parameters as fuzzy numbers and taking their fuzzy characteristics into account in the scheduling process. |
