Job Shop Scheduling and Its Fuzzification Based on Operations and Disjunctive Graph Representations

In this paper, several approaches to job shop scheduling problem are presented. A mixed integer programming model is derived and, based on this result, it is implemented in the GAMS optimisation software tool. Since the problem is NP-hard, this approach may not be used for large instances, its reasonable bounds are indicated using benchmarks from OR-Library. Here, strategies based on operations and disjunctive graph representations are applied and their time complexities are derived. These representations are also used to heuristically generate feasible solutions from their searching space. Finally, a modification is described of the problem using uncertain processing times of jobs based on fuzzy numbers. Methods for comparing fuzzy numbers are then discussed.