RENTAL COST REDUCTION IN TWO-STAGE HYBRID FSSP USING BB: A MATLAB-BASED COMPARISON WITH GA

The paper addresses the classical two-stage FSSP with a single machine in the second stage and equipotential machines in the first. The uniqueness of this problem arises from the fact that the machine at the second stage is rented, with the objective being to minimize the rental cost. Efficient scheduling of jobs is critical in such environments to optimize resource usage and reduce operational costs. A distinguishing feature of this study is the representation of processing times on both stages using trapezoidal fuzzy numbers, which better capture uncertainty and variability in processing times compared to deterministic values. This fuzzy representation aligns well with real-world scenarios where exact processing times are often unavailable or subject to fluctuations. This paper's primary contribution is the creation of an optimization algorithm that uses the branch and bound (B&B) approach to tackle the issue. By breaking the problem space down into smaller subproblems and utilizing bounds to exclude less likely solutions, the B&B technique methodically explores the solution space. This method minimizes the expense of renting the second-stage machine while guaranteeing the identification of the ideal timetable. The fuzzy nature of the problem adds complexity to the scheduling task, as it requires handling the fuzziness in processing times while maintaining optimality. To ensure the robustness of the algorithm, it is implemented in MATLAB and tested against a variety of job sequences and machine configurations, along with the comparison of results with GA.