Flow shop scheduling to minimize total flow time: a case study of t-shirt production

This project addresses the Flow Shop Scheduling Problem with the objective of minimizing total flow time in a multi-stage garment production system. A Mixed Integer Linear Programming (MILP) formulation was developed to capture machine processing times, precedence relationships, and sequencing constraints. The model was implemented and solved using Microsoft Excel with OpenSolver. Instead of focusing on fixed instances or expanding production stages, the study applies a single MILP model to three distinct problem sets, each representing different job configurations within the same manufacturing framework. These variations simulate realistic production diversity—such as differences in garment sizes—without altering the station structure. For each problem set, OpenSolver is used to determine the optimal job sequence, evaluate total flow time, and assess solver performance in terms of solution time and scalability. Gantt charts are employed to visualize representative schedules and support interpretation of the results. The findings indicate that the MILP formulation combined with OpenSolver can effectively minimize total flow time while remaining adaptable to varied job characteristics. This approach demonstrates the practical applicability of mathematical programming to garment production scheduling and highlights the computational boundaries of using OpenSolver for increasingly complex job configurations.