Flow Shop Scheduling for BRC Ltd

Abstract

This MSc project considers a multistage flexible flow shop scheduling problem with parallel unrelated machines at each stage. An extensive literature review is given followed by the presentation of a flow shop model. Moreover the model takes into consideration machine dependent setup times and different processing speeds for every machine in each stage. The study is motivated by the necessity for job allocation within the production line for coils and bars on behalf of BRC Ltd, who is among the major steel reinforcement manufacturer in UK. We develop an integer program that minimizes the convex sum of makespan and the lateness of tardy jobs over a finite time horizon. Our model is applicable to a part of the factory and specifically for bay 3. The corresponding optimization problem is quite challenging to be solved optimally even for small instances. We report the mathematical and implementation challenges and how we tackle them. Also we suggest some extensions by adding some extra parameters making the model ready to be compatible with real data. Last but not least, we generate and analyze some preliminary computational results based on a beta version code developed in Python using the Pyomo library.