Mathematical Formulation of the Permutation Flow-Shop Scheduling Problem Considering Transport Activity

In this paper, we extend the well-known Permutation Flow Shop Scheduling Problem (PFSP) by integrating a flood of identical Automated Guided Vehicles (AGVs) for the transport of semi-finished jobs between machines. The objective of this study is to mathematically formulate the problem of minimizing the maximum completion time. This parameter is known as the makespan. A Mixed Integer Linear Programming (MILP) model is therefore proposed to model formally the PFSP with AGVs. This model can be used to solve small instances. To validate the proposed mathematical model as well as for solving the large instances of the problem we have adapted the Artificial Bee Colony (ABC) metaheuristic.