Integration of Two-Stage Assembly Flow Shop Scheduling and Vehicle Routing Using Improved Whale Optimization Algorithm

This paper provides an integrated model for a two-stage assembly flow shop scheduling problem and distribution through vehicle routing in a soft time window. So, a Mixed-Integer Linear Programming (MILP) model has been proposed with the objective of minimizing the total cost of distribution, holding of products, and penalties of violating delivery time windows. To solve this problem, an improved meta-heuristic algorithm based on Whale Optimization Algorithm (WOA) has been developed. The main innovations in the study include considering soft time window, sequence-dependent setup time, delivery time window, heterogeneous vehicles, holding costs of final products, and unrelated assembly machines. A comparison of the integrated and non-integrated model in a case study of industrial gearboxes production shows that the integrated model compared to the non-integrated model has saved 15.6% and 13.6% in terms of delay time and total costs, respectively. Computational experiments also indicate the efficiency of improved WOA in converging to optimal solution and achieve better solution in comparison to the Genetic Algorithm (GA). The results show that increasing the setup time can lead to an increase in total costs. It can be said that the increase of setup time increases the completion of time jobs. Also, the costs increased with decreasing the transport fleet capacity to -20%. The reason for this is that by reducing the capacity of vehicles, the model has to use more vehicles.