Integrated hybrid flow shop scheduling and vehicle routing problem

In this paper, a new integrated mathematical model for production and distribution planning is presented to minimize tardiness and transportation costs. A mixed-integer linear programming (MILP) formulation is developed for the problem which consists of two parts. First, the production scheduling in a hybrid flow shop (HFS) environment with identical machines in each stage, and then, the delivery of completed jobs with a fleet of vehicles that have the same capacity. Due to the NP-hard nature of the problem, a new metaheuristic approach based on Particle Swarm Optimization Algorithm (PSO) and Genetic Algorithm (GA) is presented to solve the integrated problem. GA’s operators are used to update the particle position of the PSO algorithm. The algorithm uses dispatching rules to represent the initial solution and searches in the solution space including active schedules. To investigate the efficiency and effectiveness of the proposed method, numerical studies are carried out with random problems. The computational results show that the proposed solution approach yields fairly good results in comparison with the PSO versions in the subject literature. The algorithm is capable of generating relatively good solutions for sample cases.