Multi-trip heterogeneous vehicle routing problem coordinated with production scheduling: Memetic algorithm and simulated annealing approaches

•A new variant of the integrated production and distribution scheduling problem is studied.•A new mathematical formulation is presented to model the problem under study.•A memetic algorithm with new decoding strategy is developed.•A simulated annealing approach with five neighborhood strategies is provided. This paper studies a joint production scheduling and outbound distribution planning problem in which orders are processed by several machines in series with the same sequence known as permutation flow shop and are then distributed to destined customers in a batch by multiple heterogeneous capacitated vehicles, all of which are allowed to take multiple trips. When order is placed by a customer due date is prescribed as well. Due to the limited number of vehicles, orders need to be combined in a trip to decrease the total travelling time needed by the vehicles but in which case some of the customer orders can be tardy resulting from late deliveries. The objective of the problem is therefore to determine the minimum total tour time traversed by the vehicles and tardiness that might result from late deliveries. We present a mixed integer programming (MIP) formulation. But, due to intractability matters, optimal solution of the MIP formulation can only be obtained for small sized instances. Therefore, we also propose a Memetic Algorithm (MA) with the use of a new splitting procedure based on Prins’ algorithm for considering both total tardiness and total tour time and Simulated Annealing (SA) in order to offer favorable solutions in a reasonable time. Computational experiments are performed to assess the effectiveness of the proposed algorithms on a large number of test instances, which are randomly generated. Computational results indicate that both MA and SA can find optimal solutions for small sized instances in quite short time while MA outperforms SA in terms of solution quality for medium and big sized instances.