A Heuristic Method to Minimize Total Weighted Number of Tardy Jobs and Transportation Costs for an Integrated Production and Distribution Problem with VRP

In this paper an integrated production and outbound distribution scheduling (IPODS) with vehicle routing problem (VRP) for multi customer situation in a supply chain is addressed. There are K orders (jobs) that have to be scheduled on a single machine and delivered to K customers. Each order has its own due date. The manufacturer delivers the orders in batches which have no capacity constraint. Delivering the products in batches reduces the delivery cost but it may increase the number of tardy jobs. No other research has been conducted on this problem yet. This problem is strongly NP-Hard. The objective is to minimize the sum of the total weighted number of tardy jobs and delivery costs. Also, in this paper, an MILP model and a Heuristic Algorithm (HA) for solving this problem are presented. Full factorial Computational test is performed for evaluation of these two methods. The obtained results on 3840 problems show that the heuristic algorithm is efficient for solved problem. Also we surveyed parameter's levels effect on CPLEX and heuristic performance by analysis of variance.