A MATHEMATICAL MODEL AND A FIRST-FIT ALGORITHM FOR THE MILK RUN LOGISTICS PROBLEM IN THE AUTOMOTIVE INDUSTRY CONSIDERING PACKAGING CONSTRAINTS

Transportation cost accounts for a large portion of costs in automotive supply chain. An effective approach that can reduce the cost of transportation is essential. The supply network of automotive industry is very complex and has many conditions to consider. These include enforcing the feasibility of 3D packing of pallets into vehicles to address vehicle's capacity in terms of weight and volume, compatibility of orders to be loaded in a vehicle, returning empty pallets from assembly plants backwards to suppliers, and order delivery time window. A mixed integer linear programming (MILP) approach is proposed in this paper that takes account of these conditions with the objective of minimizing the total cost of transportation across the network. The structure of the network is a combination of direct shipment and milk-run for both forward and reverse flows of pallets. Any order that is larger than the capacity of the largest vehicle is split and shipped directly, and the remaining pallets can be consolidated in milk-run. For large-size problems where a solution cannot be obtained in a reasonable amount of time, a heuristic algorithm is proposed based on the concept of similarity to generate a reasonable list of orders. First-fit strategy is then employed to generate a feasible solution with the aid of a relaxed version of the proposed MILP. Thereafter, two improvement ``reduce'' and ``merge'' heuristics are employed. The effectiveness of the proposed heuristic is tested based on generated instances which demonstrates that it is able to provide optimal solutions for small-size problems. The proposed approach is also tested based on the data of daily auto-parts shipments gathered from SAIPA Corp network that is one of the largest Iranian automobile companies. Results demonstrate that there exists a significant potential for cost saving through milk-run strategy compared with the company's current direct shipping strategy.