Pickup and delivery of automobiles from warehouses to dealers

This paper considers a truck loading and routing problem in automobile outbound logistics. Everyday, a third-party logistics (3PL) company receives a number of orders from several auto manufacturers and needs to assign the orders to available trucks which pick up the orders from the warehouses where the orders are kept and deliver them to dealers. Each order corresponds to a specific car required by a given dealer and is associated with a value and one of the three car types, small, medium or large. The value of an order is defined by whether it is an emergency order and how many days it has been waiting to be assigned to a truck. Each delivery truck is allowed to visit a pre-specified subset of cities, and is associated with a specific capacity configuration, which specifies the number of slots available for each of the three car types. The problem is to assign a subset of the orders to available trucks and create a route for each truck to maximize the total reward of the assigned orders, defined as a given weight times the total value of the assigned orders minus the total transportation cost incurred, subject to a number of constraints. A column generation based heuristic algorithm is developed where the LP relaxation of the problem is decomposed into a master problem solved by a LP solver and a number of subproblems solved by a dynamic programming based algorithm. The proposed algorithm is evaluated by comparing its solutions to upper bounds and shown to be capable of generating near-optimal solutions for practically sized problems in reasonable computational time. The algorithm is also compared to a rule-based greedy method used in practice based on real data sets from a 3PL company and shown to outperform the greedy method by a large margin.