Inventory-Routing Problem in Sea Freight: Direct versus Transshipment Model

In this paper, we present a problem in international shipping which combines the ship routing problem with inventory considerations. A fleet of ships is responsible for the transportation of a given commodity between a supply port and the demand ports. Their routes should be selected so that the total transportation cost and the inventory cost is minimized. Although a generic mixedinteger programming model can be used to model the problem, the complexity and size of the model preclude it from practical use as it is impossible to solve the large scale MIP problem in reasonable time. Moreover, the optimal solutions obtained from the MIP model are usually complicated and sensitive to data, i.e., nervous to the input of the model. Therefore, we turn to heuristics for good practical solutions. We consider two routing strategies often used in the shipping industry the multiple ports of call (direct) and the hub-and-spoke (transshipment) system. We show that our problem for the multiple ports of call system can be viewed as a combination of the traveling salesman problem and the traveling repairman problem, and can be readily solved by extension of classical local search heuristic. For the hub-and-spoke system, we used insights from classical one-warehouse multi-retailer system to model the inventory cost in the system. We compare the performance of the two systems using sample ports in the Asia Pacific region.