Allocation of empty containers between multi-ports

Owing to imbalances in international trade activities, shipping companies accumulate a large number of unnecessary empty containers in the import-dominant ports, whilst request a large number of empty containers in export-dominant ports. The logistics challenge to shipping companies is to better manage and control their containers, which consist of company-owned containers and leased containers. The multi-port empty container allocation problem is concerned with the allocation of empty containers from supply ports to demand ports. In this paper, optimal pairs of critical policies, (U, D) for one port, which are importing empty containers up to U when the number of empty containers in the port is less than U, or exporting empty containers down to D when the number of empty containers is larger than D, doing nothing otherwise, are adapted to multi-port case so that decision-makers can make decisions about allocating the right amounts of empty containers to the right ports at the right time. This allocation problem has been formulated and the heuristic methods are designed according to that the average cost using (u, d) policy at one port is convex in u and d. Furthermore, the examples show that, using the heuristic algorithm, the result in the inland line case is quite close to the lower bound, even the distance is not so close in the global line case.