Empty container management in a port with long-run average criterion

The empty container allocation problem in a port is related to one of the major logistics issues faced by distribution and transportation companies: the management of importing empty containers in anticipation of future shortage of empty containers or exporting empty containers in response to reduce the redundance of empty containers in this port. We considered the problem to be a nonstandard inventory problem with positive and negative demands at the same time under a general holding-penalty cost function and one-time period delay availability for full containers just arriving at the port. The main result is that there exists an optimal pair of critical policies for the discounted infinite-horizon problem via a finite-horizon problem, say (U, D). That is, importing empty containers up to U when the number of empty containers in the port is less than U, or exporting the empty containers down to D when the number of empty containers is more than D, doing nothing otherwise. Moreover, we obtain the similar result over the average infinite horizon.