Quay partitioning problem

Abstract

In this paper, we introduce the quay partitioning problem (QPP), that is, a problem of partitioning quay length into berths for minimum ship waiting time. Such a problem arises when designing the terminal layout. Two schemes of quay layout are considered: with at most one ship in a berth and with at most two ships in a berth. Ship arrival times, service times, lengths, and weights are given. We show that QPP is NP-hard. The two versions of QPP are formulated as mixed integer linear programs (MIPs). Scalability of solving QPPs as MIPs is studied. We investigate, analytically and in computational experiments, features of the QPP solutions such as (i) changes in solution quality when one long berth length is used versus choosing various berth lengths flexibly, (ii) what lengths of berths are chosen when ship lengths mixture is changing, (iii) what is the impact of congestion on the chosen berth lengths, and (iv) how much is one quay layout scheme better than the other.