On integer linear programming formulations of a patrol boat scheduling problem with complete coverage requirements

Abstract

The Patrol Boat Scheduling Problem with Complete Coverage (PBSPCC) is concerned with finding a minimum size patrol boat fleet to provide continuous coverage at a set of maritime patrol regions, ensuring that there is at least one vessel on station in each patrol region at any given time. This requirement is complicated by the necessity for patrol vessels to be replenished on a regular basis in order to carry out patrol operations indefinitely. In this paper, we establish a number of important theoretical results for the PBSPCC. In particular, we establish a set of conditions under which an alternative objective function (minimize the total time not spent on patrol) can be used to derive a minimum size fleet. Preliminary results suggest that the new theoretical insights can be used as part of an acceleration strategy to improve the column generation runtime performance.