Modelling and solving an m‐location, n‐courier, priority‐based planning problem on a network

In this paper, we study an m‐location, n‐courier, priority‐based planning problem on a network, which we refer to as the Courier Planning Problem (CPP). The CPP arises on a daily basis in the context of planning the transportation of materials and personnel in peacetime for the Turkish Armed Forces. The main issue addressed in CPP is to transport as many of deliverables as possible from their origins to their destinations via a fleet of transportation assets (couriers) that operate at fixed routes and schedules. Priorities must be taken into account and constraints on the routes, operating schedules, and capacities of the transportation assets must be obeyed. Time windows may be specified for some or all transportation requests and must be satisfied. We study the CPP as well as its two extensions, and present integer programming formulations based on the multi‐commodity flow structure. The formulations are tested on real world‐based data and display satisfactory computational performance. Our main contributions are to develop an effective formulation scheme for a complicated large‐scale real world problem and to demonstrate that such problems are solvable via commercial general purpose solvers through meticulous modelling.