Mathematical models for planning in military and humanitarian logistics

Military and humanitarian logistics present unique challenges that distinguish them from logistical problems in the private sector. While logistical challenges in the private sector often focus on cost-minimisation or profit-maximisation, military and humanitarian logistics focus on the efficient and effective use of scarce resources, often in unpredictable and challenging environments. The problems often involve unique constraints that are not present in other domains, such as the need for coordination and equity. Consequently, military and humanitarian logistics problems differ significantly from those in the private sector, requiring tailored solution approaches.

In this thesis, we consider various military and humanitarian optimisation problems. In Chapter 2 and 3, we consider the Ship-to-Shore Problem, in which resources have to be transported from the ship to the shore using smaller ships and helicopters, called connectors, such that the duration of the transportation of these resources is minimised. A feasible schedule for the Ship-to-Shore Problem has to adhere to various constraints that require coordination between the pick-up and delivery of the resources by the connectors. In Chapter 4, we consider the Generalised Capacitated Resupply Problem. In this problem, locations with a given periodic demand, capacity, and resupply time have to be resupplied by vehicles from a central depot. The aim is to determine the minimum number of required vehicles to ensure none of the locations runs out of stock. We present simple policies with a corresponding approximation guarantee. In Chapter 5, we analyse the value of mobile laboratories for the surveillance of infectious diseases in low- and middle-income countries compared to investments in local health facilities. We consider a budget allocation problem where a limited budget must be allocated to different regions, either for investments in local health facilities or for deploying mobile laboratories. We also discuss potential equity concerns.