Remote supply revisited: The jeep problem with costly transfer points

Abstract

When constructing a supply chain to supply a region where resources needed for logistics activities are locally unavailable, it is not obvious how many nodes should be used in the latter (“self-sustaining”) portion of the supply chain, nor how they should be positioned. This challenge arises frequently in multimodal supply chains, particularly for military operations, resource extraction, and humanitarian aid and disaster relief. It was analyzed in the mid-20th century via a classical model known as the jeep problem, and the solution involves nodes that are increasingly farther apart as they get closer to the destination. However, the solution to the jeep problem and its variants is not easily applicable to large-scale modern logistics problems. In particular, it does not work well when establishing and maintaining a node is costly and the quantity of resources to be delivered is large. In this paper, we present a modified version of the jeep problem that addresses those issues, and show that the optimal structure is equally spaced nodes over the self-sustaining portion of the supply chain. We argue that this should be used as a baseline approach for this type of supply chain. In addition, total cost is convex in the number of nodes, which ensures that finding a global optimum is tractable.