A transshipment model for distribution and inventory relocation under uncertainty in humanitarian operations

Abstract

The number of disasters and humanitarian crises which trigger humanitarian operations is ever-expanding. Unforeseen incidents frequently occur in the aftermath of a disaster, when humanitarian organizations are already in action. These incidents can lead to sudden changes in demand. As fast delivery of relief items to the affected regions is crucial, the obvious reaction would be to deliver them from neighbouring regions. Yet, this may incur future shortages in those regions as well. Hence, an integrated relocation and distribution planning approach is required, considering current demand and possible future developments. For this situation, a mixed-integer programming model is developed containing two objectives: minimization of unsatisfied demand and minimization of operational costs. The model is solved by a rolling horizon solution method. To model uncertainty, demand is split into certain demand which is known, and uncertain demand which occurs with a specific probability. Periodically increasing penalty costs are introduced for the unsatisfied certain and uncertain demand. A sensitivity analysis of the penalty costs for unsatisfied uncertain demand is accomplished to study the trade-off between demand satisfaction and logistical costs. The results for an example case show that unsatisfied demand can be significantly reduced, while operational costs increase only slightly.