Multi-Treatment Inventory Allocation in Humanitarian Health Settings under Funding Constraints

In humanitarian operations, the amount of funding received and the timing and predictability of funding strongly influence program performance. In this paper, we study the problem of allocating inventory procured using donor funding to patients in different health states over a finite horizon with the objective of minimizing the number of disease-adjusted life periods lost. The funding received and the number of new patients of different health states entering the program in every period could be unpredictable and hence, resource allocation and rationing assume significance in this setting. We use a stochastic dynamic programming model with financial constraints to analyze the inventory allocation problem. We demonstrate that the optimal allocation policy is state dependent, provide analytical results regarding the impact of funding timing and funding variability in our problem context, and develop two heuristics for the inventory allocation problem. Our computational study indicates that the two heuristics perform reasonably well against the full information lower bound (roughly 5% gap on average) and in many instances, they offer significant benefits over the first-come-first-serve heuristic frequently used in practice. We also provide computational insights regarding the impact of funding timing and funding level on program performance. Our analysis indicates that for short planning horizons (up to 4 periods), receiving additional funding is beneficial even if the funding is delayed while for medium to long planning horizons, there exist situations where receiving less overall funding in a timely manner might be better than receiving more total funding in a delayed fashion.