Community-Based Emergency Supply Allocation Under Delayed External Relief: Balancing Cost, Deprivation, Equity, and Emissions

Abstract

Abstract

When external relief is delayed, communities must meet local needs and share limited stocks before outside supplies arrive. This study addresses the Community-Based Emergency Supply Allocation Problem under Delayed External Relief (CBESA-DER). We develop a deterministic, multi-period, multi-commodity mixed-integer linear program linking community sharing and external replenishment through inventory and backlog balances under accessibility and capacity constraints. The model balances logistics cost, a vulnerability-weighted backlog penalty, minimum-service equity, and transport emissions. Constructed scenarios based on 88 Houston Super Neighborhoods and an 84-community Nepal benchmark illustrate these trade-offs. Gurobi reaches the target 1% optimality tolerance for Houston; Nepal retains a 4.406% gap. Preference experiments show that prioritizing cost or emissions can reduce service, while backlog reduction and minimum-service equity can favor different allocations. Longer isolation reduces service with fixed initial stocks under the assumed supply schedule. A separate stock-sizing model imposes an illustrative 80% cumulative criticality-weighted service target in every community during every isolation period. In the three-period Nepal scenario, a feasible plan meets this target with approximately 59.6% more initial stock than the baseline under proportional stocking and expanded storage. These models support joint assessment of community sharing, replenishment timing, and preparedness stocks.