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

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.