Optimal Procurement Strategies for Retailers Under Concurrent Supply Disruption and Uncertain Emergency Demand: A Chance-Theoretic Approach

Reliable emergency supply systems are particularly vulnerable when a supply interruption coincides with a surge in demand. This study examines a single-period procurement problem involving a lower-cost primary supplier that may be completely disrupted and a more reliable but higher-priced backup supplier. A joint emergency event simultaneously disrupts the primary supplier and generates additional emergency demand. Routine demand is represented by a random variable, whereas additional emergency demand is modeled as a nonnegative uncertain variable. Chance theory combines these two types of demand information and provides a unified basis for evaluating expected profit. The retailer chooses among primary supplier single sourcing, backup supplier single sourcing, and dual sourcing. The analysis derives the expected profit functions, optimal order quantities, and conditional switching thresholds for the three sourcing modes. Under the analytical conditions of the benchmark model—complete primary-supplier disruption, unconstrained backup capacity, and an interior dual-sourcing solution—dual sourcing reallocates a fixed optimal total order between the two suppliers rather than changing the total quantity. Subject to the derived threshold conditions, an increase in the probability of the joint emergency event may shift the preferred mode from primary supplier single sourcing to dual sourcing and eventually to backup supplier single sourcing. Numerical comparisons using zero-truncated normal and zigzag uncertainty distributions preserve this qualitative sourcing sequence under the tested parameter settings, although the resulting profits, order allocations, and switching thresholds remain distribution-dependent. The extensions show that partial primary-supplier fulfillment may change the optimal total order, whereas a binding backup-capacity constraint limits the feasible allocation to the backup supplier. These findings provide conditional implications for sourcing-mode selection and backup-capacity planning during the initial emergency response period.