Hospital stockpiling for influenza pandemics with pre-determined response levels

This paper explores the problem of hospital stock-piling of critical medical supplies in preparation for a possible influenza pandemic.We consider a regional network of hospitals that have mutual aid agreements in place such that they may borrow or lend supplies from each other during medical emergencies. We assume that the attack rate is a random variable with known distribution and that the demand surge due to the pandemic is a function of the attack rate, and is thus stochastic. We further assume that each hospital in the network pre-determines its targeted pandemic response level, and that any demand beyond this pre-determined level is reallocated to other hospitals. Each hospital in the network must decide the stockpile level that minimizes its expected overall cost, including purchasing cost, holding cost, cost (revenue) for borrowing (lending), penalty for setting a too low targeted level, and shortage penalty. To capture the mutual aid relationships of hospitals in the network, we formulate the problem as a game theoretic model. We show that the response sets are nested and we provide an algorithm to obtain numerically the Nash Equilibrium solution of this game. We illustrate the structure of the model on a two-hospital example and perform sensitivity analysis with respect to parameters of our model.