Government's relief supplies procurement model based on quantity flexible contract and Markov chain

The sudden disaster can be regarded as a random event, occurring with a certain probability. Since the state of the sudden disaster is always shifting, the purchased relief supplies will result in waste if the disaster state gets better. The government can't meet the demand for relief supplies if the disaster state continues to deteriorate. Therefore, it is of great important to take the state transition of sudden disasters into the government's procurement strategy for relief supplies. This paper regarded the disaster state transition as a limited homogeneous Markov chain. The procurement model of government's relief supplies was established based on quantity flexible contract. We uncovered the condition that the government and the supplier reached cooperation. The optimal decisions of the government's procurement and the supplier's reserves quantity were also derived. Furthermore, numerical calculation and sensitivity analysis were used to analyze the influence of several exogenous variables on the decision strategies of the government and the supplier and their cost-profit, providing a new perspective for government's relief supplies purchasing decisions. It showed that the proposed model not only improve the level of the total quantity of relief supplies reserves, but also safeguard supplier's profit and control government's cost.