基于数量柔性契约与Markov链的应急物资采购模型

突发灾害是以一定概率发生的随机事件,其状态总是不断发生转移,使政府已采购的应急物资在状态好转时易造成浪费,在状态持续恶化时难以满足突发需求,因此考虑突发灾害状态转移的应急物资采购策略对提升政府应急物资保障能力至关重要.本文将突发灾害状态转移过程视为一个有限次的齐次Markov链,构建了基于数量柔性契约的应急物资采购模型,分析了政企达成合作的条件与双方最优决策策略.采用数值计算与敏感性分析验证该模型的有效性,讨论了若干外生变量对政企最优决策策略与双方成本收益的影响,提出了重要的管理启示.结果表明,突发灾害状态转移情形下的应急物资采购模型既能提高政府应急物资保障能力,又可以保障企业合理收益与控制政府成本.

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.