多因素扰动情景下应急数量弹性契约的供应链协调

研究突发事件发生导致多种因素干扰的情景下，数量弹性契约是否能实现二级供应链协调，并寻找供应链协调时最优订货与定价策略。针对市场价格稳定和随机两种情况，设定契约弹性系数为常量，分别建立市场价格稳定不变与随机波动两种情况下的应急数量弹性契约模型，寻找它们实现协调的内在约束条件，并与基准模型下的结论进行比较。然后将契约弹性系数由常量拓展为变量，判断是否同时存在最优的弹性系数和订货量，分析弹性系数的变化对于生产、订货决策及供应链整体收益的影响。研究结果证明：当弹性系数为常量时，只要对基准契约的批发价进行适当调整，供应链就能协调应对两种情景下的突发事件，此时，可以找到唯一的最优订货决策。当弹性系数为变量时，两种情景下的供应链均不存在唯一的最优订货决策，但存在唯一的最优供货决策，并且契约弹性系数的改变不会影响供应链期望收益。最后通过算例验证了上述结论的正确性。

Supply Chain Coordination with Quantity Flexibility Contract under the Scene of Multi-factor Disturbance

In this paper,inherent laws of two level supply chains being coordinated to deal with emergencies under multi-factor disturbance are explored. With regard to two situations of the market's price,fixed and stochastic, the emergency quantity flexibility contract is used to find the optimal ordering and pricing strategy to realize the supply chain coordination. First, it is assumed that the elastic coefficients are constants and analyze the coordination problem under three scenes——when there is no emergency, there are emergencies making the price fluctuate and there are emergencies not making the price fluctuate;Second, the elastic coefficients are turned to variables to find the inherent constraints of achieving supply chain coordination; At last, examples are used to verify the emergency quantity flexibility contract with stochastic price above by simulation and analyze the influence of elastic coefficients' change on related elements of the supply chain. The results indicate that:(1) the basic laws of realizing supply chain coordination under quantity flexibility contract are the same whenever the market price is fixed or stochastic. If only the wholesale price is adjusted appropriately, the uncoordinated supply chain can restore coordination; (2) when the contract elastic coefficients α and β are fixed,there exists the exclusive ordering and pricing strategy;(3) If elastic coefficients change, the only ordering strategy of the supply chain doesn't exist, but the exclusive purchasing strategy can be obtained. The change of elastic coefficients at the time of centralized decision making exert no influence on the optimal purchasing quantity, supplying quantity, the retailer's expected gains, the expected gains of the whole supply chain, apart from the uplink elasticity coefficient α having effect on the retailer's optimal ordering quantity. Explanation of the example data:(1) table 1 indicates that whether the market price is fixed or stochastic as well as the demand expands or shrinks, when felicitous amendment is made to the wholesale price, the uncoordinated supply chain can restore coordination; (2) table 2-7 illustrates that when the market price is fixed, the change of upside elastic coefficients will only affect the optimal order quantity (q^*), having no effect on the retailer's expected purchases N(q)^*, the supplier's optimal supply,the retailer's expected profits and the proceeds of the whole supply chain regardless of the demand expanding or shrinking. Besides, the downside elastic coefficients' change exerts no influence on the five elements referred above, and the optimal supply of the supplier is greater than the retailer's expected purchasing quantities (i.e. Q^*>N(q)^*); (3)table 11-13 shows that the results obtained under stochastic price and shrunken demand is just the same as the results when the market price is fixed; (4) table 8-10 reveals elastic coefficients α and β will change when the market price is stochastic and the demand shrinks, and the results are consistent with previous three cases except the optimal supply being equal to the retailer's expected purchasing quantity (i.e. Q^*=N(q)^*). Theoretical results are verified by case data. Inspiration is provided for the research that adopts other contracts to respond to price-stochastic or price-fixed emergencies, and foundation is laid for the further use of quantity flexibility contract to study more sophisticated emergency supply chain coordination problems under the condition of asymmetric information, different risk preferences of the participants and so on.