基于局中人平方超量的区间数均分剩余值及其在冷链物流联盟合作收益分配中的应用

Interval-valued Equal Division Values Based on Players’Square Excess and Their Applications to the Cooperative Profit Allocation of Cold Chain Logistics Coalitions

在现实决策环境中,由于受外部环境、市场状况等不确定因素的影响,收益值无法准确预估,这种情况下用区间数可以很好地表示收益值的可能范围。首先,考虑合作收益分配的公平原则以及每个局中人都希望加入联盟后分配获得的合作收益尽可能多的心理预期,基于区间数的平方距离和最小二乘法,构建使最大合作联盟中所有局中人的区间数平方超量之和最小的二次规划模型,据此确定每个局中人的收益分配值。然后,考虑局中人的权重对收益分配策略的影响,构建相应的二次规划模型,并获得其最优解的解析式,即加权区间数均分剩余值。最后,以冷链物流企业联盟为例,将所提出的(加权)区间数均分剩余值应用于解决实际的合作收益分配策略问题。结果表明:解均满足存在性、唯一性、有效性、个体合理性、超可加性、对称性等合作博弈解的基本性质,据此获得的合作收益分配策略更加公平、合理。

In decision-making environment,due to the influence of external environment and market conditions,the profit can not be estimated accurately,in this case,interval number can well represent the possible range of return value.Firstly,considering the rationality of profit allocation,the residual vectors were obtained by the players participating in the alliance were equally distributed.Based on the square distance of interval values and the least square method,a quadratic programming model was constructed to minimize the sum of the square excess of interval values of all players in the maximum cooperative alliance,and the profit allocation value of each player was determined.Then,considering the influence of the player's weight on the profit allocation strategy,the corresponding quadratic programming model was constructed,and the analytical formula of the optimal solution was obtained,that is,the weighted interval number equally divided the residual value.Finally,taking the cold chain logistics enterprise alliance as an example,the proposed(weighted)interval number average residual value was applied to solve the actual cooperative income allocation strategy problem.The results show that the solutions meet the characteristics of cooperative game such as existence,uniqueness,effectiveness,individual rationality,super additivity,symmetry,etc.The profit allocation strategies are fair and reasonable.