基于两个不确定参数乘积的鲁棒设施选址模型

传统设施选址往往被看作为确定问题,但实际存在需求、成本、风险等不确定因素,这些不确定因素增加了决策的困难.本文在考虑设施选址中单一不确定因素基础上,同时考虑需求和运输成本两个独立参数的不确定性,且在模型中两者为乘积形式,引入两个budget不确定集合刻画不确定性,建立一个新颖的鲁棒设施选址模型,并将非线性问题转化为易求解的鲁棒等价模型,然后通过CPLEX和MATLAB编程求解.最后,以四川西北部的汶川等13个县市的应急物资临时供应点的选址为例,确定最优的选址分配布局.结果表明,较之运输成本的不确定性,需求的不确定性影响更显著,且需求扰动对选址总成本和选址分配方案有明显的影响.决策者可根据其风险偏好程度,选择恰当的不确定水平参数组合,以获得最优的总成本和选址分配方案.

Robust facility location model with two multiplicative uncertainties

Traditional facility location is usually viewed as a deterministic problem. But there exist many uncertain factors (i.e. demand, cost, risk) in a varying environment, which increase difficulties in facility location. Based on considering single uncertainty respectively, we integrate two independent multiplicative uncertainties (demand and transportation cost) together, introduce two budget uncertainty parameters, formulate a novel and intractable nonlinear robust facility location model, and then converse this nonlinear problem into a robust mixed integer linear counterpart. We also use CPLEX and MATLAB for programming to solve this problem. Finally, we choose 13 cities to decide the location-allocation solutions for temporary emergency supplies in Northwest Sichuan. Numerical results show that, compared with transportation cost uncertainty, demand uncertainty has a strong impact on the total cost. Demand disturbance also affects the total cost and location-allocation solution significantly. According to their risk preferences, decision-makers choose the optimal combination of budget uncertainty and demand disturbance proportion, so as to minimize the total cost and get optimal location-allocation solution.