需求不确定的服务设施网络设计模型鲁棒性研究

由于选址决策的长期性,参数面临随机波动,在选址问题中考虑不确定因素至关重要。在选址模型中提出一种新的鲁棒方法,采用有界对称的“盒子”作为不确定需求的集合,通过调节不确定预算,来权衡解的鲁棒性与系统成本之间的关系。利用该方法得到的鲁棒模型不仅能够转化成线性规划,并且可以计算出设施的最低服务水平。然后,设计禁忌搜索算法来求解该问题,数值算例的结果表明了算法的有效性。最后,分析了不同鲁棒水平下,服务设施网络不同的拓扑结构,并得到服务水平与成本之间的权衡关系。同时对需求扰动作了敏感性分析,结果表明随着服务水平的提高,成本对需求扰动越来越敏感。

Robust Research on Service Facility Network Design Problem with Demand Uncertainty

Based on long-term facility location decisions and potential parameter variations, it is important to consider uncertainty in facility location modeling. Supposing the uncertain demands are within a bounded and symmetric multi-dimensional box,we present a novel robust approach to the service facility network design problem. The trade-offs between the robustness of the solution and the cost can be done by adjusting the budget of uncertainty. The model can be transformed into a linear programming and the service level of the facility can also be computed. An algorithm based on Tabu Search is designed to solve the problem. Numerical examples validate the effectiveness of the algorithm. Finally, we use a numerical example to illustrate the different network topology under different robustness level, and the trade-offs between the service level and the cost is analyzed. In addition, we make a sensitivity analysis of the deviation of the demand. The results show that with the improvement of the service level, the cost gets more and more sensitive to deviation.