不确定连续设施选址新鲁棒方法研究

设施选址是运筹学研究热点之一。由于实际选址中很多因素具有不确定性，研究不确定选址问题就变得尤为重要。当随机因素的概率分布信息未知时，已有的研究工作主要集中于鲁棒选址：最小化选址系统在最坏情形下的费用或缺憾函数。最坏情形也许是小概率事件，这导致传统鲁棒选址方法可能过于保守。与传统方法不同，本项目拟对不确定连续设施选址提出两种新鲁棒方法：分布鲁棒选址方法和基于随机变分不等式的鲁棒选址方法。前者将根据历史或经验数据确定随机因素的矩约束，并在满足矩约束的概率分布集上进行鲁棒选址；后者将对等价的随机变分不等式构造合适的残量函数，并通过优化残量函数进行鲁棒选址。根据并融合两种新方法，项目拟构建三种鲁棒选址模型并对其进行理论分析、算法设计与应用研究。由于考虑随机因素的所有情形以及不同情形下系统表现的差异性，新方法将比仅关注最坏情形的传统方法更具实用性，并为不确定连续设施选址研究提供重要的理论与算法基础。

Facility location is one of the popular research topics in operation research. Many factors in real-life facility location are uncertain. This fact has made it essential to study the facility location under uncertainty. When no probability distribution information of the random factors is known, the existing researches on this topic mostly focus on robust facility location, i.e., minimizing the cost function or regret function of the location system under the worst-case scenario. The worst-case scenario is perhaps a small probability event, and thus the classical robust location methods are possible to be overly conservative. Different from the classical ones, two new robust methods are proposed for continuous facility location under uncertainty in this proposal: distributionally robust location method and stochastic-variational-inequality-based (SVI-based) robust location method. For the former one, the moment constraints for the random factors are first estimated based on historical or empirical data and then a probability distribution set, whose elements satisfy the moment constraints, is constructed. The distributionally robust location method is proposed for locating facilities over the choice of a distribution in this distribution set. For the latter one, some appropriate residual functions are constructed for the equivalent stochastic variational inequality of the uncertain location problem. Through the optimization of the residual functions, the SVI-based robust location method is proposed for siting new facilities under uncertainty. Based on the two new methods and their combination, three robust location models will be built and then studied from theoretical analysis, algorithm design and application research in this proposal. Due to the consideration of all scenarios as well as the variance of system performance in different scenarios, rather than only emphasizing the worst-case scenario, the new robust location methods will be more practical than the classical ones and furthermore provide significant theoretical and algorithmic basis for continuous facility location under uncertainty.