RETRACTED ARTICLE: Conic Reformulations of a Class of Discrete Stochastic Location Problems with Congestion
研究了带随机需求和拥堵的离散设施选址问题，将其重构为混合整数二阶锥规划，并利用多面体不等式加速求解，在蒙特利尔乳腺筛查中心选址实例中验证了效率。
In this paper, we study a class of discrete facility location problems with stochastic demand and congestion that arise in the design of various service systems. The problem is to determine the location and size of the facilities, as well as the assignment of clients to these facilities, to minimize the weighted sum of the total travel time, waiting time and service time at the facilities. Traditionally, these problems are formulated as mixed-integer nonlinear optimization problems that can be computationally challenging even for moderate-sized instances. We reformulate the problem as a mixed-integer second-order cone program and present two new formulations that are further strengthened using polymatroid inequalities. An exact and efficient branch-and-cut algorithm is proposed in which polymatroid inequalities are separated to improve convergence. Through computational experiments, we show that our reformulations are approximately twenty times faster than the exact cutting plane method and outperform other conic reformulations reported in the literature. Furthermore, the average computation time is reduced further by half when polymatroid inequalities are used with the reformulations. Using the proposed method, we solved a large, real-life instance of the optimal location of mammography screening centers in the city of Montreal, Canada, in a reasonable time.