The Multiple Depot Ring-Star Problem (MDRSP) is an important combinatorial optimization problem that arises in the context of optical fiber network design, and in applications pertaining to collecting data using stationary sensing devices and autonomous vehicles. Given the locations of a set of customers and a set of depots, the goal is to (i) find a set of simple cycles such that each cycle (ring) passes through a subset of customers and exactly one depot, (ii) assign each non-visited customer to a visited customer or a depot, and (iii) minimize the sum of the routing costs, i.e., the cost of the cycles and the assignment costs. We present a mixed integer linear programming formulation for the MDRSP and propose valid inequalities to strengthen the linear programming relaxation. Furthermore, we present a polyhedral analysis and derive facet-inducing results for the MDRSP. All these results are then used to develop a branch-and-cut algorithm to obtain optimal solutions to the MDRSP. The performance of the branch-and-cut algorithm is evaluated through extensive computational experiments on several classes of test instances.

翻译：多重发包环星问题(MDRSP)是一个重要的组合优化问题,它出现在光纤网络设计以及利用固定感测装置和自主车辆收集数据的应用中。考虑到一组客户和一批仓库的位置,目标是:(一) 找到一套简单的周期,使每个周期(环)通过一组客户,确切地通过一个仓库,(二) 将每个未受访的客户指派给一个受访客户或一个仓库,(三) 尽量减少路由费用的总和,即周期的费用和分配费用。我们为MDRSP提供了一种混合的线性线性编程配方,并提出了加强线性编程松动的有效不平等。此外,我们提出了多面分析,并得出MDRSP的引力结果。所有这些结果随后被用来制定分门算法,以便为MDRSP找到最佳解决办法。分门算法的绩效是通过几个测试阶段的广泛计算实验来评估的。