Exact optimal solutions of the minisum facility and transfer points location problems on a network
Exact optimal solutions of the minisum facility and transfer points location problems on a network
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DOI：
10.1111/j.1475-3995.2008.00602.x
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发表时间：
2008-05
期刊：
影响因子：
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通讯作者：
Mihiro Sasaki;T. Furuta;Atsuo Suzuki
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文献类型：
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作者：
Mihiro Sasaki;T. Furuta;Atsuo Suzuki
我们考虑了网络上的分层设施定位问题，称为多转接点定位（MLTP）和设施和转接点定位问题（FTPLP），其中q个设施和p个转接点被定位，每个客户直接或通过一个转接点前往其中一个设施。在FTPLP中，我们需要找到一个最优的设施和转接点的位置，而在MLTP中设施的位置是给定的。虽然对于最小MLTP和FTPLP已经提出了很好的启发式方法，但由于问题的大小，没有测试过确切的最优解。我们证明了最小MLTP可以被表述为一个p中值问题，从而得到一个最优解。我们还提出了一种新的FTPLP公式和基于枚举的方法来解决单个设施的问题。
We consider hierarchical facility location problems on a network called Multiple Location of Transfer Points (MLTP) and Facility and Transfer Points Location Problem (FTPLP), where q facilities and p transfer points are located and each customer goes to one of the facilities directly or via one of the transfer points. In FTPLP, we need to find an optimal location of both the facilities and the transfer points while the location of facilities is given in MLTP. Although good heuristics have been proposed for the minisum MLTP and FTPLP, no exact optimal solution has been tested due to the size of the problems. We show that the minisum MLTP can be formulated as a p-median problem, which leads to obtaining an optimal solution. We also present a new formulation of FTPLP and an enumeration-based approach to solve the problems with a single facility.