An upgrading approach for the multi-type Maximal Covering Location Problem

Resumen

Covering location problems are among core problems in Location Science. These problems arise when facilities offer services within a specific distance or maximum time. Depending on the context, different problems may occur, but they generally fall into two categories: set covering and maximal covering. This presentation centers on the Maximal Covering Location Problem (MCLP), initially introduced by Church and ReVelle ([3]). Specifically, it explores an extension of MCLP that includes multiple types of facilities and their upgrades. While most existing literature addresses problems within a single setting, recent research examines the use of multiple settings within the same problem in MCLP ([2]). Conversely, upgrading problems are becoming increasingly prominent in recent location literature. These extensions involve coordinating facility location decisions with improvements to related infrastructure. In the MCLP, authors in [1] examine scenarios where upgrading the network reduces the distance or time from a facility to a customer. We named the model presented in this talk as the Multi-type Maximal Covering Location Problem with Upgrading (MTMCLP-U). It extends the MCLP by incorporating the two described approaches above: different types of facilities (in both continuous and networksettings) and two types of upgrades (for the facilities and the network). In this model, given a set of customers—some with access to the network and some without—the objective is to place a fixed number of facilities at network nodes and another fixed number in the continuous space to maximize covered demand. Additionally, the model includestwo types of binary upgrades (yes-or-no decisions) within a common budget. In the network setting, upgrades reduce the lengths of the edges, while in the continuous setting, upgrades increase the coverage radius, thereby reaching more customers. The MTMCLP-U responds to problems in real applications such as telecommunication networks. For instance, in rural areas where access to telecommunication services cannot be carried over the wired network, repeaters are necessary. See Figure 3 for a comparison of facility locations with (Fig. 3a) and without (Fig. 3b) upgrades.