Overview
This research note addresses the maximal covering location problem with customer preference ordering, a variant of the classical maximal covering location problem (MCLP). The work identifies a direct transformation method that converts instances of the preference-ordered problem into instances of the classical MCLP. This transformation is noted to reduce the size of the instance, effectively allowing existing classical MCLP algorithms to be applied. Computational analysis indicates that this transformation leads to significant speed enhancements, achieving at least a 'magnitude' of improvement when using exact algorithms.
Research Context
The maximal covering location problem (MCLP) is a foundational problem in facility location. A recent series of papers introduced and investigated a variant: the maximal covering location problem with customer preference ordering. For this new variant, previous work developed mixed-integer bilevel optimization models and single-level reformulations. Additionally, various heuristics, including a GRASP (Greedy Randomized Adaptive Search Procedure), Tabu search, and variable neighborhood search, were proposed for solving this problem variant. The current note builds upon this foundation by re-evaluating the underlying problem structure.
Approach
The primary approach of this study involved demonstrating a transformation mechanism. The core idea is to show that instances of the maximal covering location problem with customer preference ordering can be converted into instances of the classical MCLP. This transformation is reported to result in a reduction in the size of the instance. By enabling this conversion, the research suggests that existing algorithms developed for the classical MCLP can be directly utilized to solve the preference-ordered variant. To validate the utility of this transformation, a short computational study was conducted. This study's purpose was to evaluate the performance implications of applying the transformation, specifically focusing on the speed of exact algorithms.
Findings
- Instances of the maximal covering location problem with customer preference ordering can be transformed into instances of the classical MCLP.
- This transformation results in a reduction in the size of the problem instance.
- Existing algorithms designed for the classical MCLP can be used to solve the preference-ordered variant after transformation.
- A computational study indicated that this transformation leads to speed-ups of "at least a magnitude" when exact algorithms are employed.