A Maximal Covering Location Problem Under Uncertainty Through Possibility Theory

This study presents a practical framework for the maximal covering location problem (MCLP) under uncertainty. The approach combines possibility theory with chance-constrained programming to represent both imprecision and randomness in demand. Demand is modeled as fuzzy random variables. Using the Zadeh extension principle, both the fuzzy and fuzzy random formulations are transformed into equivalent deterministic mixed-integer programs. Clear linearization steps are provided for the objective function and constraints. Two specifications are examined to reflect different attitudes toward risk. The first specification uses possibility measures, reflecting an optimistic stance, while the second uses necessity measures and represents a conservative approach. Computational experiments conducted in an urban facility context show that increasing the possibility or probability level results in more conservative solutions and a smaller amount of covered demand. In contrast, lower thresholds lead to more exhaustive coverage with greater exposure to uncertainty. In the deterministic scenario, full coverage becomes attainable as the number of facilities increases. Under uncertainty, the models balance coverage with robustness based on the chosen risk tolerance levels. The proposed framework serves as a flexible decision support tool, enabling planners to align facility location choices with their risk tolerance while maintaining tractability with standard optimization solvers.