Multi-period maximal covering location problem with capacitated facilities and modules for natural disaster relief services

The paper aims to study a multi-period maximal covering location problem with the configuration of different types of facilities, as an extension of the classical maximal covering location problem (MCLP). The proposed model can have applications such as locating disaster relief facilities, hospitals, and chain supermarkets. The facilities are supposed to be comprised of various units, called the modules. The modules have different sizes and can transfer between facilities during the planning horizon according to demand variation. Both the facilities and modules are capacitated as a real-life fact. To solve the problem, two upper bounds—(LR1) and (LR2)—and Lagrangian decomposition (LD) are developed. Two lower bounds are computed from feasible solutions obtained from (LR1), (LR2), and (LD) and a novel heuristic algorithm. The results demonstrate that the LD method combined with the lower bound obtained from the developed heuristic method (LD-HLB) shows better performance and is preferred to solve both small-and large-scale problems in terms of bound tightness and efficiency especially for solving large-scale problems. The upper bounds and lower bounds generated by the solution procedures can be used as the profit approximation by the managerial executives in their decision-making process.