Abstract
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.
Highlights
The maximal covering location problem (MCLP), introduced by Church and Revelle [1] maximizes the demands covered by the specified number of facilities to be located
multi-period modular capacitated maximal covering location problem (MMCMCLP) is considered in a dynamic environment and capacitated facilities are located while their corresponding modules with suitable sizes are assigned to the facilities in each period
ZLB is the lower bound to the MMCMCLP that can be calculated by fixing the variables viτ and yiτlklt in constraints (3)–(6) and calculating the objective function (1) at the τth iteration and solving the problem by a branch and bound (B&B) procedure using a generalpurpose solver
Summary
The maximal covering location problem (MCLP), introduced by Church and Revelle [1] maximizes the demands covered by the specified number of facilities to be located. The proposed mathematical model in this paper locates the capacitated facilities at the beginning of the planning horizon and in each time period, assigns the optimum number of capacitated modules to the facilities with the objective of maximizing the covered demands and minimizing the module assignment cost. Demand fluctuation can be reflected by having the multi-period planning model In this application, the facilities are the disaster relief centers, the modules can be ambulances, trucks, helicopters, first aid units, food providing units, sleeping tents, shower rooms, etc. We propose a new model called multi-period modular capacitated maximal covering location problem, which in addition to the facility location decisions, it determines module assignment and demand allocation decisions in different periods of the planning horizon.
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