A Constructive Heuristic Continuous Approach for Solving Uncapacitated Location-Allocation Problem With Zone-Dependent Fixed Cost

Abstract

Location analysis is an important field within Operations Research that focuses on identifying optimal facility locations and allocating customers in a way that balances efficiency with cost reduction. This study investigates the uncapacitated continuous location-allocation problem with zone-dependent fixed costs, where making a difference in regional fixed costs adds an extra layer of complexity to the decision-making process. The  NP-hard nature of the multisource Weber problem causes obtaining the exact solutions to become computationally challenging, especially for larger problem instances. To address this issue, a constructive heuristic approach, known as the Multi-Start Version of Modified Cooper’s Method (MS-MCM), is proposed in this research. The proposed algorithm was developed and implemented using Python programming, and its performance was evaluated against the standard Modified Cooper’s method and Simulated Annealing (SA), a well-established meta-heuristic method recognized for its ability to explore a wide solutions. The final result for this study shows that MS-MCM achieved the best total cost of 138.38, which is more lowest than standard Modified Cooper’s Method (171.02) and Simulated Annealing (196.73). Those outcome demonstrates that MS-MCM is both effective and practical for solving the location-allocation problem that involves zone-dependent fixed costs.