<p>This paper studies a variant of facility location problems with dependent facility services under random utilities. An entrant company strategically places facilities in a market where existing competitors are already present. The company aims to maximize its profit by attracting customer demand. Each facility, once operational, offers a basic service by default. However, the company has the option to upgrade these facilities to provide an extended service, which includes additional features to cater to customers with more specific needs. Importantly, the extended service can only be offered if the basic service is already available, meaning that an upgrade is contingent upon a facility being operational. We adopt a random utility model to estimate the company’s market share and formulate an integer nonlinear program. The presence of dependent services results in heterogeneous net service revenues, which creates a nonconcave profit function, making our model challenging to solve. To address this challenge, we propose an approximate approach, i.e., sampling-based Benders decomposition approach (SBBD). We compare our SBBD with two well-known exact solution approaches through computational experiments. On the tested instances, SBBD compares favorably with the two benchmarks on large-scale instances in both computational time and solution quality. Finally, we conduct sensitivity analysis on the impact of market competition level, service attractiveness, and net service revenues. We also observe that the company may bear considerable profit loss if it blindly upgrades all its facilities to offer the extended service.</p>

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Profit-maximizing Facility Location with Dependent Services under Random Utilities

  • Jiajie Zhang,
  • Yun Hui Lin

摘要

This paper studies a variant of facility location problems with dependent facility services under random utilities. An entrant company strategically places facilities in a market where existing competitors are already present. The company aims to maximize its profit by attracting customer demand. Each facility, once operational, offers a basic service by default. However, the company has the option to upgrade these facilities to provide an extended service, which includes additional features to cater to customers with more specific needs. Importantly, the extended service can only be offered if the basic service is already available, meaning that an upgrade is contingent upon a facility being operational. We adopt a random utility model to estimate the company’s market share and formulate an integer nonlinear program. The presence of dependent services results in heterogeneous net service revenues, which creates a nonconcave profit function, making our model challenging to solve. To address this challenge, we propose an approximate approach, i.e., sampling-based Benders decomposition approach (SBBD). We compare our SBBD with two well-known exact solution approaches through computational experiments. On the tested instances, SBBD compares favorably with the two benchmarks on large-scale instances in both computational time and solution quality. Finally, we conduct sensitivity analysis on the impact of market competition level, service attractiveness, and net service revenues. We also observe that the company may bear considerable profit loss if it blindly upgrades all its facilities to offer the extended service.