Facility Location and Discrete Pricing under Random Utilities

This paper considers a company in a competitive market, aiming to maximize its revenue by jointly optimizing the location of its facilities and the service charges. We consider a discrete pricing scheme, in which the company chooses a certain price from a set of discrete price levels for each facility. After the company’s decisions, customers choose whether to use the company’s service. To estimate the market share and revenue, a random utility model is applied, leading to an integer nonlinear program. Due to the consideration of pricing decisions, the revenue structure becomes nonconcave, presenting challenges in finding the optimal solution. We first apply two classical reformulation approaches to recast the problem into a mixed-integer linear program and a mixed-integer second-order cone program. We further study the connection between these two reformulations and propose a mixed reformulation that combines both big-M linearization and conic constraints. Moreover, leveraging the specific feature of our model, we design an efficient heuristic approach which can quickly obtain high quality solutions. Finally, we conduct sensitivity analysis to shed light on the impact of demand distribution pattern and price sensitivity on the company’s decisions and revenue. Some interesting implications are drawn from our analysis.