Discrete location models with customers’ choice and path improvements

We examine several facility location problems within a directed network involving two distinct cost types. The first, referred to as the ‘‘customer cost’’, represents the expense each customer considers when selecting a facility to obtain service (e.g., delivery time or a measure of quality degradation). Consequently, once facilities are established, each customer chooses the one that minimizes their individual cost. The second type, termed the ‘‘company cost’’, encompasses all expenses incurred by the company due to customer allocation to their chosen facilities. Additionally, the company possesses a budget that can be allocated to reduce company costs associated with the network’s arcs (the so-called arcs upgrading). The company’s objective is to simultaneously determine facility locations and distribute the budget (or a portion of it) across the network arcs to minimize the total company cost. This total company cost comprises the post-upgrading company costs and the invested budget, while accounting for customer reactions after facility placement. Different problem variants emerge based on the facility location criteria and customers’ choice strategy. In this paper, we address the following problems: the 𝑝��-median problem, a two-stage facility location problem, a single-allocation hub location problem, and a tree-of-hubs location problem — all incorporating customers’ choice and arc upgrading.