Реферат: We consider a leader-follower model for competitive location in a discrete space. In the model, two firms compete with each other by opening their facilities to capture customers’ demand. One of the firms, called the leader, is assumed to make its decision first in a situation when the set of customers and competitor’s operational parameters are uncertain. The leader considers a finite set of environment realizations or scenarios, describing key customers’ and competitor’s parameters. In each of the scenarios, the leader anticipates an optimal reaction of the competitor firm, called the follower. The follower is assumed to make a decision when the demand scenario is revealed, and all the information about customers is known. It optimizes the location of its facilities and aims to maximize the profit. Customers’ behavior is modeled by a binary rule, where a customer chooses a single serving facility. This facility must be more preferable than any competitor’s. The leader sets goal values of the profit for each of the scenarios and aims to find a location of serving facilities so that the maximal shortage over all the scenarios is minimized. This problem can be formalized as a bi-level mixed-integer programming problem with multiple problems on the lower-level. We suggest a cut generation procedure to find its optimal solution. The procedure starts from a highpoint relaxation of the problem and enriches the set of constraints with additional inequalities simulating the optimality of the lower-level variables.

Библиографическая ссылка: Melʹnikov A.A. , Beresnev V.L.
Profit targeting in a competitive location with scenarios of environment realization
Mathematical optimization theory and operations research (MOTOR-2021) 05-10 Jul 2021