approximation algorithm – Page 2

Sequential Competitive Facility Location: Exact and Approximate Algorithms

Published: 2021/03/06, Updated: 2022/07/17

(Mixed) Integer Nonlinear Programming, Combinatorial Optimization, Facility Planning and Design approximation algorithm, branch-and-cut, competitive facility location, concave overestimation, mixed-integer nonlinear programming, submodularity

We study a competitive facility location problem (CFLP), where two firms sequentially open new facilities within their budgets, in order to maximize their market shares of demand that follows a probabilistic choice model. This process is a Stackelberg game and admits a bilevel mixed-integer nonlinear program (MINLP) formulation. We derive an equivalent, single-level MINLP reformulation … Read more

A Unified Analysis for Assortment Planning with Marginal Distributions

Published: 2020/07/02, Updated: 2023/10/15

Applications - OR and Management Sciences approximation algorithm, approximation ratio, assortment optimization, discrete choice models, marginal distribution model, multiple discrete-continuous extreme value model

In this paper, we study assortment planning under the marginal distribution model (MDM), a semiparametric choice model that only requires information about the marginal noise in the utilities of alternatives and does not assume independence of the noise terms. It is already known in the literature that the multinomial logit (MNL) model belongs to the … Read more