Fatemeh Nosrat | Searcharxiv

arXiv2025

Inverse of the Gomory Corner Relaxation of Integer Programs

We explore the inverse of integer programs (IPs) by studying the inverse of their Gomory corner relaxations (GCRs). We show that solving a set of inverse GCR problems always yields an upper bound on the optimal value of the inverse IP that is at least as tight as the optimal value of the inverse of the linear program (LP) relaxation. We provide conditions under which solving a set of inverse GCR problems exactly solves the inverse IP. We propose an LP formulation for solving the inverse GCR under the $L_1$ and $L_\infty$ norms by reformulating the inverse GCR as the inverse of a shortest path problem.

math.OC↗

arXiv2022

Assortment Optimization with Customer Choice Modeling in a Crowdfunding Setting

Crowdfunding, which is the act of raising funds from a large number of people's contributions, is among the most popular research topics in economic theory. Due to the fact that crowdfunding platforms (CFPs) have facilitated the process of raising funds by offering several features, we should take their existence and survival in the marketplace into account. In this study, we investigated the significant role of platform features in a customer behavioral choice model. In particular, we proposed a multinomial logit model to describe the customers' (backers') behavior in a crowdfunding setting. We proceed by discussing the revenue-sharing model in these platforms. For this purpose, we conclude that an assortment optimization problem could be of major importance in order to maximize the platforms' revenue. We were able to derive a reasonable amount of data in some cases and implement two well-known machine learning methods such as multivariate regression and classification problems to predict the best assortments the platform could offer to every arriving customer. We compared the results of these two methods and investigated how well they perform in all cases.

q-fin.MF↗