An Algorithm for Stochastic Convex-Concave Fractional Programs with Applications to Production Efficiency and Equitable Resource Allocation

We propose an algorithm to solve convex and concave fractional programs and their stochastic counterparts in a common framework. Our approach is based on a novel reformulation that involves differences of square terms in the constraints, and subsequent employment of piecewise-linear approximations of the concave terms. Using the branch-and-bound (B&B) framework, our algorithm adaptively refines … Read more

An Exact Method for Assortment Optimization under the Nested Logit Model

We study the problem of finding an optimal assortment of products maximizing the expected revenue, in which customer preferences are modeled using a Nested Logit choice model. This problem is known to be polynomially solvable in a specific case and NP-hard otherwise, with only approximation algorithms existing in the literature. For the NP-hard cases, we … Read more

Bi-Perspective Functions for Mixed-Integer Fractional Programs with Indicator Variables

Perspective functions have long been used to convert fractional programs into convex programs. More recently, they have been used to form tight relaxations of mixed-integer nonlinear programs with so-called indicator variables. Motivated by a practical application (maximising energy efficiency in an OFDMA system), we consider problems that have a fractional objective and indicator variables simultaneously. … Read more

An Efficient Global Optimization Algorithm for Nonlinear Sum-of-Ratios Problems

This paper presents a practical method for finding the globally optimal solution to nonlinear sum-of-ratios problem arising in image processing, engineering and management. Unlike traditional methods which may get trapped in local minima due to the non-convex nature of this problem, our approach provides a theoretical guarantee of global optimality. Our algorithm is based on … Read more

Approximation Algorithms for Linear Fractional-Multiplicative Problems

In this paper we propose a Fully Polynomial Time Approximation Scheme (FPTAS) for a class of optimization problems where the feasible region is a polyhedral one and the objective function is the sum or product of linear ratio functions. The class includes the well known ones of Linear (Sum-of-Ratios) Fractional Programming and Multiplicative Programming. Article … Read more

E-model for Transportation Problem of Linear Stochastic Fractional Programming

This paper deals with the so-called transportation problem of linear stochastic fractional programming, and emphasizes the wide applicability of LSFP. The transportation problem, received this name because many of its applications involve in determining how to optimally transport goods. However, some of its applications (e.g., production scheduling) actually have nothing to do with transportation. The … Read more

Some remarks about the transformation of Charnes and Cooper

In this paper we extend in a simple way the transformation of Charnes and Cooper to the case where the functional ratio to be considered are of similar polynomial Citation Universidad de San Luis Ejercito de Los Andes 950 San Luis(5700) Argentina Article Download View Some remarks about the transformation of Charnes and Cooper

Non-Linear Stochastic Fractional Programming Models of Financial Derivatives

Non-Linear Stochastic Fractional programming models provide numerous insights into a wide variety of areas such as in financial derivatives. Portfolio optimization has been one of the important research fields in modern finance. The most important character within this optimization problem is the uncertainty of the future returns on assets. The objective of this study is … Read more

Linear Stochastic Fractional Programming with Sum-of-Probabilistic-Fractional Objective

Fractional programming deals with the optimization of one or several ratios of functions subject to constraints. Most of these optimization problems are not convex while some of them are still generalised convex. After about forty years of research, well over one thousand articles have appeared on applications, theory and solution methods for various types of … Read more