A suggested program with fuzzy linear fractional objective and integer decision variables (FILFP) is considered. The fuzzy coefficients are involved in the numerator of the linear objective function and can be characterized by trapezoidal fuzzy numbers. The purpose of this paper is to outline an algorithm available to solve (FILFP). In addition, an illustrative example … Read more
Strong relaxations are critical for solving deterministic mixed-integer programs. As solving stochastic mixed-integer programs (SMIPs) is even harder, it is likely that strong relaxations will also prove essential for SMIPs. We consider general two-stage SMIPs with recourse, where integer variables are allowed in both stages of the problem and randomness is allowed in the objective … Read more
In this paper, we show that for a large class of optimization problems, the Lagrange multiplier rule can be derived from the so-called approximate multiplier rule. In establishing the link between the approximate and the exact multiplier rule we first derive an approximate multiplier rule for a very general class of optimization problems using the … Read more
We discuss two optimal control problems of parabolic equations, with mixed state and control constraints, for which the standard qualification condition does not hold. Our first example is a bottleneck problem, and the second one is an optimal investment problem where a utility type function is to be minimized. By an adapted penalization technique, we … Read more
A simple relaxation of two rows of a simplex tableau is a mixed integer set consisting of two equations with two free integer variables and non-negative continuous variables. Recently Andersen et al. (2007) and Cornuejols and Margot (2007) showed that the facet-defining inequalities of this set are either split cuts or intersection cuts obtained from … Read more
The p-median problem consists in locating p medians in a given graph, such that the total cost of assigning each demand to the closest median is minimized. In this work, a Lagrangean heuristic is proposed and it uses two dual information to build primal solutions. It outperforms a classic heuristic based on the same Lagrangean … Read more
Bargaining is a basic game in economic practice. Cournot duopoly game is an important model in bargaining theory. Recently, asymmetry information [20] and incomplete information [19], limited individual rationality [2] and slightly altruistic equilibrium [10] are introduced into bargaining theory. And computational game theory come into being a new research field. In this paper, we … Read more
The objective of this study is to construct fund-of-funds (FoF) that follow an absolute return strategy and meet the requirements imposed by the Value-at-Risk (VaR) market risk measure. We propose the VaR-Black Litterman model which accounts for the VaR and trading (diversification, buy-in threshold, liquidity, currency) requirements. The model takes the form of a probabilistic … Read more
Motivated by an application in highway pricing, we consider the problem that consists in setting profit-maximizing tolls on a clique subset of a multicommodity transportation network. Following a proof that clique pricing is NP-hard, we propose strong valid inequalities, some of which define facets of the 2-commodity polyhedron. The numerical efficiency of these inequalities is … Read more