On statistical bounds of heuristic solutions to location problems

Solutions to combinatorial optimization problems, such as problems of locating facilities, frequently rely on heuristics to minimize the objective function. The optimum is sought iteratively and a criterion is needed to decide when the procedure (almost) attains it. Pre-setting the number of iterations dominates in OR applications, which implies that the quality of the solution cannot be ascertained. A small, almost dormant, branch of the literature suggests using statistical principles to estimate the minimum and its bounds as a tool to decide upon stopping and evaluating the quality of the solution. In this paper we examine the functioning of statistical bounds obtained from four different estimators by using simulated annealing on p-median test problems taken from Beasley’s OR-library. We find the Weibull estimator and the 2nd order Jackknife estimator preferable and the requirement of sample size to be about 10 being much less than the current recommendation. However, reliable statistical bounds are found to depend critically on a sample of heuristic solutions of high quality and we give a simple statistic useful for checking the quality. We end the paper with an illustration on using statistical bounds in a problem of locating some 70 distribution centers of the Swedish Post in one Swedish region. 

Bounds on functionals of the distribution treatment effects

Bounds on the distribution function of the sum of two random variables with known marginal distributions obtained by Makarov (1981) can be used to bound the cumulative distribution function (c.d.f.) of individual treatment effects. Identification of the distribution of individual treatment effects is important for policy purposes if we are interested in functionals of that distribution, such as the proportion of individuals who gain from the treatment and the expected gain from the treatment for these individuals. Makarov bounds on the c.d.f. of the individual treatment effect distribution are pointwise sharp, i.e. they cannot be improved in any single point of the distribution. We show that the Makarov bounds are not uniformly sharp. Specifically, we show that the Makarov bounds on the region that contains the c.d.f. of the treatment effect distribution in two (or more) points can be improved, and we derive the smallest set for the c.d.f. of the treatment effect distribution in two (or more) points. An implication is that the Makarov bounds on a functional of the c.d.f. of the individual treatment effect distribution are not best possible.

Bounds for the probability distribution function of the linear ACD process

This paper derives both lower and upper bounds for the probability distribution function of stationary ACD(p, q) processes. For the purpose of illustration, I specialize the results to the main parent distributions in duration analysis. Simulations show that the lower bound is much tighter than the upper bound.

Indexing stock portfolios in Brazil: tracking the IBOVESPA and the FGV 100

Indexing is a passive investment strategy in which the investor weights bis portfolio to match the performance of a broad-based indexo Since severaI studies showed that indexed portfolios have consistently outperformed active management strategies over the last decades, an increasing number of investors has become interested in indexing portfolios IateIy. Brazilian financiaI institutions do not offer indexed portfolios to their clients at this point in time. In this work we propose the use of indexed portfolios to track the performance oftwo ofthe most important Brazilian stock indexes: the mOVESPA and the FGVIOO. We test the tracking performance of our modeI by a historical simulation. We applied several statistical tests to the data to verify how many stocks should be used to controI the portfolio tracking error within user specified bounds.

Does mixed frequency vector error correction model add relevant information to exchange misalignment calculus? Evidence for United States

Real exchange rate is an important macroeconomic price in the economy and a ects economic activity, interest rates, domestic prices, trade and investiments ows among other variables. Methodologies have been developed in empirical exchange rate misalignment studies to evaluate whether a real e ective exchange is overvalued or undervalued. There is a vast body of literature on the determinants of long-term real exchange rates and on empirical strategies to implement the equilibrium norms obtained from theoretical models. This study seeks to contribute to this literature by showing that it is possible to calculate the misalignment from a mixed ointegrated vector error correction framework. An empirical exercise using United States' real exchange rate data is performed. The results suggest that the model with mixed frequency data is preferred to the models with same frequency variables