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. 

Proceedings from the 2nd seminar on Development of Modular Products : December 13-14, 2004, Campus Framtidsdalen, Dalarna University, Sweden

Companies are focusing on efforts increasing the overall efficiency at the same time as the ability to meet customer needs becomes even more important. There is a need to improve the organisation and the product design at the same time through the visualisation of how a product family design should be performed in order to adapt to customers, company internal issues, and long-term strategy. Therefore, there is a need for qualified personnel in today’s companies with the knowledge of product development and modularity. The graduate course Development of Modular Products at Högskolan Dalarna has the objective to provide such knowledge. As a part of the course, each student will individually perform extensive research within a chosen area with respect to Product Development and Modularity. This proceeding is the result of the students own work and was presented during a two day seminar at Dalarna University. The contents of the papers cover many areas, from the identification of customer needs to cost effective manufacturing, and benefits of modularisation. The reader of this proceeding will not only benefit from many areas within Product Development and Modularity but also from the colour of many cultures. In this proceeding, students from nine countries are represented (Bangladesh, China, Costa Rica, Germany, Holland, India, Luxembourg Nigeria, and Sweden). Enjoy the reading.