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. 

Testing Seasonal Unit Roots in Data at Any Frequency, an HEGY approach

This paper generalizes the HEGY-type test to detect seasonal unit roots in data at any frequency, based on the seasonal unit root tests in univariate time series by Hylleberg, Engle, Granger and Yoo (1990). We introduce the seasonal unit roots at first, and then derive the mechanism of the HEGY-type test for data with any frequency. Thereafter we provide the asymptotic distributions of our test statistics when different test regressions are employed. We find that the F-statistics for testing conjugation unit roots have the same asymptotic distributions. Then we compute the finite-sample and asymptotic critical values for daily and hourly data by a Monte Carlo method. The power and size properties of our test for hourly data is investigated, and we find that including lag augmentations in auxiliary regression without lag elimination have the smallest size distortion and tests with seasonal dummies included in auxiliary regression have more power than the tests without seasonal dummies. At last we apply the our test to hourly wind power production data in Sweden and shows there are no seasonal unit roots in the series.

Testing for Seasonal Unit Roots when Residuals Contain Serial Correlations under HEGY Test Framework

This paper introduces a corrected test statistic for testing seasonal unit roots when residuals contain serial correlations, based on the HEGY test proposed by Hylleberg,Engle, Granger and Yoo (1990). The serial correlations in the residuals of test regressionare accommodated by making corrections to the commonly used HEGY t statistics. Theasymptotic distributions of the corrected t statistics are free from nuisance parameters.The size and power properties of the corrected statistics for quarterly and montly data are investigated. Based on our simulations, the corrected statistics for monthly data havemore power compared with the commonly used HEGY test statistics, but they also have size distortions when there are strong negative seasonal correlations in the residuals.

A stopping rule while searching for optimal solution of facility-location

Solutions to combinatorial optimization, such as p-median problems of locating facilities, frequently rely on heuristics to minimize the objective function. The minimum is sought iteratively and a criterion is needed to decide when the procedure (almost) attains it. However, pre-setting the number of iterations dominates in OR applications, which implies that the quality of the solution cannot be ascertained. A small branch of the literature suggests using statistical principles to estimate the minimum and use the estimate for either stopping or evaluating the quality of the solution. In this paper we use test-problems taken from Baesley's OR-library and apply Simulated Annealing on these p-median problems. We do this for the purpose of comparing suggested methods of minimum estimation and, eventually, provide a recommendation for practioners. An illustration ends the paper being a problem of locating some 70 distribution centers of the Swedish Post in a region.

Confidence in heuristic solutions?

Solutions to combinatorial optimization problems frequently rely on heuristics to minimize an objective function. The optimum is sought iteratively and pre-setting the number of iterations dominates in operations research applications, which implies that the quality of the solution cannot be ascertained. Deterministic bounds offer a mean of ascertaining the quality, but such bounds are available for only a limited number of heuristics and the length of the interval may be difficult to control in an application. A small, almost dormant, branch of the literature suggests using statistical principles to derive statistical bounds for the optimum. We discuss alternative approaches to derive statistical bounds. We also assess their performance by testing them on 40 test p-median problems on facility location, taken from Beasley’s OR-library, for which the optimum is known. We consider three popular heuristics for solving such location problems; simulated annealing, vertex substitution, and Lagrangian relaxation where only the last offers deterministic bounds. Moreover, we illustrate statistical bounds in the location of 71 regional delivery points of the Swedish Post. We find statistical bounds reliable and much more efficient than deterministic bounds provided that the heuristic solutions are sampled close to the optimum. Statistical bounds are also found computationally affordable.

From the road network database to a graph for localization purposes

The problems of finding best facility locations require complete and accurate road network with the corresponding population data in a specific area. However the data obtained in road network databases usually do not fit in this usage. In this paper we propose our procedure of converting the road network database to a road graph which could be used in localization problems. The road network data come from the National road data base in Sweden. The graph derived is cleaned, and reduced to a suitable level for localization problems. The population points are also processed in ordered to match with that graph. The reduction of the graph is done maintaining most of the accuracy for distance measures in the network.

Firm relocation and firm profits : Evidence from the Swedish wholesale trade sector

This study analyses the effects of firm relocation on firm profits, using longitudinal data on Swedish limtied liability firms and employing a difference-in-differnce propensity score method in the empirical analysis. Using propensity score matching, the pre-relocalization differneces between relocating and non-relocating firms are balanced. In addition to that, a difference-in-difference estimator is employed in order to control for all time-invariant unobserved heterogeneity among firms. For matching, nearest neighbour matching, using the one-, two- and three nearest neighbours is employed. The balanacing results indicate that matching achieves a good balance, and that similar relocating and non-relocating firms are being compared. The estimated average treatment on the treatment effects indicate thats relocations has a significant effect on the profits of the relocating firms. In other words, firms taht relocate increase their profits significantly, in comparison to what the profits would be had the firms not relocated. This effect is estimated to vary between 3 to 11 percentage points, depending on the lenght of the analysed period after relocation. 

Hushållsavfall i Borlänge kommun : analyser av material en och flerfamiljshus

In Borlänge, source separation has been the basis for management of household waste for over five years. This report reviews today?s system and gives a model for further follow-up through waste grouping. In the basic system waste is separated into three fractions: biodegradable, waste to energy and waste to landfill. All waste is packed in plastic bags, put in separate containers for each fraction, and collected from the property. Separate analyses were made of waste from single family houses and apartment buildings. The amount of waste per household and week, number of non-sorted bags, purity, recovery rate and density of each fraction was calculated. The amount of packaging collected together with the household waste is given. Material collected under the Swedish law of Producers? Responsibility is not covered in this report.

Utvärdering av det arbetsmarknadspolitiska projektet "Volvo Cars och dess underleverantörer"

Denna rapport är en utvärdering av det arbetsmarknadspolitiska projektet "Volvo Cars och dess underleverantörer", som har genomförts av Arbetsförmedlingen i samarbete med Skolverket och Svenska ESF-rådet. Den 5 juni 2009 ansökte Sveriges regering om medel hos den Europeiska globaliseringsfonen (EGF)2 för att kunna erbjuda åtgärder för personer som blivit uppsagda från Volvo Cars AB och dess underleverantörer. Syftet med projektet var att kunna erbjuda de som blivit uppsagda kompetensutveckling, nya yrkeskunskaper och möjlighet att etablera egna företag. På operativ nivå drevs projektet i samverkan mellan Arbetsförmedlingen och den kom-munala yrkesvuxenutbildningen ("Yrkesvux"). Yrkesvux i Göteborgs kommun fick i upp-drag av Skolverket att samordna den del av verksamheten som berörde kommunal yr-kesvuxenutbildning. Projektet startade 1 januari 2010 och avslutades 31 maj 2011. Enligt kommissionens beslut fick medel även användas retroaktivt för insatser som hade givits till de uppsagda i form av olika arbetsmarknadsutbildningar, det s.k. snabbspåret, under 2009 innan projektet hade startat. Av nästan 5 000 individer i målgruppen som registrerade sig vid Arbetsförmedlingen del-tog knappt en fjärdedel i projektets insatser (exkl. vägledning). Av dessa gick 55 procent i aktiviteter enbart genom Arbetsförmedlingen, 37 procent enbart genom Yrkesvux och åtta procent genom både Arbetsförmedlingen och Yrkesvux. De vanligaste förekommande utbildningsinriktningarna var industri och bygg, fordonsindustri, transport och magasine-ring, omvårdnad och handel.

High-School Students´ Summer Jobs and their Ensuing Labor Market Achievement : the Long Term Effect

In part because of high and persistent youth unemployment, adolescent students’ transition from school to work is an important policy and research topic. Many countries have implemented public programs offering summer jobs or work while in high-school as measures to smooth the transition. While the immediate effect of the programs on school attendance, school grades, and disposable income is well documented, their effect on the transition to the labor market remains an open question. Observational studies have shown strong positive effects of summer jobs, but also that the estimated effect is highly vulnerable to selection bias. In this paper, some 3700 high-school students applying for summer jobs in the period 1995-2003,via a program, are followed to 30 years of age. A quarter of the applicants were randomly offered a summer job each year. Among the remaining students, 50% had a (non-program related) summer job while in high-school. We find the income, post high-school, for the offered and non-offered groups to be similar and conclude that the effect of summer jobs on the transition to the labor market is inconsequential.

Mobile systems for monitoring Parkinson's disease

A challenge for the clinical management of Parkinson's disease (PD) is the large within- and between-patient variability in symptom profiles as well as the emergence of motor complications which represent a significant source of disability in patients. This thesis deals with the development and evaluation of methods and systems for supporting the management of PD by using repeated measures, consisting of subjective assessments of symptoms and objective assessments of motor function through fine motor tests (spirography and tapping), collected by means of a telemetry touch screen device. One aim of the thesis was to develop methods for objective quantification and analysis of the severity of motor impairments being represented in spiral drawings and tapping results. This was accomplished by first quantifying the digitized movement data with time series analysis and then using them in data-driven modelling for automating the process of assessment of symptom severity. The objective measures were then analysed with respect to subjective assessments of motor conditions. Another aim was to develop a method for providing comparable information content as clinical rating scales by combining subjective and objective measures into composite scores, using time series analysis and data-driven methods. The scores represent six symptom dimensions and an overall test score for reflecting the global health condition of the patient. In addition, the thesis presents the development of a web-based system for providing a visual representation of symptoms over time allowing clinicians to remotely monitor the symptom profiles of their patients. The quality of the methods was assessed by reporting different metrics of validity, reliability and sensitivity to treatment interventions and natural PD progression over time. Results from two studies demonstrated that the methods developed for the fine motor tests had good metrics indicating that they are appropriate to quantitatively and objectively assess the severity of motor impairments of PD patients. The fine motor tests captured different symptoms; spiral drawing impairment and tapping accuracy related to dyskinesias (involuntary movements) whereas tapping speed related to bradykinesia (slowness of movements). A longitudinal data analysis indicated that the six symptom dimensions and the overall test score contained important elements of information of the clinical scales and can be used to measure effects of PD treatment interventions and disease progression. A usability evaluation of the web-based system showed that the information presented in the system was comparable to qualitative clinical observations and the system was recognized as a tool that will assist in the management of patients.