Statistical bound of genetic solutions to quadratic assignment problems

Quadratic assignment problems (QAPs) are commonly solved by heuristic methods, where the optimum is sought iteratively. Heuristics are known to provide good solutions but the quality of the solutions, i.e., the confidence interval of the solution is unknown. This paper uses statistical optimum estimation techniques (SOETs) to assess the quality of Genetic algorithm solutions for QAPs. We examine the functioning of different SOETs regarding biasness, coverage rate and length of interval, and then we compare the SOET lower bound with deterministic ones. The commonly used deterministic bounds are confined to only a few algorithms. We show that, the Jackknife estimators have better performance than Weibull estimators, and when the number of heuristic solutions is as large as 100, higher order JK-estimators perform better than lower order ones. Compared with the deterministic bounds, the SOET lower bound performs significantly better than most deterministic lower bounds and is comparable with the best deterministic ones. 

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. 

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.

The impact of big-boxes on local retail : What happens when IKEA comes to town?

The development of large discount retailers, or big-boxes as they are sometimes referred to, are often subject to heated debate and their entry on a market is greeted with either great enthusiasm or dread. For instance, the world’s largest retailer Wal-Mart (Forbes 2014) has a number of anti- and pro-groups dedicated to its being and the event of a Wal-Mart entry tends to be met with protests and campaigns (Decamme 2013) but also welcomed by, for instance, consumers (Davis & DeBonis 2013). Also in Sweden, the entry of a big box is a hot topic and before IKEA’s opening i Borlänge 2013, the first in Sweden in more than five years, great expectations were mixed with worry (Västerbottens-Kuriren 2011).The presence of large scale discount retailers is not, however, a novel phenomenon but a part of a long-term change in retailing that has taken place globally over the past couple of decades (Taylor & Smalling, 2005). As noted by Dawson (2006), the trend in Europe has over the past few decades gone towards an increasing concentration of large firms along with a decrease of smaller firms.This trend is also detectable in the Swedish retail industry. Over the past decade, the retailing industry in Sweden has increased by around 190 Billion SEK, and its share of GDP has risen from 2,7% to 2,9%, while the number of employees have increased from 200 000 to 250 000 (HUI 2013). This growth, however, has not been distributed evenly but rather it has been oriented mainly towards out-of-town retail clusters. Parallel to this development, the number of large retailers has risen at the expense of market shares of smaller independent firms (Rämme et al 2010). Thereby, the presence of large scale retailers is simply part of a changing retail landscape.The effects of this development, where large scale retailing agents relocate shopping to out-of-town shopping areas, have been heavily debated. On the one hand, the big-boxes are accused of displacing independent small retail businesses in the city-centers and the residential areas, resulting in, to some extent, reduced employment opportunities and less availability for the consumers - especially the elderly (Ljungberg et al 2006). In addition, as access to shopping now tends to require some sort of a motorized vehicle, environmental aspects to the discussion have emerged. Ultimately these types of concerns have resulted in calls for regulations against this development (Olsson 2010). On the other hand, the proponents of the new shopping landscape argue that this evolution implies productivity gains, the benefits of lower prices and an increased variety of products (Maican & Orth 2012). Moreover it is argued that it leads to, for instance, better services (such as longer opening hours) and a creative destruction transformation pressure on retailers, which brings about a renewal of city-centerIIretail and services, increasing their attractivity (Bergström 2010). The belief in benefits of a big box entry can be exemplified by the attractivity of IKEA, and the fact that municipalities are prepared to commit to expenses amounting up to hundreds of millions in order to attract the entry of this big-box. Borlänge municipality, for instance, agreed to expenses of about 350 million SEK in order to secure the entry of IKEA, which opened in 2013 (Blomgren 2009).Against this backdrop, the overall effects of large discount retailers become important: Are the economic benefits enough to warrant subsidies or are there, on the contrary, some very compelling grounds for regulations against these types of establishments? In other words; how is overall retail in a region where a store like IKEA enters affected? And how are local retail firms affected?In order to answer these questions, the purpose of this thesis is to study how entry of a big-box retailer affects the entry region. The object of this study is IKEA - one of the world’s largest retailers, with 345 stores, active in over 40 countries and with profits of about 3.3 billion (IKEA 2013; IKEA 2014). By studying the effects of IKEA-entry, both on an aggregated level and on firm level, this thesis intends to find indications of how large discount retail establishments in general can be expected to affect the economic development both in a region overall, but also on the local firm level, something which is of interest to both policymakers as well as the retailing industry in general.The first paper examines the effects of IKEA on retail revenues and employment in the municipalities that IKEA chose to enter between 2000 and 2011; Gothenburg, Haparanda, Kalmar and Karlstad. By means of a matching method we first identify non-entry municipalities that have a similar probability of IKEA entry as the true entry municipalities. Then, using these non-entry municipalities as a control group, the causal effects of IKEA entry can be estimated using a treatment-control approach. We also extend the analysis to examine the spatial impact of IKEA by estimating the effects on retail in neighboring municipalities. It is found that a new IKEA store increases revenues in durable goods trade with 20% in the entry municipality and the number of employees with 17%. Only small, and in most cases statistically insignificant, negative effects were found in neighboring municipalities.It appears that there is a positive net effect on durables retail sales and employment in the entry municipality. However, the analysis is based on data on an aggregated municipality level and thereby it remains unclear if and how the effects vary within the entry municipalities. In addition, the data used in the first study includes the sales and employment of IKEA itself, which could account for the majority of the increases in employment and retail. Thereby the potential spillover effects on incumbent retailers in the entry municipalities cannot be discerned in the first study.IIITo examine effects of IKEA entry on incumbent retail firms, the second paper in this thesis analyses how IKEA entry affects the revenues and employment of local retail firms in three municipalities; Haparanda, Kalmar and Karlstad, which experienced entry by IKEA between 2000 and 2010. In this second study, we exclude Gothenburg due to the fact that big-box entry appears to have weaker effects in metropolitan areas (as indicated by Artz & Stone 2006). By excluding Gothenburg we aim to reduce the geographical heterogeneity in our study. We obtain control municipalities that are as similar as possible to the three entry municipalities using the same method as in the previous study, but including a slightly different set of variables in the selection equation. Using similar retail firms in the control municipalities as our comparison group, we estimate the impact of IKEA entry on revenues and employment for retail firms located at varying distances from the IKEA entry site.The results generated in this study imply that entry by IKEA increases revenues in incumbent retail firms by, on average, 11% in the entry municipalities. In addition, we do not find any significant impact on retail revenues in the city centers of the entry municipalities. However, we do find that retail firms within 1 km of the IKEA experience increases in revenues of about 26%, which indicates large spillover effects in the area nearby the entry site. As expected, this impact decreases as we expand the buffer zone: firms located between 0-2 km experiences a 14% increase and firms in 2-5 km experiences an increase of 10%. We do not find any significant impacts on retail employment.

Optimization heuristic solutions, how good can they be? : With empirical applications in location problems

Combinatorial optimization problems, are one of the most important types of problems in operational research. Heuristic and metaheuristics algorithms are widely applied to find a good solution. However, a common problem is that these algorithms do not guarantee that the solution will coincide with the optimum and, hence, many solutions to real world OR-problems are afflicted with an uncertainty about the quality of the solution. The main aim of this thesis is to investigate the usability of statistical bounds to evaluate the quality of heuristic solutions applied to large combinatorial problems. The contributions of this thesis are both methodological and empirical. From a methodological point of view, the usefulness of statistical bounds on p-median problems is thoroughly investigated. The statistical bounds have good performance in providing informative quality assessment under appropriate parameter settings. Also, they outperform the commonly used Lagrangian bounds. It is demonstrated that the statistical bounds are shown to be comparable with the deterministic bounds in quadratic assignment problems. As to empirical research, environment pollution has become a worldwide problem, and transportation can cause a great amount of pollution. A new method for calculating and comparing the CO2-emissions of online and brick-and-mortar retailing is proposed. It leads to the conclusion that online retailing has significantly lesser CO2-emissions. Another problem is that the Swedish regional division is under revision and the border effect to public service accessibility is concerned of both residents and politicians. After analysis, it is shown that borders hinder the optimal location of public services and consequently the highest achievable economic and social utility may not be attained.

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. 

Kundernas behov i butiksmiljöer : Skillnaderna mellan handlares och kunders uppfattning av kundernas behov i klädbutiker

Konkurrensen inom detaljhandeln blir allt hårdare, både från andra butiker men även från e-handeln, vilket sätter press på fysiska butiker att ha nöjda kunder som fortsätter handla i butiken. Ett tillvägagångssätt för att möta den hårdnande konkurrensen är att ha en butiksmiljö s.k. servicescape som är utformad efter kundernas behov, vilket dock förutsätter att handlarna vet vilka behov sina kunder har. Har handlarna en felaktig uppfattning om kundernas behov föreligger det ett gap som minskar chansen att kunderna blir nöjda och därmed butikens konkurrenskraft. En avgränsning gjordes till klädbutiker, då klädbutiker är bland de butikstyper som är mest konkurrensutsatt. Syftet med uppsatsen var att kartlägga hur kundernas behov överensstämmer eller skiljer sig från handlarnas uppfattning om deras behov. För att uppfylla syftet tillämpades en kvalitativ metod men med en statistisk bearbetning dvs. en kvantitativ bearbetning då resultatet redovisades med hjälp av frekvenser och värden på en skala. Datainsamlingsverktyget som användes var enkäter och utformades efter de tio faktorerna som sammanställdes i den teoretiska referensramen. Enkäterna delades ut till både kunder och handlare i Borlänges stadskärna och Faluns stadskärna. Resultatet av uppsatsen visade att det för faktorerna ljus (4,2), trängsel (4.5) (4.6), Ljud (4.7), toaletter (4.9), (4.10) finns en skillnad ett s.k. gap mellan handlarnas uppfattning om kundernas behov och vad kundernas behov egentligen är. Det framkom även att handlarna ansåg att kunderna har större behov av att faktorerna rent & städat (4.3), (4.4) in & utgångar (4.8) är tillfredsställande än vad kunderna egentligen har. Det framkom precis som behandlades i den teoretiska referensramen att kundernas behov tenderar att variera utifrån deras demografiska faktorer ålder och kön. Om handlarna har en låg, medel eller hög prisnivå påverkade även det hur viktigt det är för kunderna att faktorerna är tillfredsställande. Slutsatsen som författarna identifierade var att det föreligger ett gap mellan handlarnas uppfattning om kundernas behov och vad kunderna anser att deras behov är gällande flera av faktorerna. Detta är dock något som kunderna säger vilket inte behöver stämma överrens med hur de verkligen tycker. Det är dock svårt att urskilja något mönster gällande gapen utan det är nästan enbart tendenser man kan urskilja, vilket gör att varje faktor bör analyseras individuellt.

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.

The Optimal trigger speed of vehicle activated signs

The thesis aims to elaborate on the optimum trigger speed for Vehicle Activated Signs (VAS) and to study the effectiveness of VAS trigger speed on drivers’ behaviour. Vehicle activated signs (VAS) are speed warning signs that are activated by individual vehicle when the driver exceeds a speed threshold. The threshold, which triggers the VAS, is commonly based on a driver speed, and accordingly, is called a trigger speed. At present, the trigger speed activating the VAS is usually set to a constant value and does not consider the fact that an optimal trigger speed might exist. The optimal trigger speed significantly impacts driver behaviour. In order to be able to fulfil the aims of this thesis, systematic vehicle speed data were collected from field experiments that utilized Doppler radar. Further calibration methods for the radar used in the experiment have been developed and evaluated to provide accurate data for the experiment. The calibration method was bidirectional; consisting of data cleaning and data reconstruction. The data cleaning calibration had a superior performance than the calibration based on the reconstructed data. To study the effectiveness of trigger speed on driver behaviour, the collected data were analysed by both descriptive and inferential statistics. Both descriptive and inferential statistics showed that the change in trigger speed had an effect on vehicle mean speed and on vehicle standard deviation of the mean speed. When the trigger speed was set near the speed limit, the standard deviation was high. Therefore, the choice of trigger speed cannot be based solely on the speed limit at the proposed VAS location. The optimal trigger speeds for VAS were not considered in previous studies. As well, the relationship between the trigger value and its consequences under different conditions were not clearly stated. The finding from this thesis is that the optimal trigger speed should be primarily based on lowering the standard deviation rather than lowering the mean speed of vehicles. Furthermore, the optimal trigger speed should be set near the 85th percentile speed, with the goal of lowering the standard deviation.

Entry, re-location and growth in the Swedish wholesale trade industry

Wholesale trade has an intermediate position between manufacturing and retail in the distributional channel. In modern economies, consumers buy few, if any, products directly from manufacture or producer. Instead, it is a wholesaler, who is in direct contact with producers, buying goods in larger quantities and selling them in smaller quantities to retailers. Traditionally, the main function of a wholesaler has been to push goods along the distributional channel from producer to retailer, or other nonend user. However, the function of wholesalers usually goes beyond the process of the physical distribution of goods. Wholesalers also arrange storage, perform market analyses, promote trade or provide technical support to consumers (Riemers 1998). The existence of wholesalers (and other intermediaries) in the distributional channel is based on the effective and efficient performance of distribution services, that are needed by producers and other members of the supply chain. Producers usually do not enjoy the economies of scale that they have in production, when it comes to providing distributional services (Rosenbloom 2007) and this creates a space for wholesalers or other intermediaries. Even though recent developments in the distributional channel indicate that traditional wholesaling activities now also compete with other supply chain organizations, wholesaling still remains an important activity in many economies (Quinn and Sparks, 2007). In 2010, the Swedish wholesale trade sector consisted of approximately 46.000 firms and generated an annual turnover of 1 300 billion SEK (Företagsstatistiken, Statistics Sweden). In terms of turnover, wholesaling accounts for 20% of the gross domestic product and is thereby the third largest industry. This is behind manufacturing and a composite group of firms in other sectors of the service industry but ahead of retailing. This indicates that the wholesale trade sector is an important part of the Swedish economy. The position of wholesaling is further reinforced when measuring productivity growth. Measured in terms of value added per employee, wholesaling experienced the largest productivity growth of all industries in the Swedish economy during the years 2000 through 2010. The fact that wholesale trade is one of the important parts of a modern economy, and the positive development of the Swedish wholesale trade sector in recent decades, leads to several questions related to industry dynamics. The three topics that will be examined in this thesis are firm entry, firm relocation and firm growth. The main question to be answered by this thesis is what factors influence new firm formation, firm relocation and firm growth in the Swedish wholesale trade sector?