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.

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.

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?

Road network and GPS tracking with data processing and quality assessment

GPS technology has been embedded into portable, low-cost electronic devices nowadays to track the movements of mobile objects. This implication has greatly impacted the transportation field by creating a novel and rich source of traffic data on the road network. Although the promise offered by GPS devices to overcome problems like underreporting, respondent fatigue, inaccuracies and other human errors in data collection is significant; the technology is still relatively new that it raises many issues for potential users. These issues tend to revolve around the following areas: reliability, data processing and the related application. This thesis aims to study the GPS tracking form the methodological, technical and practical aspects. It first evaluates the reliability of GPS based traffic data based on data from an experiment containing three different traffic modes (car, bike and bus) traveling along the road network. It then outline the general procedure for processing GPS tracking data and discuss related issues that are uncovered by using real-world GPS tracking data of 316 cars. Thirdly, it investigates the influence of road network density in finding optimal location for enhancing travel efficiency and decreasing travel cost. The results show that the geographical positioning is reliable. Velocity is slightly underestimated, whereas altitude measurements are unreliable.Post processing techniques with auxiliary information is found necessary and important when solving the inaccuracy of GPS data. The densities of the road network influence the finding of optimal locations. The influence will stabilize at a certain level and do not deteriorate when the node density is higher.

Methodological issues in applying Location Models to Rural areas

Location Models are usedfor planning the location of multiple service centers in order to serve a geographicallydistributed population. A cornerstone of such models is the measure of distancebetween the service center and a set of demand points, viz, the location of thepopulation (customers, pupils, patients and so on). Theoretical as well asempirical evidence support the current practice of using the Euclidian distancein metropolitan areas. In this paper, we argue and provide empirical evidencethat such a measure is misleading once the Location Models are applied to ruralareas with heterogeneous transport networks. This paper stems from the problemof finding an optimal allocation of a pre-specified number of hospitals in alarge Swedish region with a low population density. We conclude that the Euclidianand the network distances based on a homogenous network (equal travel costs inthe whole network) give approximately the same optimums. However networkdistances calculated from a heterogeneous network (different travel costs indifferent parts of the network) give widely different optimums when the numberof hospitals increases.  In terms ofaccessibility we find that the recent closure of hospitals and the in-optimallocation of the remaining ones has increased the average travel distance by 75%for the population. Finally, aggregation the population misplaces the hospitalsby on average 10 km.

Optimal retail location and CO2 emissions

In this paper, the p-median model is used to find the location of retail stores that minimizes CO2 emissions from consumer travel. The optimal location is then compared with the existing retail location,and the excess CO2 emissions compared with the optimal solution is calculated. The results show that by using the environmentally optimal location, CO2 emissions from consumer travel could be reduced by approximately 25percent. 

Does road network density matter in optimally locating facilities?

Optimal location on the transport infrastructure is the preferable requirement for many decision making processes. Most studies have focused on evaluating performances of optimally locate p facilities by minimizing their distances to a geographically distributed demand (n) when p and n vary. The optimal locations are also sensitive to geographical context such as road network, especially when they are asymmetrically distributed in the plane. The influence of alternating road network density is however not a very well-studied problem especially when it is applied in a real world context. This paper aims to investigate how the density level of the road network affects finding optimal location by solving the specific case of p-median location problem. A denser network is found needed when a higher number of facilities are to locate. The best solution will not always be obtained in the most detailed network but in a middle density level. The solutions do not further improve or improve insignificantly as the density exceeds 12,000 nodes, some solutions even deteriorate. The hierarchy of the different densities of network can be used according to location and transportation purposes and increase the efficiency of heuristic methods. The method in this study can be applied to other location-allocation problem in transportation analysis where the road network density can be differentiated. 

How does the use of different road networks effect the optimal location of facilities in rural areas?

The p-median problem is often used to locate P service facilities in a geographically distributed population. Important for the performance of such a model is the distance measure. Distance measure can vary if the accuracy of the road network varies. The rst aim in this study is to analyze how the optimal location solutions vary, using the p-median model, when the road network is alternated. It is hard to nd an exact optimal solution for p-median problems. Therefore, in this study two heuristic solutions are applied, simulating annealing and a classic heuristic. The secondary aim is to compare the optimal location solutions using dierent algorithms for large p-median problem. The investigation is conducted by the means of a case study in a rural region with an asymmetrically distributed population, Dalecarlia. The study shows that the use of more accurate road networks gives better solutions for optimal location, regardless what algorithm that is used and regardless how many service facilities that is optimized for. It is also shown that the simulated annealing algorithm not just is much faster than the classic heuristic used here, but also in most cases gives better location solutions.

To what extent are CO2 emissions from intra-urban shopping trips by cars affected by drivers’ travel behaviour and store location?

Transportation is seen as one of the major sources of CO2 pollutants nowadays. The impact of increased transport in retailing should not be underestimated. Most previous studies have focused on transportation and underlying trips, in general, while very few studies have addressed the specific affects that, for instance, intra-city shopping trips generate. Furthermore, most of the existing methods used to estimate emission are based on macro-data designed to generate national or regional inventory projections. There is a lack of studies using micro-data based methods that are able to distinguish between driver behaviour and the locational effects induced by shopping trips, which is an important precondition for energy efficient urban planning. The aim of this study is to implement a micro-data method to estimate and compare CO2 emission induced by intra-urban car travelling to a retail destination of durable goods (DG), and non-durable goods (NDG). We estimate the emissions from aspects of travel behaviour and store location. The study is conducted by means of a case study in the city of Borlänge, where GPS tracking data on intra-urban car travel is collected from 250 households. We find that a behavioural change during a trip towards a CO2 optimal travelling by car has the potential to decrease emission to 36% (DG), and to 25% (NDG) of the emissions induced by car-travelling shopping trips today. There is also a potential of reducing CO2 emissions induced by intra-urban shopping trips due to poor location by 54%, and if the consumer selected the closest of 8 existing stores, the CO2 emissions would be reduced by 37% of the current emission induced by NDG shopping trips.

Analysis of Optimum Location, Viability, and Potential Effects of Wind Farm Construction in Maine

Maine has the highest potential for wind energy in New England and falls within the top twenty states in the nation. It falls just behind Wisconsin and California with an estimate electrical output of 56 billion kWhs. The geological makeup of Maine’s mountains in the western part of the state, and the exposed coastline provide opportune areas to capture wind and convert it into energy. The information included in this poster will suggest the most likely areas for wind development based on a number of factors as recommended by the American Wind Energy Association.

ESTIMATED NUMBER AND LOCATION OF FUTURE MOOSE-VEHICLE COLLISIONS (MVC) IN MAINE

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Cell Phone Tower Location and Size in Maine

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