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.

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. 

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.

How do different densities in a network affect the optimal location of service centers?

The p-median problem is often used to locate p service centers by minimizing their distances to a geographically distributed demand (n). The optimal locations are sensitive to geographical context such as road network and demand points especially when they are asymmetrically distributed in the plane. Most studies focus on evaluating performances of the p-median model when p and n vary. To our knowledge this is not a very well-studied problem when the road network is alternated especially when it is applied in a real world context. The aim in this study is to analyze how the optimal location solutions vary, using the p-median model, when the density in the road network is alternated. The investigation is conducted by the means of a case study in a region in Sweden with an asymmetrically distributed population (15,000 weighted demand points), Dalecarlia. To locate 5 to 50 service centers we use the national transport administrations official road network (NVDB). The road network consists of 1.5 million nodes. To find the optimal location we start with 500 candidate nodes in the network and increase the number of candidate nodes in steps up to 67,000. To find the optimal solution we use a simulated annealing algorithm with adaptive tuning of the temperature. The results show that there is a limited improvement in the optimal solutions when nodes in the road network increase and p is low. When p is high the improvements are larger. The results also show that choice of the best network depends on p. The larger p the larger density of the network is needed. 

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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Estimated Number and Location of Future Moose-Vehicle Collisions (MVC) in Maine

Moose (Alces alces) are a keystone herbivore in Maine. Because of the large number of rural roads in Maine, there is a high rate of moose-vehicle collisions (MVCs), which is increasing. On-road encounters with animals resulted in 231 fatalities in the United States in 1999. Because of the fatality of MVCs, it is important to know where they are most likely to occur. I used GIS analysis to estimate where future MVCs would occur, factoring in the variables of land cover suitability for moose, distance from water bodies, locations of past MVCs, and speed limits on the roads. I ran four different analyses, each one weighting the variables equally. I also ran a regression to determine if increasing road speed was associated with the increase in the number of MVCs per length of road. There was not a strong positive relationship between the number of MVCs per length of road and the speed limit, but it was interesting to note that there were more MVCs per length of road on 35mph and 40mph roads than on 45, 50, 55 or 65mph roads. Future research on MVCs would benefit from the inclusion of include moose population density and road traffic data.

Firm heterogeneity and lobbying

The structure of protection across sectors is usually interpreted as the result of competition among lobbies to influence politicians, but little attention has been devoted to the importance of individual firms in this process. This paper builds a model incorporating firm heterogeneity into a lobbying setup `a la Grossman and Helpman (1994), in a monopolistic competitive environment. We obtain that increased sectorial dispersion cause a fall in equilibrium tariff provided that the exporter’s cutoff is above the mean of the distribution. Also, higher average productivity brings about a fall in the equilibrium tariff, whereas an increase in export costs cause an increase in the tariff. JEL Classification codes: D43, D7, F12, F13, L11

Brazilian international and inter-state trade flows: an exploratory analysis using the gravity model

Recent efforts toward a world with freer trade, like WTO/GATT or regional Preferential Trade Agreements(PTAs), were put in doubt after McCallum's(1995) finding of a large border effect between US and Canadian provinces. Since then, there has been a great amount of research on this topic employing the gravity equation. This dissertation has two goals. The first goal is to review comprehensively the recent literature about the gravity equation, including its usages, econometric specifications, and the efforts to provide it with microeconomic foundations. The second goal is the estimation of the Brazilian border effect (or 'home-bias trade puzzle') using inter-state and international trade flow data. It is used a pooled cross-section Tobit model. The lowest border effect estimated was 15, which implies that Brazilian states trade among themselves 15 times more than they trade with foreign countries. Further research using industry disaggregated data is needed to qualify the estimated border effect with respect to which part of that effect can be attributed to actual trade costs and which part is the outcome of the endogenous location problem of the firm.