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    <title>Transport Research International Documentation (TRID)</title>
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    <copyright>Copyright © 2026. National Academy of Sciences. All rights reserved.</copyright>
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    <managingEditor>tris-trb@nas.edu (Bill McLeod)</managingEditor>
    <webMaster>tris-trb@nas.edu (Bill McLeod)</webMaster>
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      <title>Transport Research International Documentation (TRID)</title>
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    <item>
      <title>Lagrangian relaxation for the urban snow removal problem</title>
      <link>https://trid.trb.org/View/2344857</link>
      <description><![CDATA[Snow removal problem in cities is a challenging task in Nordic countries. The problem is finding optimal tours for a certain number of vehicles with some circumstances in order to clear a number of streets in a city. We have formulated the urban snow removal problem as a time-indexed mixed integer linear programming model which is huge and complicated. In our previous work, we studied the model and its different relaxations which show that the problem is not solvable in practice. Since the problem has many sets of constraints with complicated structures, relaxing them with Lagrangian relaxation might be beneficial. In this paper, we discuss different possibilities of relaxing sets of constraints and develop a Lagrangian heuristic which consists of a suitable Lagrangian relaxation of the problem, a subgradient optimization method for solving the Lagrangian dual, and procedures for obtaining feasible solutions. The heuristic has been implemented and applied to artificial and real life city networks. The results show that the bounds have been improved.]]></description>
      <pubDate>Tue, 27 Feb 2024 14:27:14 GMT</pubDate>
      <guid>https://trid.trb.org/View/2344857</guid>
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      <title>In search of good relaxations for the urban snow removal problem</title>
      <link>https://trid.trb.org/View/2344856</link>
      <description><![CDATA[Snow removal is, in Sweden, an infrequently occurring challenge. Doing the snow removal more efficiently could give much benefits for society. Since the amounts of snow vary a lot from day to day, and from year to year, fixed plans are not the best. Optimization of the snow removal tours could save much money. In this paper, we study the multi-vehicle urban snow removal problem from a mixed integer programming perspective. It is a very hard problem, and obtaining the exact optimum seems to be out of reach. Therefore, we study relaxations of the problem. Our goal is simply to find the best bounds for the optimal objective function value that is possible in limited time. We present some promising possibilities, verified by extensive computational tests.]]></description>
      <pubDate>Tue, 27 Feb 2024 14:27:13 GMT</pubDate>
      <guid>https://trid.trb.org/View/2344856</guid>
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    <item>
      <title>Urban snow removal : tree elimination</title>
      <link>https://trid.trb.org/View/2145666</link>
      <description><![CDATA[Planning urban snow removal, which is a complex optimization problem, is an important task in some countries like Sweden. A number of streets in a city must be cleared of snow by a limited number of vehicles and the tours for the vehicles must be planned in order to minimize the time and/or cost. Since modern real life city networks often contain parts that are trees, one can take advantage of the tree structure, in order to improve the computational efficiency. In this paper, we study tree parts and develop a tree elimination procedure for the snow removal problem, to be used before searching for optimal tours. We have implemented the procedure and applied it to real life city networks.]]></description>
      <pubDate>Mon, 03 Apr 2023 16:45:48 GMT</pubDate>
      <guid>https://trid.trb.org/View/2145666</guid>
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    <item>
      <title>The non zealous snow remover problem</title>
      <link>https://trid.trb.org/View/2075161</link>
      <description><![CDATA[We study designing a tour for a snow removal vehicle. Several sweeps are required to clear a street of snow. We compare two variations for normal streets, the first is doing a middle sweep before the two side sweeps, and the second is not doing the middle sweep. We apply a previously developed method called branch-and-dive, and show that it yields very good results if the middle sweep is not used.]]></description>
      <pubDate>Fri, 02 Dec 2022 11:40:10 GMT</pubDate>
      <guid>https://trid.trb.org/View/2075161</guid>
    </item>
    <item>
      <title>Coordination of vehicles in urban snow removal</title>
      <link>https://trid.trb.org/View/2075160</link>
      <description><![CDATA[Snow removal is an unavoidable problem in Nordic countries like Sweden. A number of streets in a city need to be cleared of snow by a limited number of vehicles. The problem can be formulated as a very large mixed integer programming model, which is practically unsolvable. In order to find a feasible solution, first we break done the work into smaller parts, one for each vehicle. To find which streets a vehicle shall take care of, we solve a weighted k-Chinese postman problem. Based on the allocation obtained, we consider snow removal problems for single vehicles, where details such as turning penalties and precedences are included. These problems can be reformulated to asymmetric traveling salesman problems in extended graphs, and we have a heuristic for finding feasible solution of those. In this paper, we discuss combined solution approaches and coordination of the vehicles to find a feasible solution for the whole original problem including all details. We use an iterative procedure to combine the tours, based on the tools mentioned above, and a procedure for constructive coordination of the tours. We also have new improvement procedures for the combined solution. We have implemented the methods and applied them to real life city networks.]]></description>
      <pubDate>Fri, 02 Dec 2022 11:40:09 GMT</pubDate>
      <guid>https://trid.trb.org/View/2075160</guid>
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    <item>
      <title>Urban snow removal: modeling and relaxations</title>
      <link>https://trid.trb.org/View/1375908</link>
      <description><![CDATA[Snow removal is an important problem in certain countries. It is also difficult, especially in urban areas. The main questions are which vehicle shall do what task, when shall the tasks be done and how shall the vehicles travel. In this paper we describe the problem in detail and formulate a detailed mathematical time-indexed model that contains all practical complications we have encountered, for example different vehicles and switching times between tasks. We investigate the solvability of the model, and present a number of alternate formulations, relaxations and simplifications, yielding several different models of different sizes and different strength. We can either solve very small problems exactly or larger problems more approximately. Our main goal is to find good lower bounds on the optimal objective function value in a limited time, and we present extensive computational tests comparing the obtained bounds and the times needed for the different models. As a result we find some rather efficient models, in the sense that they yield rather good lower bounds in rather short time. With these models, we find lower bounds for several real life instances in the form of small local cities.]]></description>
      <pubDate>Wed, 25 Nov 2015 11:12:46 GMT</pubDate>
      <guid>https://trid.trb.org/View/1375908</guid>
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    <item>
      <title>A COMBINED TERMINAL LOCATION AND SHIP ROUTING PROBLEM</title>
      <link>https://trid.trb.org/View/748428</link>
      <description><![CDATA[In this paper a combined terminal location and ship routing problem at Soedra Cell AB is considered. The aim is to satisfy the customers demand for pulp products while minimizing the distribution costs. Soedra Cell AB is one of the largest producers of market pulp in the world, with operations at five pulp mills located in Sweden and Norway. The customers are supplied within various pulp products by shipping vessels, trains and lorries. The routes for the shipping vessels go from a harbour near the pulp mill to terminals in Europe. From each terminal, the products are transported to customers by lorry, train, or a combination of both. The company strives to reduce the number of terminals. A mathematical model was developed to select which terminals to use and at the same time, decide the shipping routes and which other transportation possibilities to use. The mixed integer programming model was solved using a commercial solver, directly. If the number of routes generated is large, the times required to obtain a solution is too long. Heuristics were used in order to obtain an acceptable solution in reasonable time. Five different scenarios, besides the basic case, were tested. Results based on evaluations and implementation at Soedra Cell AB are presented. (A)]]></description>
      <pubDate>Thu, 03 Mar 2005 00:00:00 GMT</pubDate>
      <guid>https://trid.trb.org/View/748428</guid>
    </item>
    <item>
      <title>MODELLING OF ROAD INVESTMENTS</title>
      <link>https://trid.trb.org/View/685725</link>
      <description><![CDATA[Public and private roads, which have an insufficient bearing capacity or blocking due to thawing or heavy rains, annually contribute to a considerable profit loss in the Swedish forestry sector. One method to reduce costs related to road blocks is to restore the road network to a standard that guarantees accessibility. The problem is to prioritise in order to attain best benefits. This problem is strategic, as upgrading roads has long-term economic effects. The planning period covers a couple of decades. The road investment problem becomes a mixed integer problem or a network design problem. Some alternative mathematical formulations to this problem are presented. The suggested models have a structure where column generation is applicable. One difficulty is to determine the amount of storage that arises due to insufficient bearing capacity. An alternative way to evaluate this is presented.]]></description>
      <pubDate>Tue, 13 Jan 2004 00:00:00 GMT</pubDate>
      <guid>https://trid.trb.org/View/685725</guid>
    </item>
    <item>
      <title>ALLOCATION PROBLEMS IN A THREE-STAGE SAMPLE SURVEY OF VEHICLE SPEEDS</title>
      <link>https://trid.trb.org/View/685776</link>
      <description><![CDATA[In a Swedish vehicle speed survey, data are collected for a stratified three-stage sample of road sites. The concern here is whether the current allocation of the sample over sampling stages is the most efficient, or if there is room for improvements. The parameter of main interest is the average speed, R, on the roads. In order to evaluate the present sample allocation, the components, arising from each sampling stage of the total variance of the estimator of R, is estimated. The sampling design is such, that in all stages but the first one, only one sampling unit per stratum is selected. This makes the variance contributions from the first and second sampling stage inseparable. This problem is circumvented by utilizing a fictitious sampling design and some experimental data. In this way, the demanded variance component estimates are calculated for a domain of study. The results indicate that for an unchanged total sample size, the precision of the estimator of R would improve if the sample sizes in stage three were increased, and the sample size in stage one decreased correspondingly. Thus, re-allocation of the sample seems to be worthwhile, and formulas for doing this in an optimal manner are provided. (A) The report is available as a PDF file: http://www.mai.liu.se/Stat/research/Reports/LiU-MAT-R-2002-04.pdf.]]></description>
      <pubDate>Tue, 13 Jan 2004 00:00:00 GMT</pubDate>
      <guid>https://trid.trb.org/View/685776</guid>
    </item>
    <item>
      <title>OPTIMISATION MODELS FOR SNOW CLEARANCE: FINAL REPORT</title>
      <link>https://trid.trb.org/View/655816</link>
      <description><![CDATA[The object of this preliminary study was to investigate quantitative problems in the field of snow clearance, to highlight areas where optimisation models may have great potential, and to outline optimisation areas of interest. It appears that greatest potential for development of models is to be found in routing snow clearance operations. International literature relating to clearance vehicle routing was studied. As a result, mathematical models have been constructed for route optimisation, both during and after snowfall. It is proposed that these models, and optimisation methods for the solution of these models, should be developed.]]></description>
      <pubDate>Thu, 15 Jun 2000 00:00:00 GMT</pubDate>
      <guid>https://trid.trb.org/View/655816</guid>
    </item>
    <item>
      <title>OPTIMIZATION METHODS FOR ALLOCATION OF RESOURCES FOR INFRASTRUCTURE OPERATIONS AND MAINTENANCE</title>
      <link>https://trid.trb.org/View/506421</link>
      <description><![CDATA[This report describes the results of a preliminary study concerning the allocation of resources for infrastructure operations and maintenance. The purpose of the study has been to survey quantitative presentations of problems and to point out areas with possible potential for the utilisation ofoptimisation models and solution methods, and also to formulate a number of interesting optimisation approaches and thereby create a basis for a project aiming at a PhD. It appears that the largest potential is found at the planning level, called the program level, where the road segments that are to be subject to maintenance actions are identified. As a result of the preliminary study, mathematical models of the maintenance problem have been developed. Also suggested is a solution method for the program level based on price control (i.e., Lagrangean relaxation). (A)]]></description>
      <pubDate>Fri, 10 Sep 1999 00:00:00 GMT</pubDate>
      <guid>https://trid.trb.org/View/506421</guid>
    </item>
    <item>
      <title>EFFICIENCY AND THE LOGIT MODEL</title>
      <link>https://trid.trb.org/View/499412</link>
      <description><![CDATA[This paper discusses model building for discrete choice problems in the simplest case - the logit model. General model building principles are formulated and used in evaluating ways of deriving logit choice probabilities, including the principle that models should represent human behaviour, and that the basic assumptions should be testable and refutable against observations. Three ways of deriving the logit model are considered: the Luce model, the additive random utility maximising approach and the efficiency approach. The equivalence of the logit formula and the independence of irrelevant alternatives assumption (the Luce model) is well known. It is also well known that the assumption of additive random utility maximisation with extreme value distribution for the unobservable stochastic components implies the logit formula. The opposite implication does not hold. The principal merit of additive random utility maximising is its coherence with standard economic theory. Its principal weakness is that the basic assumptions cannot be tested, since the stochastic components cannot be observed. The efficiency assumption - samples with higher total observable utility are more probable - is equivalent to the logit formula. The advantage of the efficiency approach lies in its simple, testable basic behavioural assumptions. The independence of irrelevant alternatives assumption is equivalent to the efficiency assumption. The additive random utility maximization approach and the efficiency approach are not equivalent.]]></description>
      <pubDate>Tue, 06 Apr 1999 00:00:00 GMT</pubDate>
      <guid>https://trid.trb.org/View/499412</guid>
    </item>
    <item>
      <title>THE COMBINED DISTRIBUTION AND STOCHASTIC ASSIGNMENT PROBLEM</title>
      <link>https://trid.trb.org/View/486185</link>
      <description><![CDATA[The combined distribution and assignment problem is the problem of the simultaneous determination of the distribution of trips between origins and destinations in a transportation network and the assignment of trips to routes in each origin-destination pair. In the model most widely used the distribution is assumed to follow a gravity model with negative exponential deterrence function and the assignment is made according to the deterministic user equilibrium principle. In this paper it is described an extension of this model in which the allocation of trips to routes is made according to the principle of stochastic user equilibrium. The behavioural foundations of trip assignment and combined models assuming deterministic or stochastic route choice are discussed. In particular, it is described how they can be derived using the efficiency principle from discrete choice theory; the combined distribution and stochastic assignment model is obtained as the continuous approximation of the discrete problem of finding the most probable flow pattern under the assumption of efficient trip making behaviour. An algorithm for the solution of the model which is based on route (column) generation, disaggregate simplicial decomposition, and partial linearization is outlined.(A)]]></description>
      <pubDate>Fri, 26 Jun 1998 00:00:00 GMT</pubDate>
      <guid>https://trid.trb.org/View/486185</guid>
    </item>
    <item>
      <title>FLOW CORRELATION, ROUTE CHOICE AND TRAVELLING TIME</title>
      <link>https://trid.trb.org/View/486186</link>
      <description><![CDATA[In non-congested traffic it is shown that covariances and regression coefficients between flow counts have information about both route selection and the travelling time. Since knowledge about routes is a part of the OD-picture, this is also a useful new source of OD-information. (A)]]></description>
      <pubDate>Fri, 26 Jun 1998 00:00:00 GMT</pubDate>
      <guid>https://trid.trb.org/View/486186</guid>
    </item>
    <item>
      <title>PROCESSING AND ANALYSIS OF TRAFFIC FLOW DATA</title>
      <link>https://trid.trb.org/View/482423</link>
      <description><![CDATA[This analysis of traffic flow measurements was performed at the Department of Mathematical Statistics, Linkoeping University of Technology. The databases used were based on Swedish Road Administration traffic flow measurements in 1990. Flow is measured every hour at 80 fixed points. The databases were reprogrammed to be more manageable. Two statistical models have been tested as a first step in building a final model. Both have a multiplicative approach. The quality of the models has been measured by the difference between predicted and real traffic flows. Both have a mean error of about 15%. There are two points where improvements can be made.Is the multiplicative approach the optimum? Secondly, more explanatory variables must be used to reduce prediction error to an acceptable level. According to the model, the factors describing traffic flow are measuring site and time of measurement. These are not enough to describe variations in traffic flow. There is a clear pattern of seasonal variation in traffic flow, and the model should therefore include a seasonal variable, and also a variable for summer holiday periods. Another way in which an improvement can be made is not to use the same model but to classify measuring sites and use a different model for each class.]]></description>
      <pubDate>Fri, 30 May 1997 00:00:00 GMT</pubDate>
      <guid>https://trid.trb.org/View/482423</guid>
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