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• 101.
A Dual Active-Set Algorithm for Regularized Monotonic Regression2017Ingår i: Journal of Optimization Theory and Applications, ISSN 0022-3239, E-ISSN 1573-2878, Vol. 172, nr 3, s. 929-949Artikel i tidskrift (Refereegranskat)

Monotonic (isotonic) regression is a powerful tool used for solving a wide range of important applied problems. One of its features, which poses a limitation on its use in some areas, is that it produces a piecewise constant fitted response. For smoothing the fitted response, we introduce a regularization term in the monotonic regression, formulated as a least distance problem with monotonicity constraints. The resulting smoothed monotonic regression is a convex quadratic optimization problem. We focus on the case, where the set of observations is completely (linearly) ordered. Our smoothed pool-adjacent-violators algorithm is designed for solving the regularized problem. It belongs to the class of dual active-set algorithms. We prove that it converges to the optimal solution in a finite number of iterations that does not exceed the problem size. One of its advantages is that the active set is progressively enlarging by including one or, typically, more constraints per iteration. This resulted in solving large-scale test problems in a few iterations, whereas the size of that problems was prohibitively too large for the conventional quadratic optimization solvers. Although the complexity of our algorithm grows quadratically with the problem size, we found its running time to grow almost linearly in our computational experiments.

fulltext
• 102.
A Dual Active-Set Algorithm for Regularized Slope-Constrained Monotonic Regression2017Ingår i: Iranian Journal of Operations Research, ISSN 2008-1189, Vol. 8, nr 2, s. 40-47Artikel i tidskrift (Refereegranskat)

In many problems, it is necessary to take into account monotonic relations. Monotonic (isotonic) Regression (MR) is often involved in solving such problems. The MR solutions are of a step-shaped form with a typical sharp change of values between adjacent steps. This, in some applications, is regarded as a disadvantage. We recently introduced a Smoothed MR (SMR) problem which is obtained from the MR by adding a regularization penalty term. The SMR is aimed at smoothing the aforementioned sharp change. Moreover, its solution has a far less pronounced step-structure, if at all available. The purpose of this paper is to further improve the SMR solution by getting rid of such a structure. This is achieved by introducing a lowed bound on the slope in the SMR. We call it Smoothed Slope-Constrained MR (SSCMR) problem. It is shown here how to reduce it to the SMR which is a convex quadratic optimization problem. The Smoothed Pool Adjacent Violators (SPAV) algorithm developed in our recent publications for solving the SMR problem is adapted here to solving the SSCMR problem. This algorithm belongs to the class of dual active-set algorithms. Although the complexity of the SPAV algorithm is o(n2) its running time is growing in our computational experiments almost linearly with n. We present numerical results which illustrate the predictive performance quality of our approach. They also show that the SSCMR solution is free of the undesirable features of the MR and SMR solutions.

• 103.
Regularized monotonic regression2016Rapport (Övrigt vetenskapligt)

Monotonic (isotonic) Regression (MR) is a powerful tool used for solving a wide range of important applied problems. One of its features, which poses a limitation on its use in some areas, is that it produces a piecewise constant fitted response. For smoothing the fitted response, we introduce a regularization term in the MR formulated as a least distance problem with monotonicity constraints. The resulting Smoothed Monotonic Regrassion (SMR) is a convex quadratic optimization problem. We focus on the SMR, where the set of observations is completely (linearly) ordered. Our Smoothed Pool-Adjacent-Violators (SPAV) algorithm is designed for solving the SMR. It belongs to the class of dual activeset algorithms. We proved its finite convergence to the optimal solution in, at most, n iterations, where n is the problem size. One of its advantages is that the active set is progressively enlarging by including one or, typically, more constraints per iteration. This resulted in solving large-scale SMR test problems in a few iterations, whereas the size of that problems was prohibitively too large for the conventional quadratic optimization solvers. Although the complexity of the SPAV algorithm is O(n2), its running time was growing in our computational experiments in proportion to n1:16.

Regularized Monotonic Regression
• 104.
An algorithm for isotonic regression problems2004Ingår i: European Congress on Computational Methods in Applied Sciences and Engineering ECCOMAS / [ed] P. Neittaanmäki, T. Rossi, K. Majava and O. Pironneau, Jyväskylä: University of Jyväskylä , 2004, s. 1-9Konferensbidrag (Refereegranskat)

We consider the problem of minimizing the distance from a given n-dimensional vector to a set defined by constraintsof the form   xi $\leq$ xj Such constraints induce a partial order of the components xi, which can be illustrated by an acyclic directed graph.This problem is known as the isotonic regression (IR) problem. It has important applications in statistics, operations research and signal processing. The most of the applied IR problems are characterized by a very large value of n. For such large-scale problems, it is of great practical importance to develop algorithms whose complexity does not rise with n too rapidly.The existing optimization-based algorithms and statistical IR algorithms have either too high computational complexity or too low accuracy of the approximation to the optimal solution they generate. We introduce a new IR algorithm, which can be viewed as a generalization of the Pool-Adjacent-Violator (PAV) algorithm from completely to partially ordered data. Our algorithm combines both low computational complexity O(n2) and high accuracy. This allows us to obtain sufficiently accurate solutions to the IR problems with thousands of observations.

• 105.
An O(n2) algorithm for isotonic regression2006Ingår i: Large-Scale Nonlinear Optimization / [ed] Pillo, Gianni; Roma, Massimo, New York: Springer Science+Business Media B.V., 2006, s. 25-33Konferensbidrag (Övrigt vetenskapligt)

We consider the problem of minimizing the distance from a given n-dimensional vector to a set defined by constraints of the form xixj. Such constraints induce a partial order of the components xi, which can be illustrated by an acyclic directed graph. This problem is also known as the isotonic regression (IR) problem. IR has important applications in statistics, operations research and signal processing, with most of them characterized by a very large value of n. For such large-scale problems, it is of great practical importance to develop algorithms whose complexity does not rise with n too rapidly. The existing optimization-based algorithms and statistical IR algorithms have either too high computational complexity or too low accuracy of the approximation to the optimal solution they generate. We introduce a new IR algorithm, which can be viewed as a generalization of the Pool-Adjacent-Violator (PAV) algorithm from completely to partially ordered data. Our algorithm combines both low computational complexity O(n2) and high accuracy. This allows us to obtain sufficiently accurate solutions to IR problems with thousands of observations.

• 106.
An O(n2) algorithm for isotonic regression problems2006Ingår i: Large-Scale Nonlinear Optimization / [ed] G. Di Pillo and M. Roma, Springer-Verlag , 2006, s. 25-33Kapitel i bok, del av antologi (Refereegranskat)

Large-Scale Nonlinear Optimization reviews and discusses recent advances in the development of methods and algorithms for nonlinear optimization and its applications, focusing on the large-dimensional case, the current forefront of much research.

The chapters of the book, authored by some of the most active and well-known researchers in nonlinear optimization, give an updated overview of the field from different and complementary standpoints, including theoretical analysis, algorithmic development, implementation issues and applications

• 107.
Lehigh Univ, PA 18015 USA.
Foreword2019Ingår i: Optimization Methods and Software, ISSN 1055-6788, E-ISSN 1029-4937, Vol. 34, nr 5, s. 921-921Artikel i tidskrift (Övrigt vetenskapligt)

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• 108. Köp publikationen >>
Inverse Shortest Path Routing Problems in the Design of IP Networks2010Licentiatavhandling, monografi (Övrigt vetenskapligt)

This thesis is concerned with problems related to shortest pathrouting (SPR) in Internet protocol (IP) networks. In IP routing, alldata traffic is routed in accordance with an SPR protocol, e.g. OSPF.That is, the routing paths are shortest paths w.r.t. some artificialmetric. This implies that the majority of the Internet traffic isdirected by SPR. Since the Internet is steadily growing, efficientutilization of its resources is of major importance. In theoperational planning phase the objective is to utilize the availableresources as efficiently as possible without changing the actualdesign. That is, only by re-configuration of the routing. This isreferred to as traffic engineering (TE). In this thesis, TE in IPnetworks and related problems are approached by integer linearprogramming.

Most TE problems are closely related to multicommodity routingproblems and they are regularly solved by integer programmingtechniques. However, TE in IP networks has not been studied as much,and is in fact a lot harder than ordinary TE problems without IProuting since the complicating shortest path aspect has to be takeninto account. In a TE problem in an IP network the routing isperformed in accordance with an SPR protocol that depends on a metric,the so called set of administrative weights. The major differencebetween ordinary TE problems and TE in IP networks is that all routingpaths must be simultaneously realizable as shortest paths w.r.t. thismetric. This restriction implies that the set of feasible routingpatterns is significantly reduced and that the only means available toadjust and control the routing is indirectly, via the administrativeweights.

A constraint generation method for solving TE problems in IP networksis outlined in this thesis. Given an "original" TE problem, the ideais to iteratively generate and augment valid inequalities that handlethe SPR aspect of IP networks. These valid inequalities are derived byanalyzing the inverse SPR problem. The inverse SPR problem is todecide if a set of tentative routing patterns is simultaneouslyrealizable as shortest paths w.r.t. some metric. When this is not thecase, an SPR conflict exists which must be prohibited by a validinequality that is then augmented to the original TE problem. Toderive strong valid inequalities that prohibit SPR conflicts, athorough analysis of the inverse SPR problem is first performed. Inthe end, this allows us to draw conclusions for the design problem,which was the initial primary concern.

Inverse Shortest Path Routing Problems in the Design of IP Networks
• 109. Köp publikationen >>
Shortest Path Routing Modelling, Infeasibility and Polyhedra2012Doktorsavhandling, monografi (Övrigt vetenskapligt)

The Internet is constantly growing but the available resources, i.e. bandwidth, are limited. Using bandwidth efficiently to provide high quality of service to users is referred to as traffic engineering. This is of utmost importance. Traffic in IP networks is commonly routed along shortest paths with respect to auxiliary link weights, e.g. using the OSPF or IS-IS protocol. Here, shortest path routing is indirectly controlled via the link weights only, and it is therefore crucial to have a profound understanding of the shortest path routing mechanism to solve traffic engineering problems in IP networks. The theoretical aspects of such problems have received little attention.

Traffic engineering in IP networks leads to very difficult optimization problems and the key element in exact methods for such problems is an inverse shortest path routing problem. It is used to answer the fundamental question of whether there exist link weights that reproduce a set of tentative paths. Path sets that cannot be obtained correspond to routing conflicts. Valid inequalities are instrumental to prohibit such routing conflicts.

We analyze the inverse shortest path routing problem thoroughly. We show that the problem is NP-complete, contrary to what is claimed in the literature, and propose a stronger relaxation. Its Farkas system is used to develop a novel and compact formulation based on cycle bases, and to classify and characterize minimal infeasible subsystems. Valid inequalities that prevent routing conflicts are derived and separation algorithms are developed for such inequalities.

We also consider several approaches to modelling traffic engineering problems, especially Dantzig–Wolfe reformulations and extended formulations. We give characterizations of facets for some relaxations of traffic engineering problems.

Our results contribute to the theoretical understanding, modelling and solution of problems related to traffic engineering in IP networks.

Shortest Path Routing Modelling, Infeasibility and Polyhedra
omslag
• 110.
Inverse Shortest Path Models Based on Fundamental Cycle Bases2012Ingår i: Operations Research Proceedings 2011: Selected Papers of the International Conference on Operations Research (OR 2011), August 30 - September 2, 2011, Zurich, Switzerland / [ed] Diethard Klatte, Hans-Jakob Lüthi, Karl Schmedders, Springer Berlin/Heidelberg, 2012, s. 77-82Kapitel i bok, del av antologi (Refereegranskat)

The inverse shortest path problem has received considerable attention in the literature since the seminal paper by Burton and Toint from 1992. Given a graph and a set of paths the problem is to find arc costs such that all specified paths are shortest paths. The quality of the arc costs is measured by the deviation from some ideal arc costs. Our contribution is a novel modeling technique for this problem based on fundamental cycle bases. For LP compatible norms we present a cycle basis model equivalent to the LP dual. The LP dual of our cycle basis model is a path based model that only requires a polynomial number of path constraints. This model is valid also for LP incompatible norms. This yields the first polynomial sized path formulation of the original problem.

• 111.
Sodra Cell, Sweden .
Using robust optimization for distribution and inventory planning for a large pulp producer2014Ingår i: Computers & Operations Research, ISSN 0305-0548, E-ISSN 1873-765X, Vol. 44, s. 214-225Artikel i tidskrift (Refereegranskat)

Sodra Cell is a world leading producer of pulp and has a large distribution network for its pulp products. This network includes production mills in Sweden and Norway, terminals in European harbours and inland locations, and many customers. The company uses several transport modes including long chartered vessels, spot vessels, trains, barges and trucks. The company uses a supplier managed inventory with a large proportion of its customers. This makes the logistic planning including transportation and inventory critical, as Sodra Cell has direct responsibility of their customers inventories. However, there is still some uncertainty regarding customer demand and Sodra Cell has traditionally used a safety stock inventory approach to handle this. In this paper, we introduce a robust optimization approach to handle the uncertainty and to establish a distribution plan, together with related inventory management. With this approach there is no need for explicit safety stock levels. This is instead taken into account directly through the robust solution. In the proposed model, we can use practical characterization and historical information on the uncertainty. An important result with this is that we can avoid solutions that are too conservative and costly as in standard robust models. A large case study from Sodra Cell is used to validate the proposed approach against the traditional approach with safety stock. The analysis is based on simulations and it shows that the robust approach is more cost efficient and can be used as a basis in a decision support system.

• 112.
Södra Cell AB, SE-35189 Växjö, Sweden.
Supply chain management in forestry - Case studies at Södra Cell AB2005Ingår i: European Journal of Operational Research, ISSN 0377-2217, E-ISSN 1872-6860, Vol. 163, nr 3, s. 589-616Artikel i tidskrift (Refereegranskat)

The use of supply chain management and optimisation is of increasing importance in the forest industry. The overall wood-flow starts with standing trees in forests and continues with harvesting, bucking, sorting, transportation to terminals, sawmills, pulp mills, paper mills and heating plants, conversion into products such as pulp, paper, lumber, and ends at different customers. Many planning problems arise along the chain and these cover different time horizons. Co-ordinating the wood-flow is a vital concern for many companies. We study Södra, one of the larger Swedish forest companies, which is involved in all stages of the wood-flow. We focus in particular on Södra Cell AB, a company within Södra, which is responsible for pulp production. We describe the operations at Södra Cell and the decision support tools used for supply chain planning. We describe five major projects or cases which focus on improving their supply chain management and optimisation. These cases include the introduction of new technologies for sales and orders, new distribution structures using terminals, and the development of integrated optimisation models and methods. © 2004 Elsevier B.V. All rights reserved.

• 113.
A Conjugate Direction Frank-Wolfe Method for Nonconvex Problems2003Rapport (Refereegranskat)

In this paper we propose an algorithm for solving problems with nonconvex objective function and linear constraints. We extend the previously suggested Conjugate direction Frank–Wolfe algorithm to nonconvex problems. We apply our method to multi-class user equilibria under social marginal cost pricing. Results of numerical experiments on Sioux Falls and Winnipeg are reported.

• 114.
A Conjugate Direction Frank-Wolfe Method with Applications to the Traffic Assignment Problem2003Ingår i: Operations Research Proceedings 2002: Selected Papers of the International Conference on Operations Research (SOR 2002), Klagenfurt, September 2-5, 2002" / [ed] Leopold-Wildburger, U, Springer , 2003, s. -550Kapitel i bok, del av antologi (Övrigt vetenskapligt)

This proceedings volume contains a selection of papers presented at the International Conference on Operations Research (SOR 2002).The contributions cover the broad interdisciplinary spectrum of Operations Research and present recent advances in theory, development of methods, and applications in practice. Subjects covered are Production, Logistics and Supply Chain Production, Marketing and Data Analysis, Transportation and Traffic, Scheduling and Project Management, Telecommunication and Information Technology, Energy and Environment, Public Economy, Health, Agriculture, Education, Banking, Finance, Insurance, Risk Management, Continuous Optimization, Discrete and Combinatorial Optimization, Stochastic and Dynamic Programming, Simulation, Control Theory, Systems Dynamics, Dynamic Games, Game Theory, Auctioning and Bidding, Experimental Economics, Econometrics, Statistics and Mathematical Economics, Fuzzy Logic, Multicriteria Decision Making, Decision Theory.

• 115.
Conjugate Direction Frank-Wolfe Methods with Applications to Traffic Assignment Problem2003Ingår i: International Symposium on Mathematical Programming,2003, 2003Konferensbidrag (Övrigt vetenskapligt)
• 116.
Improved Frank-Wolfe directions with applications to traffic problems2003Licentiatavhandling, sammanläggning (Övrigt vetenskapligt)

The main contribution of this thesis is the development of some new efficient algorithms for solving structured linearly constrained optimization problems. The conventional Frank-Wolfe method is one of the most frequently used methods for solving such problems. We develop algorithms based on conjugate directions methods and aim to improve the performance of the pure Frank-Wolfe method by choosing better search directions.

In the conjugate direction Frank-Wolfe method for linearly constrained convex optimization problems, one performs line search along a direction, which is conjugate to the previous one with respect to the hessian of the objective function at the current point. The new method is applied to the single-class traffic equilibrium problem. The convergence of the presented method is also proved. In a limited set of computational tests the algorithm turns out to be quite efficient, outperforming the pure and "PARTANized" Frank-Wolfe methods.

One further refinement of the conjugate direction Frank-Wolfe methods. is derived by applying conjugation with respect to the last two directions instead of only the last one.

We also extend the conjugate direction Frank-Wolfe method to nonconvex optimization problems with linear constraints. We apply this extension to the multi-class traffic equilibrium problem under social marginal cost pricing.

• 117.
Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan. Mathematical Sciences, Chalmers University of Technology and Göteborg University, Gothenburg, Sweden. Linköpings universitet, Institutionen för teknik och naturvetenskap. Linköpings universitet, Tekniska högskolan.
A Sequential Linear Programming Algorithm with Multi-dimensional Search: Derivation and Convergence2007Artikel i tidskrift (Övrigt vetenskapligt)

We present a sequential linear programming, SLP, algorithm in which the traditional line-search step is replaced by a multi-dimensional search. The algorithm is based on inner approximations of both the primal and dual spaces, which yields a method which in the primal space combines column and constraint generation. The algorithm does not use a merit function, and the linear programming subproblem of the algorithm differs from the one obtained in traditional methods of this type, in the respect that linearized constraints are taken into account only implicitly in a Lagrangiandual fashion. Convergence to a point that satisfies the Karush-Kuhn-Tucker conditions is established. We apply the new method to a selection of the Hoch-Schittkowski’s nonlinear test problems and report a preliminary computational study in a Matlab environment. Since the proposed algorithmcombines column and constraint generation, it should be advantageous with large numbers of variables and constraints.

• 118.
Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan. Mathematical Sciences, Chalmers University of Technology and Göteborg University, Gothenburg, Sweden. Linköpings universitet, Institutionen för teknik och naturvetenskap. Linköpings universitet, Tekniska högskolan.
A Comparison of Feasible Direction Methods for the Stochastic Transportation Problem2010Ingår i: Computational optimization and applications, ISSN 0926-6003, E-ISSN 1573-2894, Vol. 46, nr 3, s. 451-466Artikel i tidskrift (Refereegranskat)

The feasible direction method of Frank and Wolfe has been claimed to be efficient for solving the stochastic transportation problem. While this is true for very moderate accuracy requirements, substantially more efficient algorithms are otherwise diagonalized Newton and conjugate Frank–Wolfe algorithms, which we describe and evaluate. Like the Frank–Wolfe algorithm, these two algorithms take advantage of the structure of the stochastic transportation problem. We also introduce a Frank–Wolfe type algorithm with multi-dimensional search; this search procedure exploits the Cartesian product structure of the problem. Numerical results for two classic test problem sets are given. The three new methods that are considered are shown to be superior to the Frank–Wolfe method, and also to an earlier suggested heuristic acceleration of the Frank–Wolfe method.

• 119.
The Stiff is Moving - Conjugate Direction Frank -Wolfe Methods with Applications to Traffic Assignment2013Ingår i: Transportation Science, ISSN 0041-1655, E-ISSN 1526-5447, Vol. 47, nr 2, s. 280-293Artikel i tidskrift (Refereegranskat)

We present versions of the Frank-Wolfe method for linearly constrained convex programs, in which consecutive search directions are made conjugate. Preliminary computational studies in a MATLAB environment applying pure Frank-Wolfe, conjugate direction Frank-Wolfe (CFW), bi-conjugate Frank-Wolfe (BFW), and "partanized" Frank-Wolfe methods to some classical Traffic Assignment Problems show that CFW and BFW compare favorably to the other methods. This spurred a more detailed study, comparing our methods to an origin-based algorithm. This study indicates that our methods are competitive for accuracy requirements ensuring link flow stability. We also show that CFW is globally convergent. We further point at independent studies by other researchers that show that our methods compare favorably with recent bush-based and gradient projection algorithms on computers with several cores

• 120.
Linköpings universitet, Institutionen för ekonomisk och industriell utveckling, Mekanisk värmeteori och strömningslära. Linköpings universitet, Tekniska fakulteten.
Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten. Volvo Car Corporation, Göteborg, Sverige. Linköpings universitet, Institutionen för ekonomisk och industriell utveckling, Mekanisk värmeteori och strömningslära. Linköpings universitet, Tekniska fakulteten. Linköpings universitet, Centrum för medicinsk bildvetenskap och visualisering, CMIV.
Accuracy and Speed for Scale-Resolving Simulations of the DrivAer Reference Model2019Ingår i: WCX SAE World Congress Experience, SAE International , 2019Konferensbidrag (Refereegranskat)

In aerodynamic development of ground vehicles, the use of Computational Fluid Dynamics (CFD) is crucial for improving the aerodynamic performance, stability and comfort of the vehicle. Simulation time and accuracy are two key factors of a well working CFD procedure. Using scale-resolving simulations, accurate predictions of the flow field and aerodynamic forces are possible, but often leads to long simulation time. For a given solver, one of the most significant aspects of the simulation time/cost is the temporal resolution. In this study, this aspect is investigated using the realistic vehicle model DrivAer with the notchback geometry as the test case. To ensure a direct and accurate comparison with wind tunnel measurements, performed at TU Berlin, a large section of the wind tunnel is included in the simulation domain. All simulations are performed at a Reynolds number of 3.12 million, based on the vehicle length. Three spatial resolutions were compared, where it could be seen that a hybrid element mesh consisting of 102 million cells only revealed small differences to the finest mesh investigated, well as showing excellent agreement with wind tunnel measurements. An investigation of the temporal resolution is performed, in order to see its effect on the simulation time/cost and accuracy of the results. The finest temporal resolution resulted in a Courant-Friedrichs-Lewy number less than unity, while the coarsest reached a CFL number of around 100. From these results, it is seen that it is possible to reduce the simulation time with more than 90 % (CFL 20) and still keep sufficient accuracy of the forces and important features of the flow field.

• 121.
Linköpings universitet, Institutionen för teknik och naturvetenskap, Kommunikations- och transportsystem. Linköpings universitet, Tekniska fakulteten.
Trafikanalys, Sweco TransportSystem AB, Stockholm. Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten.

Trängselskatt finns idag i både Stockholm och Göteborg, och det är troligt att utformningen av dessa trängselskattesystem kommer att justeras framöver med avseende på avgiftsnivå, placering och tidpunkt. För Stockholm finns beslut om ändring från januari 2016 och i Göteborg ändrades avgiftsnivåerna i januari 2015. I detta projekt utvecklas metoder som ska kunna ge stöd vid justering av avigiftsnivåer, så att en så stor samhällsekonomisk nytta som är möjligt uppnås med trängselskattesystemet.

För storstadsområden, där det under rusningstrafik är trängsel i delar av nätverket, är trängselskatt främst intressant att analysera med dynamiska transportmodeller. Tidigare utveckling av metoder för optimal avgiftssättning har dock främst fokuserat på statiska modeller, exempelvis Emme, som har kända problem med att korrekt uppskatta förändring i restider när det är trängsel i delar av trafiknätverket. I detta projekt har vi därför tillämpat surrogat-baserad optimering, som är en metodansats som ställer få krav på vilken transportmodell som används. Den dynamiska transportmodellen Regent/VisumDUE finns sedan tidigare implementerad för Stockholmsregionen, och har därför även använts i detta projekt. VisumDUE är en makroskopisk nätutläggningsmodell med dynamiskt ruttval, och Regent är en efterfrågemodell som innehåller resgenerering, färdmedelsval och destinationsval för arbetsresor[1].

Surrogat-baserad optimering erbjuder ett ramverk för optimering av problem med beräkningsmässigt kostsamma målfunktioner. Genom att approximera en funktionsyta till samplade punkter från den kostsamma målfunktionen, kan optimeringen istället göras över den approximerade funktionsytan. För Regent/VisumDUE tar utvärderingen av ett givet trängselskattescenario ca tio timmar, och det är denna beräkningstid som gör målfunktionen kostsam. Givet ett antal samplade punkter, görs ytterligare sampling utifrån en given strategi för att förbättra approximationen, så kallad iterativ sampling. Inom ramverket finns dock en mängd möjligheter för hur de olika komponenterna designas. Därför är det svårt att utvärdera surrogat-baserad optimering med endast Regent/VisumDUE. En statisk transportmodell har därför använts för att utvärdera ett antal kombinationer av samplingsstrategi och funktionsyta. Den mest lovande kombinationen har sedan även utvärderats med Regent/VisumDUE. För att vara praktiskt tillämpbart i framtiden har fokus i projektet varit att utvärdera hur metodansatsen fungerar när antalet möjliga tulluppsättningar är kraftigt begränsat (20-40 stycken).

Det scenario som har använts som grund i projektet är trängselskatt i Stockholm på nuvarande tullring, på Essingeleden samt på innerstadsbroarna. Skatten är differentierad med avseende på riktning, vilket ger sex olika skattenivåer att optimera. Optimeringen har gjorts för trängselskattenivå under maxtimmen. I det dynamiska fallet har trängselskattens nivå utanför maxtimme funnits med som indata, men samma tidsprofil som på nuvarande tullring har antagits i alla scenarier (avgiftstrappa 50%, 75%, 100%, 75%, 50%). Utvärderingen med den statiska transportmodellen visar att lösningar nära globalt optimum kan uppnås med endast 40 utvärderade trängselskattenivåer, och en tydlig förbättring av den samhällsekonomiska nyttan uppnås redan vid 20 utvärderade trängselskattenivåer.

Även med ett kraftigt begränsat antal utvärderingar av den kostsamma målfunktionen i Regent/VisumDUE, har vi visat att det är möjligt att använda metodansatsen. En tydlig förbättring av den samhällsekonomiska nyttan uppnås med endast 22 utvärderade trängselskattenivåer. Ytterligare experiment skulle dock behövas för att undersöka hur stor denna förbättring är i förhållande till vad som skulle kunna uppnås.

fulltext
• 122.
Linköpings universitet, Institutionen för teknik och naturvetenskap, Kommunikations- och transportsystem. Linköpings universitet, Tekniska fakulteten.
Centre for Transport Studies, KTH Royal Institute of Technology, Stockholm, Sweden. Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten.
Surrogate-based optimization of cordon toll levels in congested traffic networks2016Ingår i: Journal of Advanced Transportation, ISSN 0197-6729, E-ISSN 2042-3195, Vol. 50, nr 6, s. 1008-1033Artikel i tidskrift (Refereegranskat)

The benefits, in terms of social surplus, from introducing congestion pricing schemes in urban networks are depending on the design of the pricing scheme. The major part of the literature on optimal design of congestion pricing schemes is based on static traffic assignment, which is known for its deficiency in correctly predict travels in networks with severe congestion. Dynamic traffic assignment can better predict travel times in a road network, but are more computational expensive. Thus, previously developed methods for the static case cannot be applied straightforward. Surrogate-based optimization is commonly used for optimization problems with expensive-to-evaluate objective functions. In this paper we evaluate the performance of a surrogate-based optimization method, when the number of pricing schemes which we can afford to evaluate (due to the computational time) is limited to between 20 and 40. A static traffic assignment model of Stockholm is used for evaluating a large number of different configurations of the surrogatebased optimization method. Final evaluation is done with the dynamic traffic assignment tool VisumDUE, coupled with the demand model Regent, for a Stockholm network including 1 240 demand zones and 17 000 links. Our results show that the surrogate-based optimization method can indeed be used for designing a congestion pricing scheme which return a high social surplus.

fulltext
• 123.
Linköpings universitet, Institutionen för teknik och naturvetenskap, Kommunikations- och transportsystem. Linköpings universitet, Tekniska högskolan.
Surrogate-based optimisation of toll levels in congestion pricing schemes2014Ingår i: Transportation Infrastructure: Proceedings of the 19th International Conference of Hong Kong Society for Transportation Studies (HKSTS) / [ed] Z. Leng and Y. H. Wang, Hong Kong: Hong Kong Society of Transportation Studies Limited , 2014, s. 209-216Konferensbidrag (Refereegranskat)

There has recently been a growing interest in analysing road pricing schemes in urban areas using dynamic traffic assignment (DTA) tools. Finding optimal toll levels in cordon based road pricing schemes has so far mainly been studied using either derivative-free heuristics or ascent methods. For future use of DTA tools such methods are not suitable and in this paper we investigate how a surrogate modelling framework can be used instead. We focus on cases when the number of costly objective function evaluations is limited to between 20 and 40. In order to allow a large number of different configurations of the surrogate modelling framework to be evaluated, a static user equilibrium model is used for simulating the road users’ response to a given pricing scheme. The results show that for a realistic scenario, valuable information on close to optimal toll levels can be achieved with only 20 costly function evaluations.

• 124.
Linköpings universitet, Institutionen för teknik och naturvetenskap, Kommunikations- och transportsystem. Linköpings universitet, Tekniska högskolan.
Simulation based optimisation of toll levels in urban road traffic networks2014Konferensbidrag (Övrigt vetenskapligt)

There has recently been a growing interest in analysing road pricing schemes in urban areas using dynamic traffic assignment (DTA) tools. The motivation behind this development is the problem for static transportation models to accurately predict travel time savings, from introducing road pricing, in networks with severe congestion. Finding optimal toll levels and locations in urban road traffic networks has so far mainly been studied using either derivative-free heuristics (e.g. genetic algorithms and simulated annealing) or ascent methods. Both approaches rely on fast computations of the road users response (traffic flows, travel times and demands), given the road pricing scheme, and for the case of ascent methods, the methods also rely on fast computations (or rather approximation) of derivatives. Using DTA tools for evaluating the road users’ response to a pricing scheme is, however, very computationally expensive. Previously developed methods are therefore not suitable to use together with DTA.

Surrogate models, e.g. in terms of response surfaces, are commonly used for optimisation problems with expensive-to-evaluate objective functions. The surrogate model is used for approximating the expensive-to-evaluate objective function, and the optimisation is then done on the surrogate model instead. The performances of optimisation methods based on surrogate models are, however, dependent on experimental design, infill strategy and choice of surrogate model itself. The experimental design will give the initial set of toll levels, for which the DTA needs to be evaluated, the infill strategy determined additional toll levels to be evaluated by the DTA, and the choice of surrogate model will give the functional form to be fitted to the sampled toll levels.

We apply a surrogate model framework for optimising toll levels in a multiple cordon pricing scheme. In the first stage we evaluate the experimental design, infill strategy and choice of surrogate model, using a static macroscopic traffic model.  This allows a large number of experiments to be carried out, which would not be possible with a DTA tool. It also allows us to compare the performance of the surrogate modelling approach with other global optimisation methods. In the second stage, the insight which has been gained from the experiments with the static model is used when applying the surrogate modelling approach to a DTA model of Stockholm.

Computational results are presented for a Stockholm network with three cordons, each with differentiated toll level in both directions, resulting in a total of six toll level variables. Surrogate models in the form of Radial Basis Functions and Kriging models are evaluated with a static model of Stockholm, for different initial experimental designs, infill strategies and choice of surrogate models. In comparison with previously developed derivative based methods for static models, our results show that the surrogate based optimisation approach performs better, since it allows for metaheuristic methods to search for global optimal solutions efficiently.

• 125.
Multi-Class User Equilibria under Social Marginal Cost Pricing2002Ingår i: Operations Research 2002, 2002, s. 174-179Konferensbidrag (Övrigt vetenskapligt)

In the congested cities of today, congestion pricing is a tempting alternative. With a single user class, already Beckmann et al. showed that ``system optimal'' traffic flows can be achieved by social marginal cost (SMC) pricing where users have to pay for the delays the incur on others. However different user classes can have widly differing time values. Hence, when introducing tolls, one should consider multi-class user equilibria, where the classes have different time values. In the single class case, the equilibrium conditions can be viewn as optimality conditions of an equivalent optimization problem. In the multi-class case, however, netter claims that this is not possible. We show that, depending on the formulation, the multi-class SMC-pricing equilibrium problem (with different time values) can be stated either as an asymmetric or as a symmetric equilibrium problem. In the latter case, the corresponding optimization problems is in general non-convex. For this non-convex problem, we devise descent methods of Frank-Wolfe type. We apply the methods and study a synthetic case based on Sioux Falls.

• 126. Engevall, Stefan
A strong lower bound for the node weighted Steiner tree problem1998Ingår i: Networks, ISSN 0028-3045, E-ISSN 1097-0037, Vol. 31, s. 11-17Artikel i tidskrift (Refereegranskat)
• 127.
The heterogeneous vehicle-routing game2004Ingår i: Transportation Science, ISSN 0041-1655, E-ISSN 1526-5447, Vol. 38, nr 1, s. 71-85Artikel i tidskrift (Refereegranskat)

In this paper, we study a cost-allocation problem that arises in a distribution-planning situation at the Logistics Department at Norsk Hydro Olje AB, Stockholm, Sweden. We consider the routes from one depot during one day. The total distribution cost for these routes is to be divided among the customers that are visited. This cost-allocation problem is formulated as a vehicle-routing game (VRG), allowing the use of vehicles with different capacities. Cost-allocation methods based on different concepts from cooperative game theory, such as the core and the nucleolus, are discussed. A procedure that can be used to investigate whether the core is empty or not is presented, as well as a procedure to compute the nucleolus. Computational results for the Norsk Hydro case are presented and discussed.

• 128. Eriksson, Jonas
Decision support system/tools: Transportation and route planning2003Ingår i: 2nd Forest Engineering Conference,2003, 2003, s. 48-57Konferensbidrag (Övrigt vetenskapligt)
• 129.
Cost-Minimizing Choice Behavior in Transportation Planning: A Theoretical Framework fo Logit Models2010Bok (Övrigt vetenskapligt)

This book stems from a desire to understand the underlying assumptions and structureof the choice probability models most often used in transportation planning. The bookinvestigates how far a new way of defining cost minimizing behavior can take us. Allcommonly used choice probability distributions of the logit type – log linear probabilityfunctions – follow from cost minimizing behavior defined in the new way; some newnested models also appear. The new approach provides a deeper understanding of whatis at work in the models. The new way of defining cost minimizing behavior is as follows:cost minimizing behavior pertains if the likelihood (probability) of any independentsample of observations is a decreasing function of the average cost of the sample.Extreme value distributed random variables are not used in the derivation of models. Ameasure of freedom of choice related to the Shannon measure of how much "choice" isinvolved is used to obtain a welfare measure which is equal to composite cost.... more on http://springer.com/978-3-642-11910-1

• 130.
Welfare, freedom of choice and composite utility in the logit model2005Ingår i: Social Choice and Welfare, ISSN 0176-1714, E-ISSN 1432-217X, Vol. 24, nr 3, s. 509-525Artikel i tidskrift (Refereegranskat)

Discrete choice models characterize the alternatives in the choice set by utilities/attributes. The decision making is described by a probability distribution over the choice set. In this paper we introduce a welfare measure based on expected payoff and expected freedom of choice for the simple one parameter logit model. In this case the welfare measure turns out to be the so called composite utility. This means that the composite utility can be interpreted as the combined benefit of expected payoff and expected freedom of choice. The proposed welfare measure can be extended to the linear-in-parameters logit model and nested logit models and others. The proposed welfare measure is formulated in terms of the choice probability distribution. It depends on the form of the probabilities, but not on any particular derivation of the distribution.

• 131.
Linköpings universitet, Institutionen för teknik och naturvetenskap.
Cost Minimizing Behavior in Discrete Choice Modeling2003Ingår i: 50th Annual North American meetings of the Regional Science Association International,2003, 2003Konferensbidrag (Övrigt vetenskapligt)
• 132.
Cost minimizing behavior in random discrete choice modelling2004Ingår i: Urban and Regional Transportation Modeling: essays in honor of David Boyce / [ed] Der-Horng Lee, David E. Boyce, Cheltenham, UK: Edward Elgar , 2004, s. 70-82Kapitel i bok, del av antologi (Övrigt vetenskapligt)

Honoring David Boyce for his legendary contributions to the fields of transportation modeling and regional science, the chapters in this festschrift highlight and analyze state-of-the-art and state-of-the-practice methodologies and theories in transportation modeling, regional and urban planning. Authors from academia and industry, all experts in planning, engineering, management, economics and related disciplines, provide important new contributions to this wide-ranging literature, as well as extensions of David Boyce's seminal work. This volume goes well beyond the traditional festschrift and stands as an important reference tool in its own right. Academics, researchers and students will find this comprehensive volume a valuable additional to their library.

• 133.
Models and methods for school timetabling using a column generation approach2002Licentiatavhandling, monografi (Övrigt vetenskapligt)

Creating timetables for educational institutions is a complex task, and the quality of the timetables affects a large number of students and teachers. This process involves assigning teachers to courses, students to classes, classrooms to lessons and setting the starting time of the lessons.

In this thesis, models and solution methods are presented for the assignment of starting times and classrooms as appearing in Swedish schools. This school system has two aspects that make timetabling particularly hard. The first is the mix of both individual and class based timetables, and the second that lessons can have any length unlike many other school systems which only has lessons of the same length. For the timetables to be of practical interest, modelling of quality aspects of a timetable is also a major issue.

A first generalised set-packing model is presented for the problem, with a column representing a feasible schedule for one class. Solution techniques involving column generation and constraint branching are developed and presented. This model is deemed too complex to solve, and a sequential solution approach that solves the problem in several stages is presented. The models and solution techniques in the sequential solution approach also involve column generation and constraint branching. The models allow for a capturing many quality aspects of a timetable. The sequential solution approach is tested on a test database, and the results are presented and discussed. A study of improving the performance of the branch-andbound method is finally presented.

• 134.
Laps Care: an operational system for staff planning of home care2006Ingår i: European Journal of Operational Research, ISSN 0377-2217, E-ISSN 1872-6860, Vol. 171, nr 3, s. 962-976Artikel i tidskrift (Refereegranskat)

The health care system in Sweden and many other countries is facing increasing costs. The major reason is the changing age distribution of the population with more elderly people in need of support. At the same time, health care systems are often very labor and staff intensive. In this paper, we focus on a staff planning problem arising in Sweden where people receive home care from the local authorities. The objective is to develop visiting schedules for care providers that incorporate some restrictions and soft objectives. Each visit has a particular task to be performed, for example: cleaning, washing, personal hygiene and/or nursing activities. Each staff member has skills and each client should, if possible, be visited by the same contact person. The operational situation is continuously changing and planning is done each day. We describe the development of a decision support system Laps Care to aid the planners. The system consists of a number of components including information data bases, maps, optimization routines, and report possibilities. We formulate the problem using a set partitioning model and, for a solution method, we make use of a repeated matching algorithm. The system is currently in operation at a number of home care organizations. We report on the practical impact of the system in the health care organization which was involved in the development. The savings are considerably in terms of saved planning time and in the quality of the routes, as well as the measured quality for the clients. Numerical experiments of the system are presented.

• 135.
Application of operations research in operative planning in the forest industry2007Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)

The focus of this thesis is the use of Operations Research for pplications in the forest industry. Optimization models and methods have been developed for problems in the forest supply chain and they have been integrated in decision support systems. The problems considered in this thesis are operative with a planning horizon of less than a month. Short solution times for the methods and the feasibility of the models used are important aspects. The body of this thesis consists of eight research papers where six of them consider operative problems and follows the forest supply chain. The industrial applications include routing of forwarders, routing of logging trucks, a process control problem, and roll cutting problems. The other two papers consider an operative planning problem in the home care sector. They are spin offs from one of the other projects in this thesis. In these applications both linear and nonlinear problems occur.

The forwarding problem is to decide routes for forwarders to pick up the small piles of logs the harvesters have left in the harvest areas. The forwarders then put the logs adjacent to forest roads. The logging truck problem is to decide routes for logging trucks to pick up the piles created by the forwarders and transport them to demand points, for example pulp or paper mills. The process control problem appear in the bleaching stage of a pulp mill where the control variables are the bleaching chemical charges. The cost of bleaching chemicals is minimized while a finishing brightness within target values is ensured. Mainly two roll cutting problems are studied. One is to minimize the number of cutting patterns and one is to minimize the number of reels when defects in the papper reels are considered. The solution methods developed for the forwarding problem have also been applied to a routing problem which appears in staff planning for home care operations.

The different DSS developed and implemented have been tested and several are in daily industrial use. In each of the papers, we have developed robust OR models and quick and effective OR methods. The savings from using the systems vary but are typically in the range 5-20%.

1. Optimization based planning tools for routing of forwarders at harvest areas
Öppna denna publikation i ny flik eller fönster >>Optimization based planning tools for routing of forwarders at harvest areas
2007 (Engelska)Ingår i: Canadian Journal of Forest Research, ISSN 0045-5067, E-ISSN 1208-6037, Vol. 37, nr 11, s. 2153-2163Artikel i tidskrift (Refereegranskat) Published
##### Abstract [en]

The forwarding of logs at harvest areas once the harvesting is done is planned manually by experienced operators. To improve their efficiency and simplify the planning we have developed and tested a decision support system at a major Swedish forest company. The system is based on a combination of a geographic information system (GIS), global positioning system (GPS), and optimization routines to solve the underlying vehicle routing problem. The routes for the forwarders are found by using a repeated matching algorithm. The solution time is short, and it is possible to find routes dynamically in a real-time environment. The geographic information required is found by using a GPS together with data obtained from the bucking software in the harvesters. To show the routes and location of the forwarder, we make use of a GIS that is connected to the GPS. We report on a study with savings in the distance travelled of 8% and numerical tests on the solution methodology. We also compare the proposed solution method with some well-known routing methods.

##### Nationell ämneskategori
Teknik och teknologier
##### Identifikatorer
urn:nbn:se:liu:diva-47900 (URN)10.1139/X07-065 (DOI)
2. A hybrid method based on linear programming and tabu search for routing of logging trucks
Öppna denna publikation i ny flik eller fönster >>A hybrid method based on linear programming and tabu search for routing of logging trucks
2009 (Engelska)Ingår i: Computers & Operations Research, ISSN 0305-0548, E-ISSN 1873-765X, Vol. 36, nr 4, s. 1122-1144Artikel i tidskrift (Refereegranskat) Published
##### Abstract [en]

In this paper, we consider an operational routing problem to decide the daily routes of logging trucks in forestry. This industrial problem is difficult and includes aspects such as pickup and delivery with split pickups, multiple products, time windows, several time periods, multiple depots, driver changes and a heterogeneous truck fleet. In addition, the problem size is large and the solution time limited. We describe a two-phase solution approach which transforms the problem into a standard vehicle routing problem with time windows. In the first phase, we solve an LP problem in order to find a destination of flow from supply points to demand points. Based on this solution, we create transport nodes which each defines the origin(s) and destination for a full truckload. In phase two, we make use of a standard tabu search method to combine these transport nodes, which can be considered to be customers in vehicle routing problems, into actual routes. The tabu search method is extended to consider some new features. The solution approach is tested on a set of industrial cases from major forest companies in Sweden.

##### Nyckelord
Forestry, Routing, Tabu search, Linear Programming, OR in Practice
##### Nationell ämneskategori
Teknik och teknologier
##### Identifikatorer
urn:nbn:se:liu:diva-85519 (URN)10.1016/j.cor.2007.12.012 (DOI)
3. RuttOpt: a decision support system for routing of logging trucks
Öppna denna publikation i ny flik eller fönster >>RuttOpt: a decision support system for routing of logging trucks
2008 (Engelska)Ingår i: Canadian Journal of Forest Research, ISSN 0045-5067, E-ISSN 1208-6037, Vol. 38, nr 7, s. 1784-1796Artikel i tidskrift (Refereegranskat) Published
##### Abstract [en]

We describe the decision support system RuttOpt, which is developed for scheduling logging trucks in the forest industry. The system is made up of a number of modules. One module is the Swedish road database NVDB, which consists of detailed information of all of the roads in Sweden. This also includes a tool to compute distances between locations. A second module is an optimization routine that finds a schedule, i.e., set of routes for all trucks. This is based on a two-phase algorithm where linear programming and a standard tabu search method are used. A third module is a database storing all relevant information. At the center of the system is a user interface where information and results can be viewed on maps, Gantt schedules, and result reports. The RuttOpt system has been used in a number of case studies and we describe four of these. The case studies have been made in both forest companies and hauling companies. The cases range from 10 to 110 trucks and with a planning horizon ranging between 1 and 5 days. The results show that the system can be used to solve large case studies and that the potential savings are in the range 5%–30%.

##### Nationell ämneskategori
Teknik och teknologier
##### Identifikatorer
urn:nbn:se:liu:diva-85521 (URN)10.1139/X08-017 (DOI)
4. Pulp fact, not fiction
Öppna denna publikation i ny flik eller fönster >>Pulp fact, not fiction
2005 (Engelska)Ingår i: OR/MS Today, ISSN 1085-1038, Vol. 32, nr 2, s. 42-47Artikel i tidskrift (Refereegranskat) Published
##### Abstract [en]

By taking the guesswork out of the equation, operations research-based process control system helps cut costs, reduce environmental impact at Swedish paper mill.

##### Nationell ämneskategori
Teknik och teknologier
##### Identifikatorer
urn:nbn:se:liu:diva-85522 (URN)
5. Optimized on-line process control of bleaching operations with OptCab
Öppna denna publikation i ny flik eller fönster >>Optimized on-line process control of bleaching operations with OptCab
2007 (Engelska)Ingår i: Norges Handelshoeyskole. Institutt for Foretaksoekonomi. Discussion Paper, ISSN 1500-4066Artikel, forskningsöversikt (Refereegranskat) Published
##### Abstract [en]

To produce pulp for paper production or as market pulp is a complicated on-line process with many integrated stages that impact the final quality. In the bleaching plant which is at the end of pulp production, the main objective is to increase pulp brightness within specified limits. Here chemical treatments are applied in sequential stages to achieve the right brightness while striving to maintain the pulp strength as unaffected as possible. The raw material, i.e. pulp logs and wood chips from saw mills, differ in quality and properties. Due to this, it is important to continuously update the amount of chemicals added to the pulp in real-time. This is typically done by experienced operators. In this paper, we describe an on-line optimization based decision support system called OptCab that controls the bleaching process at Billerud AB's paper mill in Skärblacka. The solution approach is based on two phases. In phase one, we establish approximations of each of the processes based on process data collected on-line. These approximations are found by solving a set of constrained least square problems and are updated every 15 minutes. In phase two, we formulate an overall nonlinear control problem that links all stages together and aims to minimize the cost of chemicals. This is solved on-line every five minutes. The system has been in operation during the last three years providing a 10% reduction in the use of chemicals. Additional benefits include a more stable brightness quality.

##### Nationell ämneskategori
Teknik och teknologier
##### Identifikatorer
urn:nbn:se:liu:diva-85523 (URN)
##### Anmärkning

This is a working paper.

6. Roll cutting at paper mills
Öppna denna publikation i ny flik eller fönster >>Roll cutting at paper mills
2002 (Engelska)Ingår i: Proceedings of the Control Systems 2002, 2002, s. 159-163Konferensbidrag, Publicerat paper (Övrigt vetenskapligt)
##### Abstract [en]

Roll cutting has attracted a great deal of research attention. However, most of the development of models and methods in academic research has not considered some key industrial requirements. These are practical production aspects that often create non-tractable optimization problems. In this paper, we study two important problems and show how these can be solved efficiently in an industrial setting. These are operative roll cutting where the number of reels and different patterns should be minimized and real-time cutting, when defects and quality restrictions on ordered rolls are included.

##### Nationell ämneskategori
Teknik och teknologier
##### Identifikatorer
urn:nbn:se:liu:diva-85524 (URN)
##### Konferens
Control Systems 2002, June 3-5, Stockholm, Sweden
7. Home care operations
Öppna denna publikation i ny flik eller fönster >>Home care operations
2004 (Engelska)Ingår i: OR/MS today, ISSN 1085-1038, Vol. April, s. 38-43Artikel i tidskrift (Refereegranskat) Published
##### Abstract [en]

No abstract available.

Matematik
##### Identifikatorer
urn:nbn:se:liu:diva-22746 (URN)2060 (Lokalt ID)2060 (Arkivnummer)2060 (OAI)
8. Laps Care: an operational system for staff planning of home care
Öppna denna publikation i ny flik eller fönster >>Laps Care: an operational system for staff planning of home care
2006 (Engelska)Ingår i: European Journal of Operational Research, ISSN 0377-2217, E-ISSN 1872-6860, Vol. 171, nr 3, s. 962-976Artikel i tidskrift (Refereegranskat) Published
##### Abstract [en]

The health care system in Sweden and many other countries is facing increasing costs. The major reason is the changing age distribution of the population with more elderly people in need of support. At the same time, health care systems are often very labor and staff intensive. In this paper, we focus on a staff planning problem arising in Sweden where people receive home care from the local authorities. The objective is to develop visiting schedules for care providers that incorporate some restrictions and soft objectives. Each visit has a particular task to be performed, for example: cleaning, washing, personal hygiene and/or nursing activities. Each staff member has skills and each client should, if possible, be visited by the same contact person. The operational situation is continuously changing and planning is done each day. We describe the development of a decision support system Laps Care to aid the planners. The system consists of a number of components including information data bases, maps, optimization routines, and report possibilities. We formulate the problem using a set partitioning model and, for a solution method, we make use of a repeated matching algorithm. The system is currently in operation at a number of home care organizations. We report on the practical impact of the system in the health care organization which was involved in the development. The savings are considerably in terms of saved planning time and in the quality of the routes, as well as the measured quality for the clients. Numerical experiments of the system are presented.

##### Nyckelord
health care; home care; staff planning; modelling; heuristics; optimization; practice of OR
##### Nationell ämneskategori
Samhällsvetenskap
##### Identifikatorer
urn:nbn:se:liu:diva-53494 (URN)10.1016/j.ejor.2005.01.011 (DOI)
• 136.
Staff planning in the Swedish home care system2003Rapport (Övrigt vetenskapligt)
• 137.
Sveaskog, Östersund, Sweden (during the project, M. Forsberg was employed at the Forestry Research Institute of Sweden). Forestry Research Institute of Sweden, Uppsala, Sweden, and Norwegian School of Economics and Business Administration, Bergen, Norway.
Optimization based planning tools for routing of forwarders at harvest areas2007Ingår i: Canadian Journal of Forest Research, ISSN 0045-5067, E-ISSN 1208-6037, Vol. 37, nr 11, s. 2153-2163Artikel i tidskrift (Refereegranskat)

The forwarding of logs at harvest areas once the harvesting is done is planned manually by experienced operators. To improve their efficiency and simplify the planning we have developed and tested a decision support system at a major Swedish forest company. The system is based on a combination of a geographic information system (GIS), global positioning system (GPS), and optimization routines to solve the underlying vehicle routing problem. The routes for the forwarders are found by using a repeated matching algorithm. The solution time is short, and it is possible to find routes dynamically in a real-time environment. The geographic information required is found by using a GPS together with data obtained from the bucking software in the harvesters. To show the routes and location of the forwarder, we make use of a GIS that is connected to the GPS. We report on a study with savings in the distance travelled of 8% and numerical tests on the solution methodology. We also compare the proposed solution method with some well-known routing methods.

• 138.
Billerud AB, Skärblacka, Sweden. Department of Finance and MAnagement Science, Norwegion School of Economics and Business Administration, Bergen, Norway.
Optimized on-line process control of bleaching operations with OptCab2007Ingår i: Norges Handelshoeyskole. Institutt for Foretaksoekonomi. Discussion Paper, ISSN 1500-4066Artikel, forskningsöversikt (Refereegranskat)

To produce pulp for paper production or as market pulp is a complicated on-line process with many integrated stages that impact the final quality. In the bleaching plant which is at the end of pulp production, the main objective is to increase pulp brightness within specified limits. Here chemical treatments are applied in sequential stages to achieve the right brightness while striving to maintain the pulp strength as unaffected as possible. The raw material, i.e. pulp logs and wood chips from saw mills, differ in quality and properties. Due to this, it is important to continuously update the amount of chemicals added to the pulp in real-time. This is typically done by experienced operators. In this paper, we describe an on-line optimization based decision support system called OptCab that controls the bleaching process at Billerud AB's paper mill in Skärblacka. The solution approach is based on two phases. In phase one, we establish approximations of each of the processes based on process data collected on-line. These approximations are found by solving a set of constrained least square problems and are updated every 15 minutes. In phase two, we formulate an overall nonlinear control problem that links all stages together and aims to minimize the cost of chemicals. This is solved on-line every five minutes. The system has been in operation during the last three years providing a 10% reduction in the use of chemicals. Additional benefits include a more stable brightness quality.

• 139.
Billerud AB, Skärblacka, Sweden. Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
Pulp fact, not fiction2005Ingår i: OR/MS Today, ISSN 1085-1038, Vol. 32, nr 2, s. 42-47Artikel i tidskrift (Refereegranskat)

By taking the guesswork out of the equation, operations research-based process control system helps cut costs, reduce environmental impact at Swedish paper mill.

• 140.
Billerud Optimizes Its Bleaching Process Using Online Optimization2009Ingår i: INTERFACES, ISSN 0092-2102 , Vol. 39, nr 2, s. 119-131Artikel i tidskrift (Refereegranskat)

Billerud, a Swedish company with four integrated pulp and paper mills, serves specific packaging-market segments. In 2000, the process-engineering department at Billeruds mill in Skarblacka sought to improve the mills bleaching process. It contacted Linkoping University, which collaborated with Eurocon Automation AB to develop a decision-support system, OptCab. Eurocon Automation AB now offers OptCab as a general tool in the market. Its core is an online optimization system that dynamically updates a process description and optimizes the bleaching control process. The system, which has been fully operational since 2004, has provided numerous benefits to Billerud. Chemical use has decreased by approximately 10 percent, saving approximately two million euros since its installation; the environmental impact has also been reduced; and the brightness quality of paper that the mill produces is more uniform and stable. Moreover, OptCab requires less operator time, freeing the operators for development and analysis work.

• 141.
Skogforsk.
FlowOpt - A new decision support system in the forest supply chain2004Ingår i: NOFOMA 2004,2004, 2004Konferensbidrag (Övrigt vetenskapligt)
• 142.
Linköpings universitet, Institutionen för medicinsk teknik, Biomedicinsk instrumentteknik. Linköpings universitet, Tekniska högskolan. Perimed AB, Järfälla, Sweden.
Inverse Monte Carlo in a multilayered tissue model: merging diffuse reflectance spectroscopy and laser Doppler flowmetry2013Ingår i: Journal of Biomedical Optics, ISSN 1083-3668, E-ISSN 1560-2281, Vol. 18, nr 12, s. 127004-1-127004-14Artikel i tidskrift (Refereegranskat)

The tissue fraction of red blood cells (RBCs) and their oxygenation and speed-resolved perfusion areestimated in absolute units by combining diffuse reflectance spectroscopy (DRS) and laser Doppler flowmetry(LDF). The DRS spectra (450 to 850 nm) are assessed at two source–detector separations (0.4 and 1.2 mm), allowingfor a relative calibration routine, whereas LDF spectra are assessed at 1.2mmin the same fiber-optic probe. Data areanalyzed using nonlinear optimization in an inverse Monte Carlo technique by applying an adaptive multilayeredtissue model based on geometrical, scattering, and absorbing properties, as well as RBC flow-speed information.Simulations of 250 tissue-like models including up to 2000 individual blood vessels were used to evaluatethe method. The absolute root mean square (RMS) deviation between estimated and true oxygenation was 4.1percentage units, whereas the relative RMS deviations for the RBC tissue fraction and perfusion were 19% and23%, respectively. Examples of in vivo measurements on forearm and foot during common provocations arepresented. The method offers several advantages such as simultaneous quantification of RBC tissue fractionand oxygenation and perfusion from the same, predictable, sampling volume. The perfusion estimate is speedresolved, absolute (% RBC × mm∕s), and more accurate due to the combination with DRS.

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• 143.
Artikelplacering i lager: Simulering med Arena2018Självständigt arbete på grundnivå (kandidatexamen), 10,5 poäng / 16 hpStudentuppsats (Examensarbete)

Fallstudier visar att man kan erhålla betydliga fördelar om man designar och driver ett lager på ett lämpligt sätt. Man har även genom analytiskamodeller och simuleringar visat att transporttiden kan hållas nere om artiklarna lagerhålls på bestämda platser i lagret. Det är dock inte alltid självklart vilken strategi som är bäst i verkligheten. Företaget i fråga, som önskar vara anonymt, undrade om man kunde minska tiden för utsortering av artiklar till utlastningslagret samt orderplock genom att ändra utseendet på lagret. I detta arbete har vi använt oss av simuleringsprogrammet Arena för att ta fram en rekommendation för hur artikelplaceringen bör se ut för två utvalda produkter hos företaget. Dagens lagerlayout jämförs med en alternativ lagerlayout där valda artiklar placeras efter produkttyp istället för orderns destination, detta för att jämföra tidsåtgången under de olika placeringarna. Enligt resultaten kan företaget dra ner på kostnaderna genom att ändra utseendet på lagret. För den ena produkten var dessutom placering efter produkttyp statistiskt signifikant bättre än nuvarande placering baserad på artikelns destination. Men då den alternativa placeringen inte uppfyller önskad besparing på 20–25% så kan vi inte rekommendera företaget att byta till den för någon av produkterna. Det företaget skulle kunna jobba mer med är hur man kan minska avlastningstiden av artiklarna, då det visade sig vara den mest tidskrävande processen under utsorteringen.

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• 144.
Optimal Routing of Snowplows - A Column generation Approach2003Ingår i: Operations Research 2002,2002, Heidelberg: Springer , 2003, s. 199-Konferensbidrag (Refereegranskat)
• 145.
Rotating Workforce Scheduling2015Självständigt arbete på avancerad nivå (masterexamen), 20 poäng / 30 hpStudentuppsats (Examensarbete)

Several industries use what is called rotating workforce scheduling. This often means that employees are needed around the clock seven days a week, and that they have a schedule which repeats itself after some weeks. This thesis gives an introduction to this kind of scheduling and presents a review of previous work done in the field. Two different optimization models for rotating workforce scheduling are formulated and compared, and some examples are created to demonstrate how the addition of soft constraints to the models affects the scheduling outcome. Two large realistic cases, with constraints commonly used in many industries, are then presented. The schedules are in these cases analyzed in depth and evaluated. One of the models excelled as it provides good results within a short time limit and it appears to be a worthy candidate for rotating workforce scheduling.

Rotating Workforce Scheduling
• 146.
Isotonic regression and normalisation of environmental quality data2003Ingår i: TIES The International Environmetrics Society 2003,2003, 2003Konferensbidrag (Övrigt vetenskapligt)
• 147.
Optimization approaches to tactical planning problems in the forest industry2004Licentiatavhandling, sammanläggning (Övrigt vetenskapligt)

By using decision support tools based on operations research (OR) and optimization in the supply chain in the forest industry, the planning process can be improved and higher profitability can be obtained. The focus of this thesis is on modelling two real-life problems. The problems are united by the facts that they concern tactical (annual) planning in the forest industry, and that the models are developed and tested with real data at Swedish companies.

In the first paper, a problem of the supply chain of forest fuel is modelled and solved. The problem of deciding when and where forest residues are to be converted into forest fuel, and how the residues are to be t ransported and stored in order to satisfy demand at heating plants is studied. Decisions also include whether or not additional harvest areas and saw-mills are to be contracted. In addition, we consider the flow of products from saw-mills and import harbours, and address the question about which terminals to use. The planning horizon is one year and monthly time periods are considered. The test data is from Sydved Energileveranser AB.

The second paper is a case study from Södra Cell AB. A combined problem of terminal location and ship routing is studied. The objective is to minimize the costs of distributing pulp products from pulp mills to customers (paper mills). Shipping vessels chartered on short or long term are used to transport products to terminals in Europe. In addition, trains and lorries are used for direct transports to customers from mills. From each terminal, the products are transported to customers by lorry, train, or a combination of both. Decisions about which terminals to use, which shipping routes to use, and which other transportation possibilities to use are included.

In both problems, relatively large mixed integer programming (MIP) models have been developed and solved using a commercial lp (linear programming) solver. Heuristics have also been developed in both problems in order to obtain faster solutions. Several scenarios of the problems have been tested and evaluated.

1. Supply chain modelling of forest fuel
Öppna denna publikation i ny flik eller fönster >>Supply chain modelling of forest fuel
2004 (Engelska)Ingår i: European Journal of Operational Research, ISSN 0377-2217, Vol. 158, nr 1, s. 103-123Artikel i tidskrift (Refereegranskat) Published
##### Abstract [en]

We study the problem of deciding when and where forest residues are to be converted into forest fuel, and how the residues are to be transported and stored in order to satisfy demand at heating plants. Decisions also include whether or not additional harvest areas and saw-mills are to be contracted. In addition, we consider the flow of products from saw-mills and import harbors, and address the question about which terminals to use. The planning horizon is one year and monthly time periods are considered. The supply chain problem is formulated as a large mixed integer linear programming model. In order to obtain solutions within reasonable time we have developed a heuristic solution approach. Computational results from a large Swedish supplying entrepreneur are reported.

##### Nyckelord
Supply chain management, Integer programming, Inventory, Transportation
Matematik
##### Identifikatorer
urn:nbn:se:liu:diva-14461 (URN)10.1016/S0377-2217(03)00354-0 (DOI)
2. A combined terminal location and ship routing problem
Öppna denna publikation i ny flik eller fönster >>A combined terminal location and ship routing problem
2006 (Engelska)Ingår i: Journal of the Operational Research Society, ISSN 0160-5682, Vol. 57, nr 8, s. 928-938Artikel i tidskrift (Refereegranskat) Published
##### Abstract [en]

In this paper, we consider a combined terminal location and ship routing problem at Södra Cell AB. The purpose is to supply the customers' annual demand for pulp products while minimizing the distribution costs. Customers are supplied with various pulp products from pulp mills in Scandinavia by ships, trains, or lorries. The ship routes go from the pulp mills to terminals in Europe. From each terminal, the products are transported to customers by lorry, train, or barge. Some customers can be supplied directly from the pulp mills by trains or lorries. We have developed a mathematical model to select which terminals to use and, at the same time, determine the shipping routes. The mixed integer programming model was solved directly using a commercial solver. When the number of routes generated is large, the time required to obtain an optimal solution is too long. Hence, we have developed heuristics in order to obtain an acceptable solution in reasonable time. In addition to the basic case, five different scenarios were tested. Our heuristics provide solutions that are within 0.12% of the optimal ones.

##### Nyckelord
mixed integer programming, facility location, transportation, ship routing
Matematik
##### Identifikatorer
urn:nbn:se:liu:diva-14462 (URN)10.1057/palgrave.jors.2602057 (DOI)
• 148.
Decision support system/tools: Optimization of transportation, storage and chipping of forest fuel2003Ingår i: 2nd Forest Engineering Conference,2003, 2003, s. 74-82Konferensbidrag (Övrigt vetenskapligt)
• 149.
Linköpings universitet, Institutionen för teknik och naturvetenskap, Kommunikations- och transportsystem. Linköpings universitet, Tekniska högskolan. Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Optimeringslära.
Supply chain modelling of forest fuel2003Ingår i: Systems analysis in forest resources :: proceedings of the eighth symposium, held September 27-30, 2000, Snowmass Village, Colorado, USA / [ed] Greg J. Arthaud and Tara M. Barrett, Kluwer , 2003, s. -326Kapitel i bok, del av antologi (Övrigt vetenskapligt)

Systems analysis in forestry has continued to advance in sophistication and diversity of application over the last few decades. The papers in this volume were presented at the eighth symposium in the foremost conference series worldwide in this subject area. Techniques presented include optimization and simulation modelling, decision support systems, alternative planning techniques, and spatial analysis. Over 30 papers and extended abstracts are grouped into the topical areas of (1) fire and fuels; (2) networks and transportation; (3) forest and landscape planning; (4) ecological modeling, biodiversity, and wildlife; and (5) forest resource applications. This collection will be of interest to forest planners and researchers who work in quantitative methods in forestry.

• 150.
Department of Finance and Management Science, Norwegian School of Economics and Business Administration.
Solving a multi-period supply chain problem for a pulp company using heuristics—An application to Södra Cell AB2008Ingår i: International Journal of Production Economics, ISSN 0925-5273, E-ISSN 1873-7579, Vol. 116, nr 1, s. 75-94Artikel i tidskrift (Refereegranskat)

In this paper, the integrated planning of production and distribution for a pulp company is considered. The tactical decisions included regard transportation of raw materials from harvest areas to pulp mills; production mix and contents at pulp mills; inventory; distribution of pulp products from mills to customers and the selection of potential orders and their levels at customers. The planning period is one year and several time periods are included. As a solution approach we make use of two different heuristic approaches. The main reason to use heuristics is the need for quick solution times. The first heuristic is based on a rolling planning horizon where iteratively a fixed number of time periods is taken into consideration. The second heuristic is based on Lagrangian decomposition and subgradient optimization. This provides optimistic bounds of the optimal objective function value that are better than the LP relaxation value, which can be used as a measure of the heuristic (pessimistic) solution quality. In addition, we apply the proposed rolling horizon heuristic in each iteration of the subgradient optimization. A number of cases based on real data is analysed which shows that the proposed solution approach is simple and provides high quality solutions.

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