The BMW Group uses load units for the transportation of assembly parts from the suppliers to the plants and for the internal material flow. This thesis analyses the advantageousness of introducing a load unit with a new size. There are three reasons why the current choice of containers is not sufficient. Firstly, there is a certain range of assembly parts that does not fit very well into the existing standard load units. Secondly, the average measurements of the parts have grown in the last years and thirdly, several of the existing containers leave unused space in the transportation vehicles. For this the relevant costs and other, more qualitative aspects like the placing at the assembly line are considered. A container size is identified that offers a significant savings potential. For this potential the handling and transportation costs are identified as the relevant leverages. These costs are found to depend mainly on the utilisation degree of the load units. To calculate the different utilisation degrees, a packing-algorithm in form of a four-block heuristic is applied and its results are extrapolated on the basis of existing BMW packing information. Thus, several assembly parts are identified that fit better into the suggested load unit than in the existing ones. These results are assessed using BMW’s expense ratios for handling and transportation. 80 parts are determined for which the migration to the new size would result in savings of more than 5,000 EUR for each per year in Dingolfing. Together, these parts offer a savings potential of about 0.9 million Euro.

I avhandlingen studeras hur kostnadseffektiva underhålls- (uh-)planer för belagd väg kan genereras, på basis av information om aktuellt vägytetillstånd och funktionella modeller för kostnads- och tillståndsförändringar, delvis utvecklade i samarbete med svenska Vägverket (VV). Tilltänkt användning är på strategisk och programnivå, innan mer detaljerad objektinformation finns att tillgå. Till skillnad från hittills använda modeller, så genereras individuella uh-planer för varje vägsegment (en homogen vägsträcka vad gäller aktuellt beläggningstillstånd och beläggningshistorik), i kontinuerliga tillstånds- och åtgärdsrum. Genom användning av Lagrangerelaxerande optimeringsteknik, så kan de speciella nytto/kostnads-kvot-villkor som VV ålägger varje uh-objekt naturligen hanteras med dualpriser för budgetvillkoren. Antalet vägsegment som konkurrerar om budgetmedlen är vanligtvis stort. Data från VV:s Vägdatabank för Värmland har använts, omfattande ca 9000 vägsegment. Genom den stora datamängden har datorprogrammen implementerats för parallellbearbetning. Under avhandlingsarbetet har projektet beviljats tillgång till Monolith PCklustret vid NSC. För att kunna reducera optimeringskörtiderna har modell- och metodutveckling varit nödvändig. Genom att aggregera vägsegmenten till vägklasser har goda startvärden på dualpriserna erhållits. Genom utvecklingen av en speciell restvärdesrutin har den explicit behandlade tidsperioden kunnat reduceras. Vid lösandet av det duala subproblemet har speciell uppmärksamhet ägnats åt de diskretiseringseffekter som uppstår i metoden dynamisk programmering. En typ av tillämpning avser ett delvägnät, exempelvis en väg. Valideringsstudier har genomförts på väg 63 i Värmland – med lovande men inte tillfredsställande resultat (se nedan). En speciell modell för samordnat uh beaktar stordriftsfördelarna vid samtidig åtgärd på en hel vägsträcka. Den andra huvudtypen av studier gäller ett helt nätverk. Flera metodtyper har tillämpats, både för att lösa de relaxerade optimeringsproblemen och för att generera uhplaner som uppfyller budgetvillkoren. För en anständig diskretisering är körtiderna för hela Värmland mindre än 80 CPU-timmar. Genom en a posteriori primal heuristik reduceras kraven på parallellbearbetning till ett litet PC-kluster. Avhandlingen studerar vidare effekterna av omfördelade budgetmedel samt en övergång till en transparent, stokastisk modell – vilka båda visar små avvikelser från basmodellen. Optimeringsresultaten för Värmland indikerar att budgetnivåer på ca 40% av Värmlands verkliga uh-budget är tillräckliga. Dock saknas viktiga kostnadsdrivande faktorer i denna första modellomgång, exempelvis vissa funktionella prestanda (säkerhet), all miljöpåverkande prestanda (buller etc.) och strukturell prestanda (ex.vis bärighet, som enbart modelleras via ett åldersmått). För ökad tilltro till PMS i allmänhet och optimering i synnerhet, bör avvikelserna analyseras ytterligare och leda till förbättringar vad gäller tillståndsmätning, tillståndseffekt- & kostnadsmodellering samt matematisk modellering & implementering. / The thesis deals with the generation of cost efficient maintenance plans for paved roads, based on database information about the current surface conditions and functional models for costs and state changes, partly developed in cooperation with Vägverket (VV, Swedish Road Administration). The intended use is in a stage of budgeting and planning, before concrete project information is available. Unlike the up to now used models, individual maintenance plans can be formulated for each segment (a homogeneous road section as to the current pavement state and paving history), in continuous state and works spaces. By using Lagrangean relaxation optimisation techniques, the special benefit/cost-ratio constraints that VV puts on each maintenance project can be naturally mastered by dual prices for the budget constraints. The number of segments competing for budget resources is usually large. Data from VV Vägdatabank (SRA Road Database) in county Värmland were used, comprising around 9000 road segments. Due to the large data amount the implemented programs rely on parallel computation. During the thesis work, access to the PC-cluster Monolith at NSC was granted. In order to reduce optimisation run times, model & method development was needed. By aggregating the road segments into road classes, good initial values of the dual prices were achieved. By adding new state dimensions, the use of the Markov property could be motivated. By developing a special residual value routine, the explicitly considered time period could be reduced. At solving the dual subproblem special attention was paid to the discretization effects in the dynamic programming approach. One type of study is on a sub-network, e.g. a road. Validation studies were performed on road 63 in Värmland – with promising but not satisfactory results (see below). A special model for co-ordinated maintenance considers the fine-tuned cost effects of simultaneous maintenance of contiguous road segments. The other main type of study is for a whole network. Several method types have been applied, both for solving the relaxed optimisation problems and for generating maintenance plans that fit to the budgets. For a decent discretization, the run time for the whole Värmland network is less than 80 CPU-hrs.A posterior primal heuristics reduces the demands for parallel processing to a small PC-cluster.The thesis further studies the effects of redistributing budget means, as well as turning to a transparent stochastic model – both showing modest deviations from the basic model. Optimisation results for Värmland indicate budget levels around 40% of the actual Värmland budget as sufficient. However, important cost triggers are missing in this first model round, e.g., certain functional performance (safety), all environmental performance (noise etc.) and structural performance (e.g. bearing capacity, only modelled by an age measure). For increased credibility of PMS in general and optimisation in particular, the discrepancies should be further analysed and lead to improvements as to condition monitoring, state effect & cost modelling and mathematical modelling & implementation.

<p>This thesis studies the allocation of stock in a two-level inventory system with stochastic demand. The system consists of one central warehouse which supplies N non-identical retailers with one single product. Customer demand occurs solely at the retailers and follows independent Poisson processes. The purpose is to investigate the value of using a more advanced allocation policy than First Come-First Serve at the central warehouse. The focus is on evaluating how well the simple First Come-First Serve assumption works in a system where the warehouse has access to real-time point-of-sale data, and where shipments are time based and consolidated for all retailers. The considered allocation policy is a myopic policy where the solution to a minimization problem, formulated as a constrained newsvendor problem, determines how the warehouse allocates its stock to the retailers. The minimization problem is solved using (a heuristic method based on) Lagrangian relaxation, and simulation is used to evaluate the average inventory holding costs and backorder costs per time unit when using the considered policy. The simulation study shows that cost savings around 1-4 percent can be expected for most system configurations. However, there were cases where savings were as high as 5 percent, as well as cases where the policy performed worse than First Come-First Serve. The study also shows that the highest cost savings are found in systems with relatively low demand, few retailers, short transportation times and a short time interval between shipments.</p>

<p>Using mathematical models with the purpose to understand and store knowlegde about a system is not a new field in science with early contributions dated back to, e.g., Kepler’s laws of planetary motion.</p><p>The aim is to obtain such a comprehensive predictive and quantitative knowledge about a phenomenon so that mathematical expressions or models can be used to forecast every relevant detail about that phenomenon. Such models can be used for reducing pollutions from car engines; prevent aviation incidents; or developing new therapeutic drugs. Models used to forecast, or predict, the behavior of a system are refered to predictive models. For such, the estimation problem aims to find one model and is well known and can be handeled by using standard methods for global nonlinear optimization.</p><p>Descriptive models are used to obtain and store quantitative knowledge of system. Estimation of descriptive models has not been much described by the literature so far; instead the methods used for predictive models have beed applied. Rather than finding one particular model, the parameter estimation for descriptive models aims to find every model that contains descriptive information about the system. Thus, the parameter estimation problem for descriptive models can not be stated as a standard optimization problem.</p><p>The main objective for this thesis is to propose methods for estimation of descriptive models. This is made by using methods for nonlinear optimization including both new and existing theory.</p>

<p>Integer programming can be used to provide solutionsto complex decision and planning problems occurring in a wide varietyof situations. Applying integer programming to a real life problembasically involves a first phase where a mathematical model isconstructed, and a second phase where the problem described by themodel is solved. While the nature of the challenges involved in therespective two phases differ, the strong relationship between theproperties of models, and which methods that are appropriate for theirsolution, links the two phases. This thesis constitutes of threepapers, of which the third one considers the modeling phase, while thefirst and second one consider the solution phase.</p><p> </p><p>Many applications of column generation yield master problems of setpartitioning type, and the first and second papers presentmethodologies for solving such problems. The characteristics of themethodologies presented are that all successively found solutions arefeasible and integral, where the retention of integrality is a majordistinction from other column generation methods presented in theliterature.</p><p> </p><p>The third paper concerns nurse scheduling and describes the results ofa pilot implementation of a scheduling tool at a Swedish nursing ward.This paper focuses on the practical aspects of modeling and thechallenges of providing a solution to a complex real life problem.</p>

<p>The Swedish National Debt Office (SNDO) is the Swedish Government’s financial administration. It has several tasks and the main one is to manage the central government’s debt in a way that minimizes the cost with due regard to risk. The debt management problem is to choose currency composition and maturity profile - a problem made difficult because of the many stochastic factors involved. </p><p>The SNDO has created a simulation model to quantitatively analyze different aspects of this problem by evaluating a set of static strategies in a great number of simulated futures. This approach has a number of drawbacks, which might be handled by using a financial optimization approach based on Stochastic Programming. </p><p>The objective of this master’s thesis is thus to apply financial optimization on the Swedish government’s strategic debt management problem, using the SNDO’s simulation model to generate scenarios, and to evaluate this approach against a set of static strategies in fictitious future macroeconomic developments. </p><p>In this report we describe how the SNDO’s simulation model is used along with a clustering algorithm to form future scenarios, which are then used by an optimization model to find an optimal decision regarding the debt management problem. </p><p>Results of the evaluations show that our optimization approach is expected to have a lower average annual real cost, but with somewhat higher risk, than a set of static comparison strategies in a simulated future. These evaluation results are based on a risk preference set by ourselves, since the government has not expressed its risk preference quantitatively. We also conclude that financial optimization is applicable on the government debt management problem, although some work remains before the method can be incorporated into the strategic work of the SNDO.</p>

<p>This thesis grew out of a problem encountered by a subsidiary of a Swedish multinational industrial corporation. This subsidiary is responsible for the corporation’s customer financing activities. In the thesis, we refer to these entities as the Division and the Corporation. The Division needed to find a new approach to finance its customer loan portfolio. Risk control and return maximization were important aspects of this need. The objective of this thesis is to devise and implement a method that allows the Division to make optimal funding decisions, given a certain risk limit. </p><p>We propose a funding approach based on stochastic programming. Our approach allows the Division’s portfolio manager to minimize the funding costs while hedging against market risk. We employ principal component analysis and Monte Carlo simulation to develop a multicurrency scenario generation model for interest and exchange rates. Market rate scenarios are used as input to three different optimization models. Each of the optimization models presents the optimal funding decision as positions in a unique set of financial instruments. By choosing between the optimization models, the portfolio manager can decide which financial instruments he wants to use to fund the loan portfolio. </p><p>To validate our models, we perform empirical tests on historical market data. Our results show that our optimization models have the potential to deliver sound and profitable funding decisions. In particular, we conclude that the utilization of one of our optimization models would have resulted in an increase in the Division’s net income over the past 3.5 years.</p>

This thesis grew out of a problem encountered by a subsidiary of a Swedish multinational industrial corporation. This subsidiary is responsible for the corporation’s customer financing activities. In the thesis, we refer to these entities as the Division and the Corporation. The Division needed to find a new approach to finance its customer loan portfolio. Risk control and return maximization were important aspects of this need. The objective of this thesis is to devise and implement a method that allows the Division to make optimal funding decisions, given a certain risk limit. We propose a funding approach based on stochastic programming. Our approach allows the Division’s portfolio manager to minimize the funding costs while hedging against market risk. We employ principal component analysis and Monte Carlo simulation to develop a multicurrency scenario generation model for interest and exchange rates. Market rate scenarios are used as input to three different optimization models. Each of the optimization models presents the optimal funding decision as positions in a unique set of financial instruments. By choosing between the optimization models, the portfolio manager can decide which financial instruments he wants to use to fund the loan portfolio. To validate our models, we perform empirical tests on historical market data. Our results show that our optimization models have the potential to deliver sound and profitable funding decisions. In particular, we conclude that the utilization of one of our optimization models would have resulted in an increase in the Division’s net income over the past 3.5 years.