Operations Research Proceedings 2006

At an airport, a large number of activities required for serving an aircraft while on the ground have to be scheduled. These activities include, for example, passenger and flight crew transportation, check-in and boarding services, various technical services, loading and unloading of cargo and baggage, or catering and cleaning services. With the steady increase of civil air traffic and the corresponding growth of airports over the past decades, the complexity of the task has increased significantly.

Seit dem inzwischen schon legendär gewordenen Ausspruch von Henry Ford „Any customer can have a car painted any colour that he wants so long as it is black.“ hat ein fundamentaler Wandel bezüglich der Anforderungen an Produktionssysteme stattgefunden. So bietet heute etwa Daimler-Chrysler seine Mercedes C-Klasse aufgrund einer Vielzahl an vom Kunden individuell auswählbarer Optionen in 2

27

theoretisch möglichen Varianten an [10]. Nichtsdestoweniger kann trotz dieser enormen Variantenvielfalt mittels Universalmaschinen mit automatisiertem Werkzeugwechsel und flexibel ausgebildeter Werker die effiziente Produktionsform der Fließfertigung aufrechterhalten werden. Eine solche Organisationsform der Fließfertigung, die eine Vielzahl an Varianten eines einheitlichen Grundmodells in wahlfreier Fertigungsfolge (Losgröße Eins) produzieren, bezeichnet man als Variantenfließfertigung. Man findet sie nicht nur bei der Endmontage von Autos und verwandten Produkten wie Bussen und sonstigen Nutzfahrzeugen, sondern auch in weiten Teilen der Elektroindustrie. Als Tribut an die gestiegene Variantenvielfalt muss jedoch eine größere Komplexität der Produktionsplanung in Kauf genommen werden. War es in den traditionellen Ein-Produkt-Fließsystemen mehr oder minder ausreichend eine einmalige Fließbandabstimmung bei der Installation des Fließsystems vorzunehmen, so treten bei einer Variantenfließfertigung gänzlich neue Planungsprobleme auf, deren hierarchisches Zusammenspiel in Abbildung 1 dargestellt ist [5].

Traffic peaks are peaks in cost. This in particular holds for rural counties, where the organization of public mass transportation is focused on the demand of pupils. About half to two third of pupils in rural areas take a bus to get to school. Most of them are integrated in the public bus system, a minority is transfered by special purpose school buses. In all cases the respective county in which the pupils live is responsible for the transfer, meaning that the county administration pays the fees. Since tax money is a scarce resource, the administration has great interest in reducing these payments.

Quantitative Ansätze zum Bestandsmanagement im Rahmen der Kreislauflogistik fokussieren hauptsächlich auf Losgrößen- und Sicherheitsbestände. Aufgrund der dabei genutzten statischen Modellannahmen sind sie kaum in der Lage, die häufig in der Praxis vorzufindenden hohen Bestände insbesondere an Altprodukten zu erklären. Eine explizite Berücksichtigung dynamischer Einflüsse, wie sie beispielsweise Saisonalitäten, Produktlebenszyklen oder auch die Kostendynamik darstellen, führt zu neuen Motiven für die Lagerhaltung. Aufgabe der Dissertation [5] war es, solche Motivationen zu identifizieren. Dabei wurde auf eine zeitstetige Modellierung zurückgegriffen. Als Lösungsmethodik wurde Pontryagins Maximumprinzip genutzt, mit welchem generelle Struktureigenschaften optimaler Lösungen für ganze Problemklassen ermittelt werden können. Dieser Artikel gibt einen Überblick über wesentliche Resultate der Dissertation.

„The timetable is the essence of the service offered by any provider of public transport.“ (Jonothan Tyler, CASPT 2006)

We treat a simplified model of a Simulated Moving Bed (SMB) chromatographic separation process that contains time-dependent discrete decisions. SMB processes have been gaining increased attention lately, see [3], [4] for further references. The related optimization problems are challenging from a mathematical point of view, as they combine periodic nonlinear optimal control problems in partial differential equations (PDE) with time-dependent discrete decisions. For this problem class of mixed-integer optimal control problems (MIOCP) a novel numerical method, developed in [5], is applied.

Game theory in general and the concept of Nash equilibrium in particular have lately come under increased scrutiny by theoretical computer scientists. Computing a mixed Nash equilibrium is a case in point. For many years, one of the most important open problems was the complexity of computing a mixed Nash equilibrium in games with only two players. Only recently was it solved by a sequence of significant papers (Goldberg and Papadimitriou (2006), Daskalakis et.al. (2006), Chen and Deng (2005), Daskalakis and Papadimitriou (2005), and Chen and Deng (2006)).

The optimization of traffic flow in congested urban road networks faces a well-known dilemma: Optimizing system performance is unfair with respect to the individual drivers’ travel times; and a fair user equilibrium may result in bad system performance. As a remedy, computing a system optimum with fairness conditions, realized by length constraints on the routes actually used by drivers, has been suggested in [5]. This poses interesting mathematical challenges, namely the nonlinearity of the objective function and the necessity to deal with path constraints in large networks. While the authors present results suggesting that solutions to this constrained system optimum problem (CSO) are indeed equally good and fair, they rely on a standard Frank-Wolfe/Partan-algorithm to obtain them.

In this paper, we present a Lagrangian relaxation of the CSO problem for which the Lagrangian dual function can be evaluated by a decomposition into constrained shortest path problems which we solve exactly employing state-of-the-art acceleration techniques. The Lagrangian dual problem is then solved by a special cutting plane method.

Finally, we obtain test results which suggest that this approach outperforms previously described solution schemes for the CSO problem.

In this paper we investigate the

fare planning model

for public transport, which consists in designing a system of fares maximizing the revenue. We discuss a discrete choice model in which passengers choose between different travel alternatives to express the demand as a function of fares. Furthermore, we give a computational example for the city of Potsdam and discuss some theoretical aspects.

We will briefly survey the state of the art of the Robust Optimization (RO) methodology for solving convex conic optimization problems, both static and dynamic (multi-stage) emphasizing issues of computational tractability, and probabilistic guarantees satisfied by the optimal robust solution. We then introduce a recent extension of the methodology in which the solution is required to exhibit a controlled deterioration in the performance for uncertain data outside the nominal uncertainty set. Finally we discuss uncertainly affected linear control systems and introduce a novel reparameterization scheme that converts the, otherwise nonconvex, control problem into a convex programming one.

Neuro-dynamic programming is a methodology for sequential decision making under uncertainty, which is based on dynamic programming. The key idea is to use a scoring function to select decisions in complex dynamic systems, arising in a broad variety of applications from engineering design, operations research, resource allocation, finance, etc. This is much like what is done in computer chess, where positions are evaluated by means of a scoring function and the move that leads to the position with the best score is chosen. Neuro-dynamic programming provides a class of systematic methods for computing appropriate scoring functions using approximation schemes and simulation/evaluation of the system’s performance.

In late June 2004, the Basel Committee on Banking Supervision approved and published a document entitled “International Convergence of Capital Measurement and Capital Standards: A revised Framework”, better known as the “Basel II framework”. The publication of this document marked the final milestone of a process that was over five years in the making. The fundamental improvements over the Basel I Accord of 1988 help explain this relatively long time span. The main objectives of the new framework, stated by the Basel Committee in its June 1999 Consultative Paper, were the following:

To promote safety and soundness in the financial system.

To enhance competitive equality.

To adopt a more comprehensive approach to addressing risks.

To continue to focus on internationally active banks, although the new framework’s principles should also be applicable to banks of varying levels of complexity and sophistication.

Whereas the first two goals pick up where the Basel I Accord left off, the last two represent important advancements. The desire to develop a more comprehensive approach was a direct consequence of recognizing that the current regime lacks risk sensitivity in its minimum capital requirements and encourages market participants to exploit mechanisms of regulatory capital arbitrage.

Both under Solvency 2 and Basel II, operational risk is an important risk category for which the financial industry has to come up with a capital charge. Under Basel II, Operational Risk is defined as the risk of loss resulting from inadequate or failed internal processes, people and systems or from external events. This definition includes legal risk, but excludes strategic and reputational risk. In this talk I will discuss some of the issues underlying the quantitative modelling of operational risk.

This presentation has two purposes: (1) show operations researchers how they can apply quadratic binary programming to current problems in molecular biology, and (2) show formulations of some combinatorial optimization problems as integer programs. The former purpose is primary, and I wish to persuade researchers to enter this exciting frontier. The latter purpose is part of a work in progress.

Since 90s power markets are being restructured worldwide and nowadays electrical energy is traded as a commodity. Therewith the question how to manage and hedge the financial risks resulting from uncertain electrical power and fuel prices is essential for market participants. There exists a rich literature on risk management in energy markets. Some noteworthy references can be downloaded from our web resources [1] and are reviewed in the cited literature. Let us first investigate the market structure and then discuss two different pricing schemes for risk management in power industries.

Consider a general taxation model involving two levels of decision-making. The upper level (leader) imposes taxes on a specified set of goods or services while the lower level (follower) optimizes its own objective function, taking into account the taxation scheme devised by the leader. This model belongs to the class of bilevel optimization problems where both objective fucntions are bilinear.

Reliable implementation of geometric algorithms is a notoriously difficult task. Algorithms are usually designed for the Real-RAM, capable of computing with real numbers in the sense of mathematics, and for non-degenerate inputs. But, real computers are not Real-RAMs and inputs are frequently degenerate.

Many financial decision problems are most naturally formulated as optimization problems. This is the case, for example, in (arbitrage, utility, risk measure,...) pricing and hedging of (European, American, real,..) options, portfolio optimization and asset liability management. The optimization approach becomes even more natural in the presence of market imperfections such as transaction costs or portfolio constraints, where more traditional approaches of mathematical finance fail. Common to many financial problems, when properly formulated, is convexity with respect to the decision variables. This opens up possibilities of using numerical techniques that have been developed for large scale optimization problems.

A common issue for firms is how to allocate capital resources to various investment alternatives. An extensive literature in finance has examined various aspects of capital budgeting, including capital constraints, the determination of discount rates, and alternative approaches to estimating cash flows and handling risk, such as real options techniques. In terms of organizational structure, a central feature of the capital budgeting process in large firms is that relevant information about the profitability of potential investment projects resides with one or several managers. It is generally accepted that preferences of these managers may not coincide with those of the firm’s owners (the principal). Consequences of asymmetric information include strategic reporting by better-informed managers (for example, “sandbagging” or “creative optimism”) and a need to measure performance

ex post

. Surveys consistently find that internal rate of return (IRR) criteria remain prevalent in capital budgeting decisions. Furthermore the use of artificially high hurdle rates suggests widespread capital rationing [15, 20].

In the classical Vehicle Routing Problem (VRP) a fleet of capacitated vehicles is available to serve a set of customers with known demand. Each customer is required to be visited by exactly one vehicle and the objective is to minimize the total distance traveled. In the Split Delivery Vehicle Routing Problem (SDVRP) the restriction that each customer has to be visited exactly once is removed, i.e., split deliveries are allowed. In this paper we present a survey of the state-of-the-art on this important problem.

SCM is concerned with the coordination of material, information and financial flows within and across legally separated organizational units. Software vendors have developed so called Advanced Planning Systems (APS) to provide decision support at different hierarchical planning levels of an intra-organizational supply chain. However, since APS are based on principles of hierarchical planning further ideas and concepts are required to coordinate activities and flows between adjacent planning levels of each partner.

A major goal in any optimization or decision-making process is to identify a single or all best solutions within a set of feasible alternatives. In multiple objective programming (MOP), while it is theoretically possible to identify the complete set of efficient solutions, finding an exact description of this set often turns out to be practically impossible or computationally too expensive. Thus many research efforts during the last thirty years have focused on concepts and procedures for the efficient set approximation.

Support vector machines (SVM) from statistical learning theory are powerful classification methods with a wide range of applications including credit scoring. The urgent need to further boost classification performance in many applications leads the machine learning community into developing SVM with multiple kernels and many other combined approaches. Owing to the huge size of the credit market, even small improvements in classification accuracy might considerably reduce effective misclassification costs experienced by banks. Under certain conditions, the combination of different models may reduce or at least stabilize the risk of misclassification. We report on combining several SVM with different kernel functions and variable credit client data sets. We present classification results produced by various combination strategies and we compare them to the results obtained earlier with more traditional single SVM credit scoring models.

Finanzmarktakteure müssen ihren Investitionsentscheidungen Erwartungen bzgl. der zukünftigen Marktentwicklung zugrunde legen. Sie stehen vor einer Entscheidung unter Unsicherheit und sind bestrebt mittels Prognoseverfahren die zukünftige Kursentwicklung möglichst gut vorherzusagen.

Für marketingrelevante Fragestellungen und für die strategische Bewertung von Technologiealternativen ist die Untersuchung des Diffusionsverlaufs bei Netzeffektgütern, wie z.B. Telekommunikationsdiensten, von hohem Interesse. Es wird ein Entscheidungsunterstützungssystem vorgestellt, dass insbesondere Marketingvariable zur Ausgestaltung relevanter Merkmale von netzeffektbasierten Gütern unterstützt. Ausgehend von dynamischen Nutzenfunktionen wird ein Modellansatz auf Grundlage der Mastergleichung der Physik bzw. den Mittelwertgleichungen vorgestellt, der Wechselwahrscheinlichkeiten zwischen den Produktalternativen ableitet. Die Anwendungsrelevanz des Modellansatzes wird durch entscheidungsrelevante What-If-Analysen verdeutlicht.

Solving discrete optimization problems (DOP) can be a rather hard task. Many real DOPs contain a huge number of variables and/or constraints that make the models intractable for currently available solvers. There are few approaches for solving DOPs: tree search approaches (e.g., branch and bound), relaxation and decomposition methods. Large DOPs can be solved due to their special structure. Among decomposition approaches we can mention poorly known local decomposition algorithms using the special block matrix structure of constraints and half-forgotten nonserial dynamic programming algorithms which can exploit sparsity in the dependency graph of a DOP.

Monden [11] defined two goals for the mixed-model assembly line sequencing problem: (1) Leveling the load on each station on the line, and (2) Keeping a constant rate of usage of every part used by the line. To handle these problems, Goal chasing I and II (GC- I and GC- II ) were developed by Toyota corporation. Miltenburg [9]developed a nonlinear programming for the second goal and solved the problem by applying tow heuristic procedures. Miltenberg et al [10] solved the same problem with a dynamic programming algorithm. The objective considered by Bard et al [1] was the minimization of overall line length. Bard et al [2] used Tabu search (TS) algorithm to solve a model involving two objectives: minimizing the overall line length and keeping a constant rate of part usage. Hyun et al [4] addressed three objectives: minimizing total utility work, keeping a constant rate of part usage and minimizing total setup cost. This problem was solved by proposing a new genetic evaluation. Mcmullen [6] considered two objectives: minimizing number of setups and keeping a constant rate of part usage. He solved this problem with a TS approach. Mcmullen [7,8] has also solved the same problem by using genetic algorithm, and ant colony optimization, respectively.

This paper presents a fuzzy goal programming approach for solving a multi-objective mixed- model assembly line sequencing problem in a just-in-time production system. A mixed-model assembly line is a type of production line that is capable of diversified small lot production and is able to respond promptly to sudden demand changes for a variety of models. Determining the sequence of introducing models to such an assembly line is of particular importance for the efficient implementation of just-in-time (JIT) systems. In this paper, we consider three objectives, simultaneously: minimizing total utility work, total production rate variation, and total setup cost. Because of existence conflicting objectives, we propose a fuzzy goal programming based approach to solve the model. This approach is constructed based on the desirability of decision maker (DM) and tolerances considered on goal values. To illustrate the behavior of the proposed model, some of instances are solved optimally and computational results reported.

In the paper the m-layer planar 3-dimensional assignment problem is considered. It is an NP-hard modification of well-known planar 3-dimensional assignment problem. Approximation algorithm, proposed by Gimadi and Korkishko is analysed. Its asymptotical optimality for a special class of random instances is proved.

Mixed-model assembly line sequencing is one of the most important strategic problems in the field of production management. In this paper, three goals are considered for minimization; That is, total utility work, total production rate variation, and total setup cost. A hybrid multi-objective algorithm based on Particle Swarm Optimization (PSO) and Tabu Search (TS) is devised to solve the problem. The algorithm is then compared with three prominent multi-objective Genetic Algorithms and the results show the superiority of the proposed algorithm.

FLOPC++ is an open source algebraic modeling language implemented as a C++ class library. It allows linear optimization problems to be modeled in a declarative style, similar to algebraic modeling languages, such as GAMS and AMPL, within a C++ program. The project is part of COmputational INfrastructure for Operations Research (COIN-OR) and uses its Open Solver Interface (OSI) to achieve solver independence.

In this paper, we consider two-machine permutation flow shop scheduling problem to minimize the makespan in which some of the jobs have to be processed with no-wait in process. We also consider precedence constraints which impose some jobs to be processed before or after some others. We propose a constructive algorithm to find a feasible solution. We also develop a Tabu Search algorithm to solve this problem. Our computational analysis indicates its good performance.

We consider a generalization of the Steiner tree problem on graphs suitable for the design of the last mile in fiber optic networks and propose a multi commodity flow formulation for the exact solution of this problem. Some experimental results are discussed.

This paper continues the investigation of the cycle polytope of a directed graph begun by Balas and Oosten [2]. Given a digraph

G

= (

N,A

) and the collection

C

of its simple directed cycles, the cycle polytope defined on

G

is

P

C

≔ conv {

X

C

:

C

∈

C

}, where

χ

C

is the incidence vector of

C

. According to the integer programming formulation given in [2],

P

C

is the convex hull of points

x

∈ℝ satisfying

(1)

$$ x(\delta ^ + (i)) - x(\delta ^ - (i)) = 0{\text{ }}for{\text{ all }}i \in N $$

,

(2)

$$ x(\delta ^ + (i)) \leqslant 1{\text{ }}for{\text{ all }}i \in N $$

,

(3)

$$ \begin{array}{*{20}c} { - x(S,N\backslash S) + x(\delta ^ + (i)) + x(\delta ^ + (j)) \leqslant 1{\text{ }}for{\text{ all }}S \subseteq N,2 \leqslant |S| \leqslant n - 2,} \\ {i \in S,j \in N\backslash S} \\ \end{array} $$

,

(4)

$$ \sum\limits_{i = 1}^{n - 1} {\sum\limits_{j = i + 1}^n {x_{\pi (i)\pi (j)} } \geqslant 1{\text{ for all permutations }}\pi {\text{ of }}N} $$

,

(5)

$$ x_{ij} \in \{ 0,1\} {\text{ }}for all (i,j) \in A $$

In this paper, we deal with modelling robust design problems via conic optimization. A robust design problem deals with finding a robust optimal solution of an uncertain design problem. The uncertain data is assumed to belong to a so-called uncertainty set

$$ \mathcal{U} $$

. Uncertainty means that the data is not known exactly at the time when the solution has to be determined. In order to find a robust optimal solution, we use the robust optimization (RO) methodology of Ben-Tal and Nemirovskii. We demonstrate this on the robust shortest path problem (RSPP), the robust maximum flow problem (RMFP) and the robust resistance network topology design (RNTD) problem.

Several hard optimization problems of finding spanning connected subgraphs with extreme total edge weight are considered. A number of results on constructing polynomial algorithms with performance guarantees for these problems is presented.

1

In multidimensional poverty measurement

k

≥ 2 different quantitative basic needs variables

y

j

,

j

= 1...

k

have to be considered. Let the respective variables be substitutable. Then for a single person

i

= 1...

n

poverty can be aggregated across variables as follows:

(1)

$$ C_{1i}^* = \left( {\frac{1} {k}\sum\limits_{j = 1}^k {p_{ij}^{*\alpha } } } \right)^{\frac{1} {\alpha }} ,\alpha \geqslant 2 $$

(see Kocklaeuner (2002) with respect to an unidimensional ethical poverty index aggregating poverty across persons).

We consider a model for a financial market where the asset prices satisfy a stochastic differential equation. For the volatility no new source of randomness is introduced, but the volatility at each time depends deterministically on all previous price fluctuations. Such non-constant volatility models preserve the completeness of the market while they allow for many attractive features.

We intend to optimize harvesting of two populations within a business cycle of an economy with appropriate means. The simulation model we have in mind concentrates on the problem of profit maximization within an interdependent system. Furthermore, we deal with the task of explaining phenomena of the typical behavior of the subjects while operating a complex system, e.g., a market, a company, ...

Variable selection in cross-country growth regression models is currently a major open research topic and has inspired theoretical and empirical literature, see [6]. There are two categories of research problems that are intimately connected. The first problem is model uncertainty and the second is data heterogeneity. Recent literature aims to overcome the first problem by applying Bayesian Model Averaging (BMA) approaches in finding important, robust and significant variables to explain economic growth. While BMA offers an appealing approach to handle model uncertainty very little research has been undertaken to consider the problem of data heterogeneity. In this paper we analyze the issue of data heterogeneity on the basis of the exclusion of countries, i.e. we will take a closer look at the robustness of approaches when countries are eliminated from the data set. We will show that results of BMA are very sensitive to small variations in data. As an alternative to BMA in the cross-country growth regression debate we suggest the use of “classical” Bayesian Model Selection (BMS). We will argue that there is much in favor of BMS and will show that BMS is less sensitive in the identification of important, robust and significant variables when small variations in data are made. Our empirical results are undertaken on the most frequently used data set in the cross-country growth debate provided by [4].

Many events such as conferences or informational events at institutions consist of a number of single workshops among which participants can choose a limited number to visit. The workshop assignment problem is a linear optimization problem that finds a feasible assignment of participants to workshops maximizing the social welfare function expressed by preferences of participants for workshops. Several problem constraints reflect the structure and limitations of the event and define possible workshop combinations.

Due to the increasing competition in liberalized electricity markets, a succesful customer retention as well as a cost efficient allocation of electric energy become more and more important. Therefore, new, innovative strategies are sought, which promise on the one hand a long-term customer retention and assure, on the other hand, a more cost-efficient provision of electric energy.

In the process of the generation and trading planning, generation companies maximize the contribution margin, i.e. the difference of the revenues of energy trades and the costs for generating and purchasing electrical energy. The planning time horizon of this process covers a period of one month to one year. The complex planning task necessitates the application of computer-based tools [1]. Due to structural changes within the power industry, these tools have to be adapted continuously to the new conditions.

After years of rapid economic development, China is calling for development of a circular economy and resource recycling, to solve both the resource shortage problem and the environmental problems. Based on the analysis of the current status and the challenges of the electronic waste (e-waste) recycling in China, this paper seeks to design a financially feasible and environmentally safe e-waste recycling system. An integrated assessment model is proposed, in which the environmental, social and economic impact of recycling scenarios can be assessed simultaneously. The economic impact can be derived from an optimization model for the reverse logistics network.

The challenge in modelling electricity prices is mainly caused by it’s non-storability. Spot prices are thus determined by the current demand/supply interaction, but hardly by expectations about the future. They show characteristics as mean-reversion, seasonal patterns, an immense volatility and spikes, which cannot be captured with standard stock market models. On contrary, there exists growing markets, where financial futures contracts are traded. These contracts are storable and show similar characteristics to other financial assets. In particular they feature a significant lower volatility then spot prices. Moreover, the volatility is decreasing in the time to maturity.

Due to substantial changes in competition, capital market conditions, and supervisory frameworks, holistic analysis of an insurance company’s assets and liabilities takes on special relevance. An important tool in this context is dynamic financial analysis (DFA). DFA is a systematic approach to financial modeling in which financial figures are projected under a variety of possible scenarios by showing how outcomes are affected by changing internal and/or external factors. The discussion in Europe about new risk-based capital standards (Solvency II project) and the development of International Financial Reporting Standards (IFRS), as well as expanding catastrophe claims, have made DFA an useful tool for cash flow projection and decision making, especially in the non-life and reinsurance businesses (for an overview, see [2]).

Reinsurance contracts represent a very important tool for insurance companies to manage their risk portfolio. In general, they are used if an insurer is not willing or not able to hold certain risk exposures or parts thereof on its own. There exist two main contract types to cede claims to a reinsurer, namely proportional and non-proportional ones. With the

quota share reinsurance

, a well-known variant of the former ones, a fixed percentage of the claim sizes is ceded to the reinsurance company.

Excess of loss

and

stop loss

are non-proportional types and the reinsurer is only liable to pay if certain losses are exceeded. In practice insurance companies usually place a number of different reinsurance contracts, a so-called

reinsurance program

.

One of the main differences in measuring capital requirements for credit risk due to the Internal Ratings Based Approach (IRBA) of the new regulatory Capital Standards (Basel II) is the enlarged acceptance of collaterals in order to reduce (supervisory) credit risk. Whereas in the Advanced IRBA own models for estimating the effects of collaterals can be used, in the Foundation IRBA concrete formulas are given. However, these regulations only explain the case of a single claim collateralized by a single asset or guarantee. If numerous collaterals are available for multiple loans, we receive an allocation problem of collaterals to loans with the objective of keeping regulatory capital low. In this article we model the corresponding optimization problem. Since numerical standard procedures often converge towards the wrong local minimum, we show how to apply evolutionary algorithms as well as simulated annealing.

While over the past few years both banking supervisors and researchers have focussed their attention on banks’ credit risk, the spotlight is now being turned again on interest rate risk. One reason for this is its character as a kind of systemic risk: there is evidence that a rise in interest rates affects most banks negatively. An historical example of a banking crisis caused by high interest rates is the ‘Savings and Loan Crisis’ which occurred in the USA during the 1980s.3 Between 1980 and 1988, 563 of the approximately 4,000 savings and loan institutions failed, while further failures were prevented by 333 supervisory mergers. The total costs of the crisis are estimated at USD160 billion. Recently, the Basel Committee on Banking Supervision published principles for the management and supervision of interest rate risk that go far beyond current practice.

4

However, few data are available concerning banks’ interest rate risk exposure.

For a long time, interest rates have been considered one of the macroeconomic factors determining stock returns. The role of interest rates in the return generating process of stocks has therefore been extensively investigated in general, but particularly so with regard to financial institutions, which are often deemed to be more sensitive to changes in interest rates than stocks from other industries. Generally, this specific sensitivity has been attributed to i.) the predominant role of financial (i.e. nominal) assets and liabilities on the balance sheets of financial intermediaries and ii.) the maturity transformation performed especially by depository institutions and the resulting maturity mismatch of assets and liabilities (see [14] for an extensive review).

Localization investments are made mainly to increase the domestic content of manufacturing, thereby to reduce the costs and import dependency. Since localization investments include technology transfer, they positively affect the developing economies. The arrival of the new technology to the country has a positive impact on development of the equipment, workforce and the final product. It is often applied in automotive industry. Through localization investments not only improvement of OEMs, but also development of involved subsidiary industry can be induced. As a developing economy itself, Turkey encourages these kinds of investments and gives governmental incentives. The problem here is the valuation of these investment projects accurately by including all strategic impacts. Just because localization projects involve many future growth opportunities, conventional valuation tools cannot value those embedded opportunities correctly and the value of the project mostly appears negative or very low. This situation can cause a misjudgment at the incentives stage. This paper analyzes the localization project, first with conventional NPV analysis, then with real options analysis and finally compares the results. As for the options analysis, the results of potential involvement of various option types such as sequential options approach are used in the valuation of a case from Turkish automotive industry.

The widely deplored shortage of qualified personal in the nursing sector all over Europe can be traced to a number of reasons among which the relatively short duration that personal remains on the job ranks prominently. Besides the high psychic pressure involved with many nursing jobs, the degree of job satisfaction is also decreased by irregular working hours and inflexible working schedules.

The hospital field in Germany, with its 1.1 million employees and 62 billion Euro annual turnover (figures from 2001), represents a large and socially important field of activities [3, pp. 13]. If one considers the patients as “action object”, the work system (cf. [4, p. 81]) “hospital” is characterized by a number of particularities: First, treatment decision have to be made based on incomplete information and the treatment sequences must be carried out individually, meaning that they can only be planned to a limited degree. Furthermore, the complex treatment sequences must fulfil the treatment order reliably and efficiently. On the other hand, treatment processes must also take occupational health and safety and hygiene requirements of the medical and nursing personnel into account [10, p. 224].

The implementation of appropriate inventory control rules delivers the logistics operations of organizations a competitive advantage on the market place. This is also true for special types of networked manufacturing supply chains such as production networks which have complex topologies and increased complexity due to their logistic and production processes, information delays and the globalized markets. The paper builds the case of a production network and determines which inventory control policies applied in practice, order points and periodic-reviews, suit most the functions of the production network. Basically the production net consists of four manufacturing units that proceed to the joint development of products. In order to produce the four different items, the manufacturer orders from the other units as well as from the external supplier according to the exogenous customer demand. Although the case portrays a simplified instance of a production net, yet it already exhibits complex non linear dynamics inherent to such systems. The model is simulated with the system dynamics method which demonstrates the aptitude to describe distributed environments as long as product aggregation is permitted. The simulation results derived from the application of the inventory control rules on the production net will allow a detailed assessment of the suitability of each of the policies, in terms of the inventory costs criterion. A discussion on when to implement which inventory rule in respect to the functionalities of the production net will be pursued.

In this article we propose a new model for the simultaneous vehicle and crew scheduling problem occuring in the planning of urban mass transit systems. Our model incorporates the possibility of

trip shifting

in a given range in order to achieve a better solution.

Am 11. April 2007 werden in der Europäischen Union neue Vorschriften bezüglich der Lenk- und Ruhezeiten im Straßengütertransport in Kraft treten. Den neuen Vorschriften zufolge können Spediteure und Verlader für Verstöße der Fahrer haftbar gemacht werden. Da zudem Lenk- und Ruhezeiten einen signifikanten Einfluss auf Reisezeiten haben, ist eine Berücksichtigung der entsprechenden Regelungen bei der Tourenplanung unumgänglich. In diesem Beitrag wird gezeigt wie die neuen EU-Vorschriften in die Tourenplanung eingebracht werden können und das Vehicle Routing Problem mit Lenk- und Ruhezeiten (VRPLR) vorgestellt.

The share of logistics and transportation in the overall cost of a product is increasing. Subsequently, there is a growing pressure in the logistics industry for optimization and cost reduction. In this paper, we consider the issue of transport channel selection, a problem that has been overlooked for a long time. Typical choices for transport channels include round-trips from and to the depot, one-way tours (often called “milkruns”), delivery over a hub, or fixed-cost delivery services (e.g. a postal service). The overall optimization problem consists of two interdependent sub-problems: assigning shipments to transport channels, and optimizing the routes within each channel.

In this paper we address a rich variant of the vehicle routing problem which occurs in real-life applications. Among other aspects we take into consideration time windows, simultaneous delivery and pick-up at customer locations, multiple use of vehicles, and timely allocation of vehicles to loading bays at the depot. In order to solve practical instances of the resulting real-life rich vehicle routing problem, efficient methods are required. For this reason, we present a sampling procedure, which is a multi-start algorithm that executes in each call a substantial extension of the well-known savings algorithm. Using a set of suitable benchmark instances, we assess the performance of the proposed sampling procedure.

The decision of an airline about its service offering is a challenging task as it involves various decisions at the interface of operations and marketing: which origin-destination (OD) markets to serve, over which routes, and at which departure times (schedule design), at which price and other ticket conditions (pricing/fare product design), and what aircraft type to assign to each of these flights (fleet assignment). These decisions are highly interdependent with regard to their profit impact: on the one hand, the fleeted schedule fixes a large part of the cost; on the other hand, schedule, price and fare conditions are the most important factors influencing passenger’s choice and thus revenue. While schedule- and fare-related decisions are often treated in isolation in airline planning, profit maximizing service design should encompass the simultaneous determination of all features in the service package that drive profit. We develop a market-oriented model for airline network service design integrating flight schedule design, fleet assignment and pricing. Under suitable assumptions, the model is a mixed-binary problem with concave objective function and linear constrained that can be solved exactly by standard techniques. The optimal solution obtained at the strategic level can be used as input for operational revenue management models providing an interface for hierarchical decision making.

Even in its most basic form, the Vehicle Routing Problem and its variants are notoriously hard to solve. More often artificially intelligent algorithms are employed to provide near-optimal solutions. To be classified as “intelligent”, however, a solution strategy should be able to first analyze the environment in which the problem occurs, then solve it, and afterwards reflect on the solution process so as to improve future decision-making. Although reference is made to the entire context of the intelligence research project, this paper reports on the Tabu Search algorithm designed that catered for a problem with multiple soft time windows, a heterogeneous fleet, double scheduling, and time dependent travel time. An adaptive memory procedure was employed, initially populated with good initial feasible solutions, and the algorithm was tested on 60 problems based on established benchmark sets. The complex variant of the Vehicle Routing Problem required between 670 and 4762 seconds on a standard laptop computer, which is considered to be reasonable in the proposed application, and was consistent between different runs with an absolute mean deviation of 3.6%. The contribution is significant as it provides an algorithm that efficiently addresses a complex and practical application of the Vehicle Routing Problem. The algorithm can easily be extended to make use of multiple processors so as to reduce computational time.

Outsourcing (subcontraction) makes use of external entities as an alternative to the usage of own resources (self-fulfillment). The arising ‘make-or-buy’ decision combining the two clusters of self-fulfillment and subcontraction evolves in a complex reference analysis among items involved [13].

We analyze investment incentives of goal incongruent performance measures in an experiment in which ‘managers’ make one-period investment decisions and ‘owners’ predict these decisions. Three alternative performance measures are considered: earnings, ROI, and residual income. These measures serve as archetypes for a wide variety of measures used in practice. Standard theoretical predictions with respect to the investment incentives of earnings, ROI, and residual income are well documented, and they have become part of the management accounting education (e.g., [5]). They illustrate one of the basic principles of management accounting: ‘you get what you pay for’. As is well known, neither earnings nor ROI is a goal congruent performance measure, whereas residual income is goal congruent due to its conservation property.

Management simulation allows students to apply their theoretical knowledge in a safe, feedback-learning context. The quality of the simulation model is important for the achievable learning effect. A model always simplifies reality, but should still strive for a realistic implementation of key factors and relationships of the modeled situation. Vague information and qualitative relationships have a great significance in practical business. In management games, however, such qualitative aspects are often excluded from the simulation as it is difficult to model them adequately [1]. Concepts like “competence”, “image” and “credit rating” are meaningful to business, but difficult to grasp with conventional simulation modeling. In our contribution an approach based on fuzzy sets is presented to help overcoming these difficulties.

Creating a movie shoot schedule is an important part of the movie production process. Even for a small movie project already 50 activities requiring 130 resources such as different actors, director, team, special effects and locations etc. have to be scheduled respecting complex constraints which may be imposed on single resources as well as on every activity.

Maintaining logical consistency in a knowledge base that receives asynchronous events from collaborative agents poses a challenge, due to multiple agent perspectives of the knowledge base. Facades and filters further complicate this problem by distorting the definition of consistent knowledge. Therefore, maintaining logical consistency of the knowledge base requires an infrastructure for handling truth maintenance. This paper presents a generic, object-oriented framework for truth maintenance in collaborative multi-agent systems. The core of the framework is an agent that autonomously reasons on system events, thus guaranteeing the integrity of the knowledge base independent of external agents. Specialization to a particular domain is achieved through the description of tests that verify the consistency of the knowledge base. This paper shows an example of this approach in a real-world, multi-agent system and discusses performance and maintainability in such a system.

Contributing to transparency and traceability of decision making processes and taking into account the preferences of the decision makers, multi-criteria decision analysis (MCDA) is suitable to bring together knowledge from different disciplines and fields of expertise. The modelling of the decision makers’ preferences is a crucial part of any multi-criteria analysis. In multi-attribute value theory (MAVT), preferential information is modelled by weighting factors (i.e.

inter-criteria

comparisons) and value functions (i.e.

intra-criteria

preferences). However, the uncertainties associated with the determination of these preferential parameters are often underestimated. Thus, the focus of this paper is the description of an approach to explore the impact of simultaneous variations of these subjective parameters. Special attention is paid to the consideration of variations of the value functions’ shapes. The aim of the presented methods is to facilitate the process of preference modelling and to comprehensibly visualise and communicate the impact of the preferential uncertainties on the results of the decision analysis.

The outranking analysis has been frequently used to deal with the complex decisions involving qualitative criteria and imprecise data (see [5]).

The number of objectives in a multiobjective optimization problem strongly influences both the performance of generating methods and the decision making process in general. On the one hand, with more objectives, more incomparable solutions can arise, the number of which affects the generating method’s performance. On the other hand, the more objectives are involved the more complex is the choice of an appropriate solution for a (human) decision maker. In this context, the question arises whether all objectives are actually necessary and whether some of the objectives may be omitted; this question in turn is closely linked to the fundamental issue of conflicting and non-conflicting optimization criteria. Besides a general definition of conflicts between objective sets, we here introduce the

$$ \mathcal{N}\mathcal{P} $$

-hard problem of computing a minimum subset of objectives without losing information (

MOSS

). Furthermore, we present for

MOSS

both an approximation algorithm with optimum approximation ratio and an exact algorithm which works well for small input instances. We conclude with experimental results for a random problem and the multiobjective 0/1-knapsack problem.

Der Grundstein für eine erfolgreiche Ersatzteil-Lagerlogistik wird mit der Entscheidung über die passenden Lagersysteme gelegt. In der Praxis konkurrieren dabei multiple Zielsetzungen wie z.B. ein zu maximierender Automatisierungsgrad mit den resultierenden zu minimierenden Investitionen. Der Beitrag stellt ein multikriterielles Entscheidungsmodell vor, das speziell im Ersatzteilbereich die Auswahlproblematik anhand von Kennzahlen strukturiert und Möglichkeiten zur Entscheidungsunterstützung anbietet. Zum Einsatz kommt ein dreistufiges Modell auf Grundlage des Analytic Hierarchy Process, das mit Hilfe der Software Expert Choice die Eignung verschiedener Alternativen in unterschiedlichen Lagerzonen ermitteln kann. In Abhängigkeit der zugrunde liegenden Teilestruktur des betrachteten Unternehmens werden zunächst in Frage kommende Lagersysteme ausgewählt und anschließend mit Hilfe des Modells bewertet. Eine Sensitivitätsanalyse sichert die Stabilität des Ergebnisses ab.

In this paper we propose an automatic method for spectral clustering of weighted directed graphs. It is based on the eigensystem of a complex Hermitian adjacency matrix H

n

×

n

. The number of relevant clusters is determined automatically. Nodes are assigned to clusters using the inner product matrix S

n

×

n

calculated from a matrix R

n

×

l

of the l eigenvectors as column vectors which correspond to the positve eigenvalues of

H

. It can be shown that by assigning the vertices of the network to clusters such that a node

i

belongs to cluster

p

c

if

Re

$$ {\text{(}}S_{i,p_c } {\text{)}} $$

=

max

j

Re

(

S

i,j

) an good partitioning can be found. Simulation results are presented.

The Dial-A-Ride Problem (DARP) has often been used to organize transport of elderly and handicapped people, assuming that these people can book their transport in advance. But the DARP can also be used to organize usual passenger or goods transportation in real online scenarios with time window constraints. This paper presents an efficient exact algorithm with significantly reduced calculation times.

Der vorliegende Beitrag zeigt die in der WestLB angestrebte Anwendung des Verlustverteilungsansatzes, der zur Quantifizierung operationeller Risiken nach der Basel II-Rahmenvereinbarung herangezogen werden kann. Der Verlustverteilungsansatz gehört zur Klasse der fortgeschrittenen Messverfahren für operationelle Risiken und stellt in dieser den in der Bankenlandschaft am weitesten verbreiteten Ansatz dar.

Schwerpunkt des traditionellen Produktions-Controlling ist der Bereich der Kosten. In Abhängigkeit davon, welche Rolle Lieferfähigkeit und Liefertreue in der Branche spielen, werden output-bezogene Performance-Indikatoren eingeführt. Während damit im Allgemeinen nur Symptome diagnostiziert werden können, stellt sich die Frage nach den Gründen von Planabweichungen und Möglichkeiten zur Verbesserung der Lieferperformance. Um Produkte gemäß Kundenwunsch auszuliefern sind mit Sicherheit die Durchlaufzeit und deren Varianz von Interesse. Eine ex-post Messung dieser Größen ist hilfreich; wichtiger ist jedoch eine Verringerung der Werte. Daher ist es zweckdienlich, die logistische Leistung bereits innerhalb des Fertigungsablaufs zu messen, statt an dessen Ende. Somit sollte es leichter fallen, Abweichungen früher zu erkennen und rechtzeitig Gegenmaßnahmen zu ergreifen. Mit Hilfe geeigneter Daten ist möglich, nicht nur die Durchlaufzeit zu verstehen, sondern auch Durchsatz- und Kostenthemen zu erklären und diese für planerische Zwecke zu verwenden.

Der Bedarf an Modellen zur realitätsnahen Abbildung von Fertigungsprozessen ist nach wie vor aktuell. Gerade für das Verständnis fundamentaler Zusammenhänge in der Produktion sind geeignete Modelle von unschätzbarerem Wert, denn logistische Prozesse sind in der Praxis oft schwer nachzuvollziehen, so dass für die Beschreibung des Verhaltens bestehender Systeme flexible und transparente Methoden gefordert werden, die mit einem vertretbaren Ermittlungsaufwand einher gehen. Kaum ein anderer Industriezweig als die Halbleiterbranche ist durch die verschärften Rahmenbedingungen eines überaus komplexen, kapital- und zeitintensiven Produktionsprozesses gekennzeichnet. Eingebettet in einem wechselhaften Umfeld nimmt die Prämisse des wirtschaftlichen Produzierens einen zentralen Stellenwert ein, so dass nicht nur marktseitige Forderungen mit den betriebsseitigen Bedingungen in Einklang gebracht werden müssen, sondern vor allem auch ein Konsens zwischen den betrieblichen Anforderungen gefunden werden muss. Die typischen Charakteristika der Mikrochipfertigung hinsichtlich Fertigungslogistik, Materialfluss in einem Fertigungsverbund und die Herausforderungen bei der Modellierung von Arbeitsschritten zur Lösung verschiedener planerischer und operationeller Probleme werden in [9] ausführlich dargestellt.

Stochastic yields from disassembly complicate the planning of so-called disassemble to order problems, where a specified amount of components must be harvested from various models of returned products. Chance constraint programming, a branch of stochastic programming, has proven useful in several applications of operations management. This contribution will first formulate a novel chance constrained programming model for the single-period disassemble-to-order problem. We will then illustrate its application using an example, and highlight the tradeoff between service and costs which emerges. We also suggest a variety of extensions to the basic model, many of which will likely prove to be trivial and relevant to industry.

Scope of this work is the development of an optimization approach to find the optimal configuration of automotive plant capacities for a time horizon of one to seven years regarding market demand, planning premises, and dependencies between the shops (body shop, paint shop, final assembly) and between planning periods (e.g. learning curves). The methodology has been implemented in a planning tool and includes production and workforce planning. The optimization algorithm is based on a dynamic programming approach.

Contributions to multi-echelon safety stock optimization can be classified as being either of the stochastic- or guaranteed-service framework. Though both approaches have been used in inventory theory for a long time, there is still a lack of a detailed comparison. In this paper, such a comparison is presented. Differences in the materials flow are outlined and insights into the performance of both approaches are gained from a simulation study.

In the academic world, as well as in Industry, there is a wide unity that companies with a combination of high customer-value products and good logistics are especially successful in competition. Good logistics are marked by low production- and inventory costs as well as by a high ability to deliver timely.

Due to the increasing environmental awareness of their customers, manufacturing firms have to incorporate an ecological aspect in their corporate identity to remain competitive. In several cases these firms offer an option for their customers to return the product to them after its end-of-use or alternatively its end-of-life. The field of reverse logistics presents an overall approach on how these backward flows of products can be handled efficiently. Therefore, it expands the original focus of logistics to a closed-loop supply chain perspective.

Advanced Planning Systems decompose Supply Chain Management into long-term, mid-term, and short-term planning tasks. In this paper, we outline these tasks and reference application-oriented state-of-the-art solution approaches with regard to the process industries.

In chemical engineering, pinch analysis holds a long tradition as a method for determining optimal target values for heat or mass exchanger networks by calculating an optimal alignment of available flows. A graphical representation of the time-material production relationship derived from the original pinch analysis can be used for aggregate production planning. This can deliver insights in the production planning problem as several production strategies can be compared. The approach is applied to a case study on bicycle coating.

Supply chain network are considered as solution for effectively meeting customer requirements such as low cost, high product variety, quality and shorter lead times. The success of a supply chain lies in good strategic and tactical planning and monitoring at the operational level. Strategic planning is long term planning and usually consists in selecting providers and distributors, location and capacity planning of manufacturing/servicing units, among others.

Scheduling a sports league requires to solve a hard combinatorial optimization problem. We consider a league of a set

T

of

n

teams supposed to play in a single round robin tournament (SRRT). Accordingly, each team

i

∈

T

has to play against each other team

j

∈

T, j

≠

i

, exactly one match. The tournament is partitioned into matchdays (MD) being periods where matches can be carried out. Each team

i

∈

T

shall play exactly once per MD. Hence, we have a compact structure resulting in an ordered set

P

of

n

−1 MDs.

In many practical applications of resource-constrained project scheduling a work content (e.g., in man months) is specified for each activity instead of a fixed duration and fixed resource requirements. In this case, the resource usages of the activities may vary over time. The problem then consists in determining the resource usage of each activity at each point in time such that precedence constraints, resource scarcity, and specific constraints on the evolution over time of resource usages are respected and the project duration is minimized. We present two priority-rule methods for this problem and report on results of an experimental performance analysis for instances with up to 200 activities.

Die Projektportfolioplanung stellt ein multikriterielles Entscheidungsproblem dar, das neben der Projektauswahl unter Berücksichtung von Projektabhängigkeiten und Synergieeffekten verschiedener Art auch die zeitliche Einplanung von Projekten umfasst. Dabei sollen auch die Begrenzungen für den Ressourcenverbrauch von erneuerbaren und nicht erneuerbaren Ressourcen beachtet werden. Um eine Entscheidungsunterstützung hierfür zu bieten, wird zunächst ein mathematisches Modell aufgestellt, um darauf folgend den Einsatz von Standardoptimierungssoftware wie auch von heuristischen Verfahren als Möglichkeit zum Umgang mit mehreren Zielfunktionen vorzustellen.

Es wird die Architektur eines entwickelten Multi-Agenten Systems (MAS) zur dezentralen Lösung des Decentral Resource Constrained Multi Projekt Scheduling Problem (DRCMPSP) vorgestellt. Die Systemarchitektur basiert auf Web-Services, welche die einfache Integration und somit auch Evaluation alternativer Koordinationsmechanismen von Agenten ermöglichen. Bei dem System handelt es sich um eine internetbasierte Anwendung, deren Funktionalität über einen Internetbrowser zur Verfügung gestellt wird (http://www.agentcopp.de). Auf diese Weise kann das MAS auch zukünftig von Systementwicklern und Wissenschaftlern in den von ihnen gewählten IT-Umgebungen benutzt und mit anderen Systemen unter identischen IT-Rahmenbedingungen verglichen werden. Ferner werden 80 Benchmarkprobleme und Lösungen für das DRCMPSP präsentiert. Mit dem Beitrag wird das Ziel verfolgt, das Benchmarking von Systemen für das DRCMPSP transparenter zu gestalten.

In the work a resource-constrained project scheduling problem (RCPSP) is considered. This classical NP-hard problem evokes interest from both theoretical and applied points of view. Thus we can divide effective (i.e. polynomial) approximation algorithms in two groups: fast heuristic algorithms for the whole problem and generalizations and algorithms with performance guarantee for particular cases. In first section we consider the statement of the problem and some generalizations. Along with renewable resources we consider consumable resources which can be stored to be used at any moment after the moment of allocation. A polynomial optimal algorithm for solving the problem with consumable resources only was suggested by Gimadi, Sevastianov and Zalyubovsky [2]. So we can consider polynomially solved relaxation of RCPSP. In this relaxation instead of each renewable resource we have consumable resource which is allocated at each moment of time in one and the same amount. Then we can use information about the solution of this relaxation for approximate solving the original problem in polynomial time (for example, the order of starting times can be used as a heuristic for serial scheduling scheme). Furthermore, the optimal value of relaxation gives the lower bound for the optimal value of the original problem.

The usual optimization criteria for Markov decision processes (e.g. total discounted reward or mean reward) can be quite insufficient to fully capture the various aspects for a decision maker. It may be preferable to select more sophisticated criteria that also reflect variability-risk features of the problem. To this end we focus attention on risk-sensitive optimality criteria (i.e. the case when expectation of the stream of rewards generated by the Markov processes evaluated by an exponential utility function is considered) and their connections with mean-variance optimality (i.e. the case when a suitable combination of the expected total reward and its variance, usually considered per transition, is selected as a reasonable optimality criterion). The research of risk-sensitive optimality criteria in Markov decision processes was initiated in the seminal paper by Howard and Matheson [6] and followed by many other researchers (see e.g. [1, 2, 3, 5, 4, 8, 9, 14]). In this note we consider a Markov decision chain

X

=

X

n

,

n

= 0,1, ... with finite state space

$$ \mathcal{I} $$

= 1,2, ...,

N

and a finite set

$$ \mathcal{A}_i $$

= 1,2, ...,

K

i

of possible decisions (actions) in state

i

∈

$$ \mathcal{I} $$

. Supposing that in state

i

∈

$$ \mathcal{I} $$

action

k

∈

$$ \mathcal{A}_i $$

is selected, then state

j

is reached in the next transition with a given probability

p

ij

k

and one-stage transition reward

r

ij

will be accrued to such transition.

In the Black-Scholes model optimal trading for maximizing expected power utility under proportional transaction costs can be described by three intervals

B, NT, S

: If the proportion of wealth invested in the stocks lies in

B, NT, S

, then buying, not trading and selling, respectively, are optimal. For a finite time horizon, the boundaries of these trading regions depend on time and on the terminal condition (liquidation or not). Following a stochastic control approach, one can derive parabolic variational inequalities whose solution is the value function of the problem. The boundaries of the active sets for the different inequalities then provide the boundaries of the trading regions. We use a duality based semi-smooth Newton method to derive an efficient algorithm to find the boundaries numerically.

Classical floating point random numbers fail simple tests when considered as rational numbers.

We consider Markov-modulated risk reserves which can be invested into a stock index following a geometric Brownian motion. Within a special class of investment policies we identify one which maximizes the adjustment coefficient. A comparison to the compound Poisson case is also given.

This paper considers the optimal selection of portfolios for utility maximizing investors under a shortfall risk constraint for a financial market model with partial information on the drift parameter. It is known that without risk constraint the distribution of the optimal terminal wealth often is quite skew. In spite of its maximum expected utility there are high probabilities for values of the terminal wealth falling short a prescribed benchmark. This is an undesirable and unacceptable property e.g. from the viewpoint of a pension fund manager. While imposing a strict restriction to portfolio values above a benchmark leads to considerable decrease in the portfolio’s expected utility, it seems to be reasonable to allow shortfall and to restrict only some shortfall risk measure.

This is an expository paper to promote the potential of OR (Operations Research) for simulation. Three applications will therefore be presented which include call centers, check-in at airports, and performance bounds for production lines. The results indicate that (classical and new) OR results might still be most fruitful if not necessary for practical simulation and its optimization.

A multistage stochastic programming problem can be introduced as a finite system of parametric one-stage optimization problems with an inner type of dependence and mathematical (mostly conditional) expectation in objective functions of the individual problems (for more details see e.g. [1], [3], [8]). The constraints sets can depend on the “underlying” probability measure.

This paper describes the features of a multistage ALM recourse model in light of the recent pension reform in the Netherlands. The main results are explicit modeling of indexation decisions and modeling of new regulatory rules.

Since the 1960s qualitative problem structuring methods have evolved mainly in the UK from traditional operational research, which are called „soft OR“. These methods focus on generating understanding of systems as a whole, on improving systems, and on personal learning. System dynamics has similar goals; therefore, it might be useful to combine it with soft OR. Some examples of combinations exist; however, these are mainly anecdotal. Thus, systematic research promises new insights and knowledge about the useful combination of soft OR and system dynamics in practice and theory. This has often been asked for but has not yet been established. In this paper a characterization of system dynamics is presented that can be used to find potential combinations of system dynamics and soft OR. More precisely, a framework designed by [11] for mapping methods is described. This framework characterizes methods along two dimensions: four steps of intervention processes and three domains, in which problem situations manifest: social, personal, and material world. System dynamics is mapped and thus characterized by this framework. On the one hand, the mapping highlights the strengths of system dynamics; on the other hand, it shows possibilities for useful combinations with soft OR. With this study, further steps to a systematic research of combinations between system dynamics and soft OR are undertaken. Based on the method characterization of system dynamics and soft OR, proposals for concrete combinations can be derived and contextual factors for successful combinations can be investigated.