Optimal R&D investments of the firm

This paper examines irreversible decisions on innovative activities where it takes time to complete an R&D project. The total amount of R&D investments that the firm needs to undertake in order to obtain the breakthrough in the innovation process is uncertain. R&D investments are limited by the restriction that they must be self-financed. It is shown that R&D investments are more valuable when the level of uncertainty is large. Especially, it is very attractive to undertake R&D investments if a project faces many uncertainties during its early phases. Furthermore we study how R&D behavior is influenced by different levels of the discount rate and the financing limit. Moreover, the effects of R&D subsidies, spillover benefits and a payoff that decreases over time are analyzed. Received: 9 October 1997 / Accepted: 19 March 1998     

The resource renting problem subject to temporal constraints

We introduce a project scheduling problem subject to temporal constraints where the resource availability costs have to be minimized. As an extension of known project scheduling problems which consider only time-independent costs, this problem includes both time-independent procurement costs and time-dependent renting costs for the resources. Consequently, in addition to projects where all resources are bought, we can deal with projects where resources are rented. Based on the enumeration of a finite set of schedules which is proved to contain an optimal schedule, we develop a depth-first branch-and-bound procedure. Computational experience with a randomly generated test set containing 10800 problem instances is reported.

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Received: December 1, 1999 / Accepted: November 8, 2000     

A survey and annotated bibliography of multiobjective combinatorial optimization

This paper provides a survey of the research in and an annotated bibliography of multiple objective combinatorial optimization, MOCO. We present a general formulation of MOCO problems, describe the main characteristics of MOCO problems, and review the main properties and theoretical results for these problems. The main parts of the paper are a section on the review of the available solution methodology, both exact and heuristic, and a section on the annotation of the existing literature in the field organized problem by problem. We conclude the paper by stating open questions and areas of future research. Received: February 7, 2000 / Accepted: April 14, 2000     

Strategic technology investment under uncertainty

In this paper the technology investment decision of a firm is analyzed, while competition on the output market is explicitly taken into account. Technology choice is irreversible and the firms face a stochastic innovation process with uncertainty about the speed of arrival of new technologies. The innovation process is exogenous to the firms. For reasons of market saturation and the fact that more modern technologies are invented as time passes, the demand for a given technology decreases over time. This implies that also the sunk cost investment of each technology decreases over time. The investment decision problem is transformed into a timing game, in which the waiting curve is introduced as a new concopt. An algorithm is designed for solving this (more) general timing game. The algorithm is applied to an information technology investment problem. The most likely outcome exhibits diffusion with equfal payoffs for the firms. Received: December 16, 1999 / Accepted: February 7, 2001     

Estimating financial risk under time-varying extremal return behavior

Potentially increasing volatility and downside risk is essential to financial risk management which is concerned with the tails, or particularly, the lower tail, of the distribution of speculative asset returns. Applying extreme value theory, the present paper outlines a simple model capturing time-varying tail behavior and studies conditional daily return quantiles for the German DAX. Our results indicate an overall increased risk of large one-day holding-period losses related to a structural break given by the 1987 crash, systematic out-of-sample underestimation of the magnitude of extreme quantiles as well as clustering in estimated quantile exceedances which cannot be fully explained by the forecasting model. RID="*" ID="*" Part of the paper was written while the author was visiting the Center for Mathematical Sciences at Munich University of Technology. He is grateful for the members' hospitality and thanks Claudia Klüppelberg for helpful discussions as well as two anonymous referees for comments improving the paper.     

Planning and scheduling in the process industry

Since there has been tremendous progress in planning and scheduling in the process industry during the last 20 years, it might be worthwhile to give an overview of the current state-of-the-art of planning and scheduling problems in the chemical process industry. This is the purpose of the current review which has the following structure: we start with some conceptional thoughts and some comments on special features of planning and scheduling problems in the process industry. In Section 2 the focus is on planning problems while in Section 3 different types of scheduling problems are discussed. Section 4 presents some solution approaches especially those applied to a benchmark problem which has received considerable interest during the last years. Section 5 allows a short view into the future of planning and scheduling. In the appendix we describe the Westenberger-Kallrath problem which has already been used extensively as a benchmark problem for planning and scheduling in the process industr y.     

A-Design: An Agent-Based Approach to Conceptual Design in a Dynamic Environment

This paper provides an introduction to a new design methodology known as A-Design, which combines aspects of multi-objective optimization, multi-agent systems, and automated design synthesis. The A-Design theory is founded on the notion that engineering design occurs in interaction with an ever-changing environment, and therefore computer tools developed to aid in the design process should be adaptive to these changes. In this paper, A-Design is introduced along with some simple test problems to demonstrate the capabilities of different aspects of the theory. The theory of A-Design is then shown as the basis for a design tool that adaptively creates electro-mechanical configuration designs for changing user preferences.     

On the location of antennas for treatment planning in hyperthermia

Abstract. In this paper we investigate how to determine optimal locations of the microwave antennas being circularly ordered in a hyperthermia device. The heated area containing the tumor should have minimal volume. Based on a simple geometric model for the two and three dimensional case we develop algorithms for the computation of these volumes and present numerical results for the optimal locations. Correspondence to: J. Jahn     

Evaluation of Product and Process Design Robustness

Critical design decisions are commonly made throughout the product development process assuming known material and process behavior. However, stochastic variation during manufacture can inadvertently result in inferior or unacceptable product performance and reduced production yields. Stochastic simulations have been developed to estimate the end-use performance distribution prior to the commitment of hard tooling. This article proposes a definition for integrated product and process robustness, and extends existing stochastic methods to model the important role of the manufacturing flexibility in elimination of defects and product optimization. The goal is to enable the designer to understand and account for not only the negative effects of manufacturing variation, but also the positive impact of manufacturing flexibility wherein instantaneous corrections in the manufacturing process can frequently improve the product quality and eliminate flaws in the product design. Then, a methodology is introduced and contrasted with conventional development methods in the evaluation of best practices for development of a molded plastic component.     

Portfolio management in the binomial model: conditions for outperforming benchmarks

The performance of a portfolio manager is in practice usually measured by the result of his trading strategy compared to a benchmark. Therefore the information whether there exists a strategy that allows to outperform the benchmark is of high value for an active investor. The article shows how this information can be generated in the binomial model. In this context the connection between trading strategies and the investor's expectations concerning future asset prices is analyzed. Based on these findings several conditions are derived that allow the portfolio manager to judge whether the benchmark can be outperformed by an active trading strategy. RID="*" ID="*" Thomas Balzer now works in the Risk Measurement & Management Department of Credit Suisse First Boston in London. The views expressed in this article are those of the author, and do not necessarily represent those of Credit Suisse Group or Credit Suisse First Boston. The author thanks Dr. Michael Olbrich for careful reading and several useful comments.     

Intensity-modulated radiotherapy – a large scale multi-criteria programming problem

Abstract. Radiation therapy planning is often a tight rope walk between dangerous insufficient dose in the target volume and life threatening overdosing of organs at risk. Finding ideal balances between these inherently contradictory goals challenges dosimetrists and physicians in their daily practice. Todays inverse planning systems calculate treatment plans based on a single evaluation function that measures the quality of a radiation treatment plan. Unfortunately, such a one dimensional approach cannot satisfactorily map the different backgrounds of physicians and the patient dependent necessities. So, too often a time consuming iterative optimization process between evaluation of the dose distribution and redefinition of the evaluation function is needed. In this paper we propose a generic multi-criteria approach based on Pareto's solution concept. For each entity of interest – target volume or organ at risk – a structure dependent evaluation function is defined measuring deviations from ideal doses that are calculated from statistical functions. A reasonable bunch of clinically meaningful Pareto optimal solutions are stored in a data base, which can be interactively searched by physicians. The system guarantees dynamic planning as well as the discussion of tradeoffs between different entities. Mathematically, we model the inverse problem as a multi-criteria linear programming problem. Because of the large scale nature of the problem it is not possible to solve the problem in a 3D-setting without adaptive reduction by appropriate approximation schemes. Our approach is twofold: First, the discretization of the continuous problem results from an adaptive hierarchical clustering process which is used for a local refinement of constraints during the optimization procedure. Second, the set of Pareto optimal solutions is approximated by an adaptive grid of representatives that are found by a hybrid process of calculating extreme compromises and interpolation methods. Correspondence to: K.-H. Küfer     

Coordination Approaches and Systems – Part II: An Operational Perspective

This is the second of two papers surveying research in coordination approaches and systems. This paper is concerned with operational coordination, which is aimed at coordinating activities such that the design process can be performed in a near optimal manner with respect to time, and the allocation and utilisation of resources. Aspects of coordination categorised as operational include resource management, scheduling and planning. The first of these two papers presents a review of coordination from a strategic perspective, which is concerned with the decision management aspects of coordination. Greater emphasis is now being placed on the significance of organising the design process as this affects time to market, product quality, cost, and consequently product success. The aim of this paper is to present a fundamental review of operational coordination approaches and systems. The 1990s has seen much progress being made towards a greater understanding and appreciation of coordination in various disciplines through the development of a wide range of approaches and systems. However, there remains a requirement to formally identify the key issues involved in coordination such that a widely accepted representation can be agreed upon. Consequently, research should continue to be supported in the exploration for a unified approach to coordination which will permit a broader and greater understanding of those aspects involved.     

Campaign planning for multi-stage batch processes in the chemical industry

Inspired by a case study from industry, the production of special chemical products is considered. In this industrial environment, multi-purpose equipment is operated in batch mode to carry out the diverse processing tasks. Often, extensive set-up and cleaning of the equipment are required when production switches between different types of products. Hence, processes are scheduled in campaign mode, i.e. a number of batches of the same type are processed in sequence. The production of chem ical products usually involves various stages with significant cumulative lead times. Typically, these production stages are assigned to different plants. A hierarchical modelling approach is presented which co-ordinates the various plant operations within the entire supply network. In the first stage, the length of the campaigns, their timing, the corresponding material flows, and equipment requirements have to be determined. At this stage, an aggregation scheme based on feasibility constraints is employed in order to reflect the limited availability of the various types of production equipment. The second stage consists of an assignment model, which allocates the available equipment units between the production campaigns determined in the first stage of the solution procedure. In the third stage, resource conflicts are resolved, which may occur if clean-out operations and minimal campaign lengths have to be considered. The proposed hierarchical approach allows a more compact model formulation compared to ot her approaches known from the literature. As a result, a very efficient and flexible solution approach is obtained. In particular, commercially available standard solvers can be used to solve a wide range of campaign planning problems arising in the chemical industry.     

A scheduling method for Berth and Quay cranes

This paper discusses a method for scheduling Berth and Quay cranes, which are critical resources in port container terminals. An integer programming model is formulated by considering various practical constraints. A two-phase solution procedure is suggested for solving the mathematical model. The first phase determines the Berthing position and time of each vessel as well as the number of cranes assigned to each vessel at each time segment. The subgradient optimization technique is applied to obtain a near-optimal solution of the first phase. In the second phase, a detailed schedule for each Quay crane is constructed based on the solution found from the first phase. The dynamic programming technique is applied to solve the problem of the second phase. A numerical experiment was conducted to test the performance of the suggested algorithms. RID="*" ID="*" This research has been supported in part by Brain Korea 21 Program (1999–2002). Correspondence to: Y.-M. Park     

Strategic technology planning in hospital management

Abstract. Hospital managers regularly are confronted with their patients' demand for increased service performance on the one hand and tight budgets on the other. As medical technologies influence both the costs and the service spectrum, strategic technology planning is among the critical tasks in hospital management. This paper addresses the corresponding problem of selecting the “best” portfolio of medical devices and proposes an appropriate decision support system. It starts with a multiobjective mathematical programming model that determines the solution space of all efficient portfolios of medical technology investments. The members of the planning committee with their diverging interests then are supported by their interactive exploration of that space until they jointly reach a satisfying portfolio and are not willing to make any further compromises between its objective levels. As one of its salient features the system does not require a priori preference information. RID="*" ID="*" A previous version of this paper has been presented at the Wiesbaden 2000 Meeting of the GOR-Working Group “Operations Research in Health Care”. The authors thank Andrea Lührs and Thomas Rollins, both from Siemens AG, for their valuable support. Moreover, thanks are due to the anonymous referees for their comments on a previous version of this paper. Correspondence to: C. Stummer     

On scalarizing functions in multiobjective optimization

Scalarizing functions play an essential role in solving multiobjective optimization problems. Many different scalarizing functions have been suggested in the literature based on different approaches. Here we concentrate on classification and reference point-based functions. We present a collection of functions that have been used in interactive methods as well as some modifications. We compare their theoretical properties and numerical behaviour. In particular, we are interested in the relation between the information provided and the results obtained. Our aim is to select some of them to be used in our WWW-NIMBUS optimization system. Received: June 11, 2001 / Accepted: October 31, 2001     

A Theory of Complexity, Periodicity and the Design Axioms

One of the topics that has received the attention of mathematicians, scientists and engineers is the notion of complexity. The subject is still being debated, as it lacks a common definition of complexity, concrete theories that can predict complex phenomena, and the mathematical tools that can deal with problems involving complexity. In axiomatic design, complexity is defined only when specific functional requirements or the exact nature of the query are defined. Complexity is defined as a measure of uncertainty in achieving a set of specific functions or functional requirements. Complexity is related to information, which is defined in terms of the probability of success of achieving the Functional Requirements (FRs). There are two classes of complexity: time-dependent complexity and time-independent complexity. There are two orthogonal components of time-independent complexity, i.e., real complexity and imaginary complexity. The vector sum is called absolute complexity. Real complexity of coupled design is larger than that of uncoupled or decoupled designs. Imaginary complexity can be reduced when the design matrix is known. As an example of time-independent imaginary complexity, the design of a printing machine based on xerography is discussed. There are two kinds of time-dependent real complexity: time-dependent combinatorial complexity and time-dependent periodic complexity. Using a robot-scheduling problem as an example, it is shown that a coupled design with a combinatorial complexity can be reduced to a decoupled design with periodic complexity. The introduction of periodicity simplifies the design by making it deterministic, which requires much less information. Whenever a combinatorial complexity is converted to a periodic complexity, complexity and uncertainty is reduced and design simplified.     

Evaluation Metrics for the Rating and Optimization of Snap-fits

Current snap-fit design guides recommend sizing snap-fit features on the basis of insertion force and allowable strain during assembly. Retention force information in such guides is often inaccurate, although this is considered to be the primary attribute of the snap-fit after assembly. The authors contend that these (insertion force, allowable strain, retention force) are not the only critical performance criteria for snap-fit features. Designers have to contend with several other constraints and design requirements. Additional performance metrics for snap-fit features are proposed by drawing upon considerable experience with plastic part design issues. Locking ratio, dimensional and volumetric retention force, consideration of the characteristic dimension of the joint and snap-fit, feature stiffness, required over-insertion and consideration of snap-fit strength relative to part strength are proposed to supplement currently used metrics for evaluating and rating snap-fit designs. The applicability of these metrics is illustrated with real-life examples, and their merits and demerits discussed. A chart of achievable locking ratios for different snap-fit topologies is presented for use as a design tool for the initial selection of snap-fit topologies. Its use as a rational basis for selection and optimization of snap-fits is suggested. Adoption of proposed metrics will allow designers to better quantify, and thereby optimize the performance of, snap-fit features. These ideas will be built upon in the future, and used as a basis for a comprehensive snap-fit selection and detailed design tool.     

Internet-Based Design Catalogue for the Shaft and Bearing

The Internet and World Wide Web (WWW) are evolving as an important communication technology. This paper examines the development of an Internet-based online catalogue on the WWW. An interactive website is prepared that helps a remote designer to design shafts and bearings based on various input parameters provided. The web site also provides solid models of the shaft to perform CAD and FEM analysis. This permits the user to make further investigations, and helps to modify the design satisfactory.     

Functional Interdependence and Product Similarity Based on Customer Needs

In this paper, related product functions are determined for a group of approximately 70 consumer products. Using customer need data, a new matrix approach is introduced to identify these relationships. Techniques are then created for determining product similarity. These techniques are clarified and validated through three case studies, including beverage brewers and material-removal products. The results of these case studies are argued to have significant impact on design-by-analogy procedures, benchmarking methods, mass customization strategies and modular design. The paper concludes with a discussion of applications and related procedures for product development.