Showing papers in "OR Spectrum in 2003"

A scheduling method for Berth and Quay cranes

Abstract: 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.

Reduced outpatient waiting times with improved appointment scheduling: a simulation modelling approach

Abstract: An outpatient department represents a complex system through which many patients with varying needs pass each day. An effective appointment system is a critical component in controlling patient waiting times within clinic sessions. Current waiting times are often unacceptable and place great stress on clinic staff. This paper describes the development and use of a detailed simulation model of an Ear, Nose and Throat (ENT) outpatient department. The simulation allows various appointment schedules to be examined and their effects on the clinic evaluated. The model has been used to identify a number of critical factors that influence patient waiting times and the build up of queues in the clinic. Alternative appointment schedules have been shown to drastically reduce patient waiting times, without the need for extra resources, and enable the department to move towards meeting the UK Government's Patient's Charter.

Optimization of cardinality constrained portfolios with a hybrid local search algorithm

Abstract: One of the main advantages of portfolios over single assets is that risk can be diversified without necessarily reducing the expected return - provided "proper" assets are selected and they are assigned the "proper" weights. Since in practice investors tend to restrict themselves to a rather small number of different assets, the decision which securities to include is a crucial one that turns out to be NP-hard.

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.

Risk hedging via options contracts for physical delivery

Abstract: We develop an analytical framework for the valuation of options contracts for physical delivery that enable risk-sharing between the trading partners. The spot market price risk, the buyer's demand risk and the seller's marginal cost risk, which are key to many industrial settings such as the chemical industry, are explicitly incorporated. Analytical expressions for the buyer's optimal reservation quantity and the seller's optimal tariff are derived and related to the risk management needs in the industry. The ensuing discussion shows how contingency contracts for physical delivery can complement financial derivative instruments within a company's risk management approach.

Lot-sizing for a single-stage single-product production system with rework of perishable production defectives

Abstract: We consider a single-stage single-product production system. Produced units may be non-defective, reworkable defective, or non-reworkable defective. The system switches between production and rework. After producing a fixed number (N) of units, all reworkable defective units are reworked. Reworkable defectives are perishable or can become technologically obsolete. We assume that the rework time and the rework cost increase linearly with the time that a unit is held in stock. Therefore, N should not be too large. On the other hand, N should not be too small either, since there are set-up times and costs associated with switching between production and rework. For a given N, we derive an explicit expression for the average profit (sales revenue minus costs). Using this expression, the optimal value for N can be determined numerically. Moreover, it is easy to perform a sensitivity analysis, as we illustrate.

Integrated planning of acquisition, disassembly and bulk recycling: a case study on electronic scrap recovery

Abstract: . Due to national and supranational legislation activities, the recovery of discarded products will attain an increasing momentum. Electronic equipment consists of many different parts and materials. Therefore, the related recovery process is often divided into disassembly to remove harmful substances or reusable parts and into bulk recycling to recover ferrous and non-ferrous metals. In order to consider the interactions between choice of scrap to be recovered (acquisition problem), disassembly and bulk recycling, a mixed-integer linear programming model for integrated planning of these stages is presented in this case study. It is applied to determine the daily allocation of products to processes for a major electronic scrap recovery centre that faces limited processing capacities and market restrictions. The optimization calculations covering typical discarded electronic products to be recycled in the related centre lead to a relevant improvement of the economic success.

Flow-shop problems with intermediate buffers

Abstract: In this paper the following extension of the classical flow-shop problem is considered: Between each two successive machines a buffer of limited capacity is given in which jobs can be stored. After finishing processing on a machine, a job either directly has to be processed on the following machine or it has to be stored in the buffer between these machines. If the buffer is completely occupied the job may wait on its current machine but blocks this machine for other jobs. The objective is to determine a feasible schedule minimizing the makespan. To model such a problem setting, the classical disjunctive graph model for shop problems is extended. A tabu search procedure is described where neighborhoods based on an extension of the classical block approach theorem are used. Computational results for extended flow-shop benchmark instances are presented.

A bottleneck assignment approach to the multiple container loading problem

Abstract: The container loading problem addresses the question of how to store several three dimensional, rectangular items (e.g. boxes) in one or more containers in such a way that maximum use is made of the container space. The multiple container problem concentrates on the situation where the consignment to be loaded cannot be accommodated in a single container. To minimize the number of required containers the repeated application of a single container approach is often suggested in the literature. In contrast, in this paper an approach based on a set partitioning formulation of the problem is presented. Within this approach a single container algorithm is used to produce alternative loading patterns. This approach easily allows introducing additional aspects, e.g. separation of boxes or complete shipment of boxes.

Meta-heuristic based decision support for portfolio optimization with a case study on tracking error minimization in passive portfolio management

Abstract: In this paper we describe the concept and design of a meta-heuristic based decision support system generator (DSS-generator) for portfolio optimization. We report extensively on experience with the application of a specific DSS that has been customized for controlling and optimizing passively managed stock funds. Here, the constraints from the law on investment trust companies as well as several fund specific guidelines prohibit that the benchmark can be identically reproduced. For measuring the performance of the portfolio a tracking error model with data stemming from a factor model is applied. Our results show that the system provides proposals for the fund manager in acceptable time which are feasible with respect to the guidelines and excellent in quality.

Plant co-ordination in pharmaceutics supply networks

Abstract: The production of active ingredients in the chemical-pharmaceutical industry involves numerous production stages with cumulative lead times of up to two years. Mainly because of rigorous purity requirements and the need of extensive cleaning of the equipment units, production is carried out in campaigns, i.e. multiple batches of the same product type are produced successively before changing to another product type. Each campaign requires a specific configuration of equipment units according to the recipes of the particular chemical process. In the chemical-pharmaceutical industry, production stages are often assigned to different locations, even different countries. Hence the co-ordination of plant operations within the resulting multi-national supply network is of major importance. A key issue is the co-ordination of campaign schedules at different production stages in the various plants. In practice, it is almost impossible to determine exact optimal solutions to the corresponding complex supply network problem with respect to overall logistics costs. In order to reduce the required computational effort, we introduce several aggregation schemes and a novel MILP model formulation which is based on a continuous representation of time. Moreover, we propose an iterative near-optimal solution procedure which can be successfully applied to even exceptionally large real life problem instances. The applicability of the approach suggested is shown using a case study from industry.

Optimisation of beam directions in intensity modulated radiation therapy planning

Abstract: . In this paper we consider the problem of selecting optimal beam directions as well as optimal intensity profiles for radiation therapy. Our multiobjective mixed integer programming problem is based on and extends a multiobjective LP formulation for intensity optimisation by Hamacher and Kufer. We use a weighted sum scalarisation to explore the benefits of beam direction optimisation. We propose exact and heuristic methods for solving the problem and present some numerical results.

Advanced preprocessing techniques for linear and quadratic programming

Abstract: The paper presents an overview on the preprocessing techniques of linear programming. A new reduction technique is also introduced and the presolve is extended to mixed integer and quadratic programming problems. Numerical results are presented to demonstrate the impact of presolving in interior point and simplex implementations. The demonstrative results are given on large-scale linear, mixed integer and quadratic programming test problems.

A dispatching method for automated guided vehicles by using a bidding concept

Abstract: A dispatching method is suggested for automated guided vehicles by using an auction algorithm. The dispatching method in this study is different from traditional dispatching rules in that it looks into the future for an efficient assignment of delivery tasks to vehicles and also in that multiple tasks are matched with multiple vehicles. The dispatching method in this study is distributed in the sense that the dispatching decisions are made through communication among related vehicles and machines. The theoretical rationale behind the distributed dispatching method is also discussed. Through a simulation study, the performance of the method is compared with that of a popular dispatching rule.

Estimating financial risk under time-varying extremal return behavior

Abstract: 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

Modelling the effects of the Austrian inpatient reimbursement system on length-of-stay distributions

Abstract: . This paper analyses the effects of the new Austrian performance-oriented inpatient payment system on discharge strategies of hospitals by investigating length-of-stay (LOS) distributions. Using generalised linear models applied to data from 1998, we calculate the impact of day and month of admission as well as types of admission and discharge on the LOS of inpatients with major diagnoses. Hereby, we prove significant interdependencies among these variables and reveal hospital behaviour such as 1) premature discharges of inpatients or “unbundling” and 2) “patient splitting”. Hence, our findings illustrate that hospitals react to incentives set by the new system in order to maximise their revenues. Hence, the current reimbursement system still has potential for cost reduction while maintaining high quality of health care. Our strategic policy model supports decision makers in disclosing these effects and provides policy implications to close exploitable gaps within the new reimbursement system.

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.

Decision support for AIDS control programmes in Eastern Africa

Abstract: The Acquired Immune Deficiency Syndrome (AIDS) constitutes the worst hazard to health care systems in Eastern Africa. Misallocation of scarce resources of AIDS Control Programmes will unavoidably lead to additional infections and casualties. The following paper discusses a system dynamics model which allows to assess the impact of different interventions on a pattern population in Eastern Africa. It becomes obvious that short- and long-term consequences of these programmes differ significantly. The optimal allocation of resources, therefore, is highly complex and calls for decision support systems to sustain AIDS control programmes.

Strategic capital budgeting: asset replacement under market uncertainty

Abstract: In this paper the impact of product market uncertainty on the optimal replacement timing of a production facility is studied. The existing production facility can be replaced by a technologically more advanced and thus more cost-effective one. We take into account strategic interactions among the firms competing in the product market by analyzing the problem in a duopolistic setting. We calculate the value of each firm and show that i) a preemptive (simultaneous) replacement occurs when the associated sunk cost is low (high), ii) despite the preemption effect uncertainty always raises the expected time to replace, and iii) the relationship between the probability of optimal replacement within a given time interval and uncertainty is decreasing for long time intervals and humped for short time intervals. Furthermore it is shown that result ii) carries over to the case where firms have to decide about starting production rather than about replacing existing facilities.

Optimal lower bounds on the contribution margin in the case of stochastic order arrival

Abstract: In customer order driven production, decisions on the acceptance of customer orders usually have to be based on variable costs and contribution margins (abbreviated CM), since in the short term only these quantities can be influenced. If we assume that customer orders arrive according to a stochastic process and that the decisions on order acceptance have to be made on each order separately, a customer order usually should be accepted only if its contribution margin exceeds a positive lower bound. This paper shows by means of a stochastic model that, under certain assumptions, this lower bound on the contribution margin can be determined using full costing, provided that the available capacity (constant over time) and the arrival process are balanced. This insight justifies, to a certain extent, the use of full costs to support decisions on the short-term production volume, which is a behaviour that can be observed in practice rather frequently. We also demonstrate the extension of the modelling approach to state-dependent lower bounds on the contribution margin.

Analysing hospital productivity changes using non-parametric approaches

Abstract: The Austrian hospital financing is currently changing, thereby altering the underlying incentive system for hospitals. The purpose of the present hospital financing system is to reduce the dynamics in hospital expenditures by enhancing hospitals' productive performance. This paper looks at the time period 1997 to 1999 and analyses whether the new financing system is already succeeding in enhancing hospital productivity using the approach proposed by Fare, Grosskopf, Norris and Zhang (FGNZ, 1994) to calculate and decompose productivity changes in its components. To analyse the stability of the empirical results based on the FGNZ approach we apply another two approaches, the Ray and Desli (RD, 1997) and the Grifell-Tatje and Lovell (GL, 1999) approaches.

Assessing the resource usage in scheduling with incompatibilities

Abstract: In the field of resource constrained scheduling, the papers in the literature are mainly focused on minimizing the maximum completion time of a set of tasks to be carried out, paying attention to respecting the maximum simultaneous availability of each resource type in the system. This work, instead, considers the issues of balancing the resource usage and minimizing the peak of the resources allocated each time in the schedule, while keeping the makespan low. To this aim we propose a local search algorithm which acts as a multi start greedy heuristic. Extensive experiments on various randomly generated test instances are provided. Furthermore, we present a comparison with lower bounds and known heuristics.

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.

Portfolio Insurance and model uncertainty

Abstract: Some real-world insurance products contain a minimum-wealth or an income-stream guarantee, both of which have to be met irrespective of capital market conditions. Therefore, sellers of such products are well advised to pursue a portfolio strategy that can meet these minimum investment goals if they want to avoid additional cash payments. Portfolio Insurance seems to be the solution to this portfolio problem. However, this paper shows that Portfolio Insurance cannot protect minimum investment goals because its strategies are fitted to a particular form of market risk. Decision makers do not know for sure (with probability one) what the true form of market risk is (model uncertainty); thus model uncertainty makes Portfolio Insurance fail.

On the steady state of the replicating portfolio: accounting for a growth rate

Abstract: For the risk management and transfer pricing of non-maturity liabilities, banks in Europe often use a so-called replicating portfolio technique. A commonly used implementation is replication of a fixed investment rule every time period. This paper deals with the development of the portfolio in the long run, when using this methodology. Applying this replicating portfolio technique yields, after a while, a steady state. Besides the straightforward result when volume is constant, we solve the steady states for the case where the funds (volume) grow with a fixed rate (e.g. due to credited interest or growth in GDP). We therefore define a system growth process, alternative to the Markov process (when volume is constant). From a transfer pricing and risk-management point of view, the resulting portfolio should satisfy certain requirements concerning return and flexibility. Once the steady state can be calculated for given growth rates, the investment policy can be specified. The importance of taking account of a growth rate is illustrated. Growth in volume implies that a different rule will converge to the desired steady state. This is illustrated analytically and with numerical examples. The purpose of the paper is not to find the ideal hedge strategy for non-maturity liabilities, but to improve the existing risk management without any implementation costs for the banks. Given the currently used methodology, accounting for a growth rate can significantly improve the risk management of non-maturity liabilities.

Analysis of a single stage production system with heterogeneous machines

Abstract: The performance of a single stage production system with two heterogeneous machines and two classes of jobs is investigated. The machines have a common buffer with jobs of both classes waiting for service. The arrivals are assumed to follow a Poisson process and the service times to be distributed exponentially.

Portfolio management in the binomial model: conditions for outperforming benchmarks

Abstract: 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.