Analysis of a single stage production system with heterogeneous machines

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. The evaluated production system differs from a classical homogeneous multiple server queueing system with regard to inhomogeneities of the two machines. Time inhomogeneity – the service times of the two machines being unequal – and functional inhomogeneity – one of the machines can handle only one class (A) of jobs – are to be distinguished. In the case of time inhomogeneity the calculation of system performance parameters may be carried out using an explicit formula, whereas for the analysis of functional inhomogeneity a numerical solution has to be derived. The impact of time inhomogeneity is very small and decreases with the system workload. On the contrary, functional inhomogeneity leads to elevated cycle times of up to 40% depending on the degree of inhomogeneity (measured by the fraction of A jobs) and the workload. Therefore, in contrast to the time-inhomogeneous case, single stage production systems with functional inhomogeneity can only be approximated tolerably by a homogeneous multiple server queueing system if the fraction of one-machine jobs is less than 30%. The increased throughput times above 30% are supplied by the diagram developed from the numerical solutions. RID="*" ID="*" While this research was constructed the author was affiliated to Institute of Conveying Technology and Logistics. Correspondence to: C. R. Lippolt     

An integrated system solution for supply chain optimization in the chemical process industry

This paper considers a complex scheduling problem in the chemical process industry involving batch production. The application described comprises a network of production plants with interdependent production schedules, multi-stage production at multi-purpose facilities, and chain production. The paper addresses three distinct aspects: (i) a scheduling solution obtained from a genetic algorithm based optimizer, (ii) a mechanism for collaborative planning among the involved plants, and (iii) a tool for manual updates and schedule changes. The tailor made optimization algorithm simultaneously considers alternative production paths and facility selection as well as product and resource specific parameters such as batch sizes, and setup and cleanup times. The collaborative planning concept allows all the plants to work simultaneously as partners in a supply chain resulting in higher transparency, greater flexibility, and reduced response time as a whole. The user interface supports monitoring production schedules graphically and provides custom-built utilities for manual changes to the production schedule, investigation of various what-if scenarios, and marketing queries. RID="*" ID="*" The authors would like to thank Hans-Otto Günther and Roland Heilmann for helpful comments on draft versions of this paper.     

Lot sizing in a production system with rework and product deterioration

Producing new and recovering defective products often takes place on a common facility, with these activities carried out in lots. Consequently, there is a necessity to coordinate the production and rework activities with respect to the timing of operations and also regarding appropriate lot sizes for both processes while completely satisfying a given demand. Thereby, it has to be taken into account whether the state of defective items may change in the course of time while they wait to be reworked. Such a deterioration of reworkable goods can result in increasing rework time and rework cost per unit. In this paper an EPQ model which addresses all of these aspects is presented. Considering set-up and inventory holding costs as well as set-up times, optimization algorithms are developed covering different planning situations. Closed-form results for optimal lot sizes can be obtained and exploited for new analytical insights into coordinated lot sizing in the case of returns and product deterioration.     

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

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. RID="*" ID="*" The research was financially supported by the Sasakawa Scientific Research Grant from The Japan Science Society. The original version of the simulation program is provided by Professor Jae Yeon Kim at Dong Yang University, Korea. Correspondence to: J. K. Lim     

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     

An MILP-based approach to the short-term scheduling of make-and-pack continuous production plants

Many fast moving consumers good manufacturing companies produce a moderate number of intermediates that are combined in many different ways to generate an enormous variety of end products. To do that, such companies usually run continuous production plants in a make-to-stock environment. The process structure includes a fabrication area yielding basic intermediates that are stocked in a large middle storage space, and a packing sector where finished products usually comprising several intermediates are manufactured. Intermediates all undergo the same sequence of processing stages and the production of any campaign is sequentially allocated to an ordered set of end products. An MILP continuous time scheduling problem formulation handling independently assignment and sequencing decisions and considering sequence-dependent setup times and specific due dates for export orders has been developed. The problem objective is to meet all end-product demands at minimum make-span. The proposed model is able to account for assorted products, multiple campaigns for a particular intermediate even at the same unit and the consecutive allocation of an intermediate campaign to different finished products. Moreover, it can easily embed powerful preordering rules to yielding reduced MILP formulations so as to tackle real-world industrial problems at low computational cost. The approach has been successfully applied to large-scale industrial examples. RID="*" ID="*" The authors acknowledge financial support from FONCYT under Grant 14-07004, and from “Universidad Nacional del Litoral” under CAI+D 121. Correspondence to: J. Cerdá     

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. RID="*" ID="*" The authors would like to express their thanks for the valuable support provided by the anonymous participants (outpatient department staff). Thanks also to Helen Gilby, Dr Arjan Shahani and Professor Valter de Senna for their useful comments and help during the research. Correspondence to: P.R. Harper     

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. RID="*" ID="*" The authors would like to thank the German “Bundesministerium für Bildung und Forschung” (Federal Ministry of Education and Research) for supporting the research project “Substance Flow Oriented Closed Loop Supply Chain Management in the Electrical and Electronic Equipment Industry (STREAM)rdquo;. Correspondence to: T. Spengler     

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     

Plant co-ordination in pharmaceutics supply networks

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. Correspondence to: H.-O. Günther     

An application of mixed-integer linear programming models on the redesign of the supply network of Nutricia Dairy &; Drinks Group in Hungary

Between 1995 and 1998 Nutricia acquired a number of dairy companies in Hungary. Each of these companies produced a wide variety of products for its regional market. Although alterations had been made to the production system in the last few years, production and transportation costs were still substantial. This paper presents a research study with regard to the optimisation of the supply network of Nutricia Hungary using a mixed-integer linear programming model. Focussing on consolidation and product specialisation of plants the objective was to find the optimal number of plants, their locations and the allocation of the product portfolio to these plants, when minimizing the sum of production and transportation costs. The model is in line with traditional location/allocation models, with a modification concerning inter-transportation of semi-finished products between plants. The production costs used in this model are based on a Green field situation, taking into account new and more advanced technologies available today. The model is used by the Nutricia Dairy and Drinks Group as a decision supporting tool. Correspondence to: F. H. E. Wouda     

Impact of random defective rate on lot size focusing work-in-process inventory in manufacturing system

Literature has focused inventory models with intensive emphasis on imperfect production processes in recent past. However, the work-in-process-based inventory models have been ignored, relatively, in general and the impact of random defects in the form of reworkable and non-reworkable defect rate on lot size and total cost function in particular. This paper develops mathematical models for work-in-process-based inventory by incorporating the effect of random defects rate on lot size and expected total cost function. Our proposed models assume that defective products produced during the production process follow random distributions. Defective products, either in the form of reworkable or rejected production units, follow four types of distribution density functions: uniform, triangular, double triangular and beta distribution. Mathematical models are derived for optimum lot size based on minimization of expected total cost function through the analytical optimization approach. Numerical examples and detailed sensitivity analysis are carried to illustrate and compare the proposed models at different levels of distribution functions’ parameters.     

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.     

Optimal locations of on-line and off-line rework stations in a serial production system

The production rate and product quality are two vital concerns for any manufacturing industry. Number of defective items reduces production rate and increases unit production cost. Moreover, if nonconforming items reach to the customers then manufacturer’s goodwill may drastically go down. Thus, quality inspection is treated as an inherent part of manufacturing. In this research, an N-stage serial production line with an inspection station at the end of it is considered to make decisions concerning this issue. On detecting a defective item at the end of the line it is scrapped or repaired at regular workstation or is sent to an off-line rework station for repair. Assuming each workstation produces a single type of defect a unit cost function is developed for alternative decisions on each type of defect. In order to minimise the unit cost of production and determine an appropriate decision for individual defect types, a fractional mixed integer nonlinear programming is formulated. After transformation to a mixed integer linear programming problem it is solved optimally. A small problem from garments industry is described in detail to show the solution procedure with a branch and bound method. Empirical tests with up to 40 workstations are permed to show the efficiency of the solution process.     

Advanced production scheduling for batch plants in process industries

An Advanced Planning System (APS) offers support at all planning levels along the supply chain while observing limited resources. We consider an APS for process industries (e.g. chemical and pharmaceutical industries) consisting of the modules network design (for long–term decisions), supply network planning (for medium–term decisions), and detailed production scheduling (for short–term decisions). For each module, we outline the decision problem, discuss the specifi cs of process industries, and review state–of–the–art solution approaches. For the module detailed production scheduling, a new solution approach is proposed in the case of batch production, which can solve much larger practical problems than the methods known thus far. The new approach decomposes detailed production scheduling for batch production into batching and batch scheduling. The batching problem converts the primary requirements for products into individual batches, where the work load is to be minimized. We formulate the batching problem as a nonlinear mixed–integer program and transform it into a linear mixed–binary program of moderate size, which can be solved by standard software. The batch scheduling problem allocates the batches to scarce resources such as processing units, workers, and intermediate storage facilities, where some regular objective function like the makespan is to be minimized. The batch scheduling problem is modelled as a resource–constrained project scheduling problem, which can be solved by an efficient truncated branch–and–bound algorithm developed recently. The performance of the new solution procedures for batching and batch scheduling is demonstrated by solving several instances of a case study from process industries.     

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.     

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

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. RID="*" ID="*" I thank Anja De Waegenaere, Peter Kort and an anonymous referee for useful comments on an earlier draft.     

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. RID="We are grateful to experts of the federal funds and the Ministry of Labour, Health and Social Affairs for providing us with detailed information on the Austrian reimbursement system for inpatients and for approving our data request. In addition, we especially thank Dr. Wilhelm Frank of the Austrian Federal Institute for Health Care for making the needed inpatient data available for us. Special thanks are due to Professor Arjan Shahani, Paul Harper and Sally Brailsford (University of Southampton, United Kingdom), Professor Lucas Delesie (Catholic University of Leuven, Belgium), Professor Bernhard Schwarz (University of Vienna, Austria) and Professor Engelbert Dockner (University of Vienna, Austria) for valuable comments on this investigation. Correspondence to:M. Rauner     

Framework for Modeling Dependencies in Collaborative Engineering Processes

This article describes an engineering process representation and modeling tool. The approach is especially suitable for describing large-scale, mature design processes involving numerous tasks, some of which may be performed by automated computer agents. The underlying representation is a graph of information-processing units with explicitly defined input and output feature elements. We show that this representation is more complete than those used in previous process modeling approaches and overcomes some of their limitations when dealing with design processes involving dependencies at multiple levels of detail. The representation is combined with rules for automatically operating upon the graph to preserve consistency when traversing to higher or lower levels of detail.     

On extreme values of orbit lengths in M/G/1 queues with constant retrial rate

In the design of waiting facilities for the units in a retrial queue, it is of interest to know probability distributions of extreme values of the orbit length. The purpose of this paper is to investigate the asymptotic behavior of the maximum orbit length in the queue with constant retrial rate, as the time interval increases. From the classical extreme value theory, we observe that, under standard linear normalizations, the maximum orbit length up to the nth time the positive recurrent queue becomes empty does not have a limit distribution. However, by allowing the parameters to vary with n, we prove the convergence of maximum orbit lengths to three possible limit distributions when the traffic intensity approaches 1 from below and n approaches infinity.

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Received: October 7, 1999 / Accepted: November 21, 2000