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     

Project scheduling with calendars

For many applications of project scheduling to real-life problems, it is necessary to take into account calendars specifying time intervals during which some resources such as manpower or machines are not available. Whereas the execution of certain activities like packaging may be suspended during breaks, other activities cannot be interrupted due to technical reasons. Minimum and maximum time lags between activities may depend on calendars, too. In this paper, we address the problem of scheduling the activities of a project subject to calendar constraints. We devise efficient algorithms for computing earliest and latest start and completion times of activities. Moreover, we sketch how to use these algorithms for developing priority-rule methods coping with renewable-resource constraints and calendars.

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Received: July 26, 2000 / Accepted: May 15, 2001     

Truncated branch-and-bound,schedule-construction,and schedule-improvement procedures for resource-constrained project scheduling

We present heuristic procedures for approximately solving large project scheduling problems with general temporal and resource constraints. In particular, we propose several truncated branch-and-bound techniques, priority-rule methods, and schedule-improvement procedures of types tabu search and genetic algorithm. A detailed experimental performance analysis compares the different heuristics devised and shows that large problem instances with up to 1000 activities and several resources can efficiently be solved with sufficient accuracy.

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Received: July 26, 2000 / Accepted: May 15, 2001     

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     

Resource–constrained project scheduling: a heuristic for the multi–mode case

This paper presents a heuristic solution procedure for a very general resource–constrained project scheduling problem. Here, multiple execution modes are available for the individual activities of the project. In addition, minimum as well as maximum time lags between different activities may be given. The objective is to determine a mode and a start time for each activity such that the temporal and resource constraints are met and the project duration is minimized. Project scheduling problems of this type occur e.g. in process industries. The heuristic is a multi–pass priority–rule method with backplanning which is based on an integration approach and embedded in random sampling. Its performance is evaluated within an experimental performance analysis for problem instances of real–life size with 100 activities and up to 5 modes per activity.

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Received: September 22, 2000 / Accepted: May 18, 2001     

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     

Scheduling vehicles in automated transportation systems Algorithms and case study

One of the major planning issues in large scale automated transportation systems is so-called empty vehicle management, the timely supply of vehicles to terminals in order to reduce cargo waiting times. Motivated by a Dutch pilot project on an underground cargo transportation system using Automated Guided Vehicles (AGVs), we developed several rules and algorithms for empty vehicle management, varying from trivial First-Come, First-Served (FCFS) via look-ahead rules to integral planning. For our application, we focus on attaining customer service levels in the presence of varying order priorities, taking into account resource capacities and the relation to other planning decisions, such as terminal management. We show how the various rules are embedded in a framework for logistics control of automated transportation networks. Using simulation, the planning options are evaluated on their performance in terms of customer service levels, AGV requirements and empty travel distances. Based on our experiments, we conclude that look-ahead rules have significant advantages above FCFS. A more advanced so-called serial scheduling method outperforms the look-ahead rules if the peak demand quickly moves amongst routes in the system. Received: June 21, 2000 / Accepted: January 22, 2001     

Approximate mean waiting time in a GI/D/1 queue with autocorrelated times to failures

In this paper, we study process completion time and propose an accurate approximation for the mean waiting time in queues with servers experiencing autocorrelated times to failure, which include only busy periods from a repair completion until the next failure. To do this, we employ a three-parameter renewal approximation that represents the stream of autocorrelated times to failure. The approximation gives rise to a renewal interruption process with two-state Hyper-exponential (H2) times to failure. Then we compute the mean waiting time exactly in a queue experiencing H2 times to failure when the job arrival process is Poisson. This model provides an approximation for the mean waiting time of the original queue having an autocorrelated disruption process. We also propose an accurate approximation for queues with renewal job arrival processes when the server interruption process is general.     

A simulation comparison of group technology with traditional job shop manufacturing

A simulation model of an actual job shop was used to compare group technology with traditional job shop manufacturing. The experiment compared shops which had four different layouts, designed to emphasize different features of traditional job shops and group technology shops, and four distributions of demand for end items. The group technology shops exhibited superior performance in terms of average move time and average set-up time. The traditional job shops had superior performance in queue related variables (average queue length, average waiting time, work-in-process inventory, etc.). This was caused by group technology's dedication of machines. The effects of the queue related variables outweighed the effects of average move time and average set-up time: the average flow time was shorter in the traditional job shop than in the group technology shops.     

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     

Critical Ratio Scheduling with Queue Waiting Time Information: An Experimental Analysis

The Critical Ratio and Slack Time priority scheduling rules have been applied by a number of firms in computer-based scheduling systems for manufacturing operations. One question in using these rules is whether queue waiting time estimates for individual machines should be used in making scheduling decisions. Simulation experiments are reported in this paper that measure the effect of including historical queue time data in the Critical Ratio and Slack Time rules. The results suggest that such data can adversely affect shop performance, measured using criteria such as job flow times, job lateness, and inventory system costs.     

Mean sojourn times in two-queue fork-join systems: bounds and approximations

This paper considers a fork-join system (or: parallel queue), which is a two-queue network in which any arrival generates jobs at both queues and the jobs synchronize before they leave the system. The focus is on methods to quantify the mean value of the ‘system’s sojourn time’ S: with S _i denoting a job’s sojourn time in queue i, S is defined as max{S ₁, S ₂}. Earlier work has revealed that this class of models is notoriously hard to analyze. In this paper, we focus on the homogeneous case, in which the jobs generated at both queues stem from the same distribution. We first evaluate various bounds developed in the literature, and observe that under fairly broad circumstances these can be rather inaccurate. We then present a number of approximations, that are extensively tested by simulation and turn out to perform remarkably well.     

Repair policies for additively degrading machines

This paper describes a method for determining repair policies for machines whose output degrades additively over time. The novelty of the models is that they consider both the state of the machines as well as the state of the repair facility when making repair decisions. The objective in the models is to maximize long-run production. In one model, we approximate the queue waiting time by a geometric random variable, while in the second model we approximate the waiting time by a sequence of geometric random variables (with different means). We show that as the average repair queue increases, the decision to repair must be made earlier. In addition, we show empirically that the simple geometric waiting time approximation becomes less accurate as the queue length increases and that the approximation understates the expected long-run output of the machine. A plastic moulding facility is used to motivate the problem. Computational results using industry supplied data are presented. The results indicate that substantial (10-20%) productivity improvement can be realized using the derived repair policies instead of policies that do not consider the repair queue.     

Makespan estimation and order acceptance in batch process industries when processing times are uncertain

Batch process industries are characterized by complex precedence relationships between operations, which renders the estimation of an acceptable workload very difficult. A detailed schedule based model can be used for this purpose, but for large problems this may require a prohibitive large amount of computation time. We propose a regression based model to estimate the makespan of a set of jobs. We extend earlier work based on deterministic processing times by considering Erlang-distributed processing times in our model. This regression-based model is used to support customer order acceptance. Three order acceptance policies are compared by means of simulation experiments: a scheduling policy, a workload policy and a regression policy. The results indicate that the performance of the regression policy can compete with the performance of the scheduling policy in situations with high variety in the job mix and high uncertainty in the processing times. Correspondence to: C.V. Ivanescu     

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     

Polling of two queues with synchronized correlated inputs and zero walktime

Abstract

This paper studies the polling of two infinite queues by a synchronous server. The inputs to these queues are correlated and restricted to occur only at equally spaced time intervals. For simplicity, the walktime for the server to move from one queue to the other is assumed to be zero in this study. In essence, the problem studied in this paper is equivalent to a fixed service time queueing system which accepts two types of synchronized correlated inputs and adopts an alternating priority discipline. This paper contains a complete analysis of both the busy period and the waiting time. The validity of the analysis has been verified by computer simulations.     

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     

A Machine Release Scheme for the Job Shop Work Center

The job shop may be viewed as a network of queues with each work center then defined as a single or multichannel service facility. In the low volume situation, manufacturing improvements may be expected of each work station. The effect of learning at the service facility will be seen as a reduction of queue congestion and a lessening of unit waiting time. This may eventually lead to excessive idle service capacity or reduced machine utilization. Where there are several machines at each work station, and learning can be expected, a scheme can be developed wherein machines could be released on a schedule to other work assignments while maintaining a relatively constant level of machine utilization.     

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

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. RID="*" ID="*"The research of Dr. Ruud H. Teunter has been made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences. The research presented in this paper is part of the research on re-use in the context of the EU sponsored TMR project REVersed LOGistics (ERB 4061 PL 97-5650) in which take part the Otto-von-Guericke Universitaet Magdeburg (D), the Erasmus University Rotterdam (NL), the Eindhoven University of Technology (NL), INSEAD (F), the Aristoteles University of Thessaloniki (GR), and the University of Piraeus (GR). We thank the anonymous referees for their many helpful comments. Correspondence to: R. H. Teunter     

Optimal tax depreciation lives and charges under regulatory constraints

Depreciation is not only a representation of the loss in asset-value over time. It is also a strategic tool for management and can be used to minimize tax payments. In this paper we derive the depreciation scheme that minimizes the expected value of the present value of future tax payments for two types of constraints on the depreciation method. We show how the optimal scheme depends on the discount factor and the cash flow distributions. Moreover, we find the somewhat surprising result that the way in which the optimum is affected by uncertainty depends crucially on the type of regulatory constraint. Received: January 9, 2001 / Accepted: Feburary 25, 2002