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An (s, Q) inventory model with remanufacturing and disposal

textabstractIn this paper we analyse an (s, Q) inventory model in which used products can be remanufactured to new ones. We develop two approximations for the average costs and compare their performance with that of an approximation suggested by Muckstadt and Isaac. Next we extend the model with the option to dispose returned products and present a heuristic optimisation procedure which is checked with full enumeration.

Admission control and routing in ATM networks using inferences from measured buffer occupancy

Addresses the issue of call acceptance and routing in ATM networks. The goal is to design an algorithm that guarantees bounds on the fraction of cells lost by a call. The method proposed for call acceptance and routing does not require models describing the traffic. Each switch estimates the additional fraction of cells that would be lost if new calls were routed through the switch. The routing algorithm uses these estimates. The estimates are obtained by monitoring the switch operations and extrapolating to the situation where more calls are routed through the switch. The extrapolation is justified by a scaling property. To reduce the variance of the estimates, the switches calculate the cell loss that would occur with virtual buffers. A way to choose the sizes of the virtual buffers in order to minimize the variance is discussed. Thus, the switches constantly estimate their spare capacity. Simulations were performed using Markov fluid sources to test the validity of the approach. >

Importance Sampling Simulations of Markovian Reliability Systems using Cross Entropy

This paper reports simulation experiments, applying the cross entropy method such as the importance sampling algorithm for efficient estimation of rare event probabilities in Markovian reliability systems. The method is compared to various failure biasing schemes that have been proved to give estimators with bounded relative errors. The results from the experiments indicate a considerable improvement of the performance of the importance sampling estimators, where performance is measured by the relative error of the estimate, by the relative error of the estimator, and by the gain of the importance sampling simulation to the normal simulation.

How Larger Demand Variability May Lead to Lower Costs in the Newsvendor Problem

In this paper we consider the Newsvendor Problem. Intuition may lead to the hypothesis that in this stochastic inventory problem a higher demand variability results in larger variances and in higher costs. In a recent paper, Song (1994a) has proved that the intuition is correct for many demand distributions that are commonly used in practice, such as for the normal distribution function. However, this paper shows that there exist demand distributions for which the intuition is misleading, i.e., for which larger variances occur in combination with lower costs. To characterize these demand distributions we use stochastic dominance relations.

STOCHASTIC INEQUALITIES FOR AN OVERFLOW MODEL

A general method to obtain insensitive upper and lower bounds for the stationary distribution of queueing networks is sketched. It is applied to an overflow model. The bounds are shown to be valid for service distributions with decreasing failure rate. A characterization of phase-type distributions with decreasing failure rate is given. An approximation method is proposed. The methods are illustrated with numerical results.

Optimal trajectory to overflow in a queue fed by a large number of sources

We analyse the deviant behavior of a queue fed by a large number of traffic streams. In particular, we explicitly give the most likely trajectory (or ‘optimal path’) to buffer overflow, by applying large deviations techniques. This is done for a broad class of sources, consisting of Markov fluid sources and periodic sources. Apart from a number of ramifications of this result, we present guidelines for the numerical evaluation of the optimal path.

An analytic model for capacity planning of prisons in the Netherlands

In this paper we describe a decision support system developed to help in assessing the need for various types of prison cells. In particular we predict the probability that a criminal has to be sent home because of a shortage of cells. The problem is modelled through a queuing network with blocking after service. The main objective of our study is to describe our analytical method and an approximate algorithm to solve this network. Through simulation studies we evaluate our method. Both the analytic and the simulation tool are elements of the decision support system.

Asymptotic optimality of the cross-entropy method for Markov chain problems

The correspondence between the cross-entropy method and the zero-variance approximation to simulate a rare event problem in Markov chains is shown. This leads to a sufficient condition that the cross-entropy estimator is asymptotically optimal.

The Cross-Entropy Method with Patching for Rare-Event Simulation of Large Markov Chains

There are various importance sampling schemes to estimate rare event probabilities in Markovian systems such as Markovian reliability models and Jackson networks. In this work, we present a general state-dependent importance sampling method which partitions the state space and applies the cross-entropy method to each partition. We investigate two versions of our algorithm and apply them to several examples of reliability and queueing models. In all these examples we compare our method with other importance sampling schemes. The performance of the importance sampling schemes is measured by the relative error of the estimator and by the efficiency of the algorithm. The results from experiments show considerable improvements both in running time of the algorithm and the variance of the estimator.

Variance Reduction Techniques in Monte Carlo Methods

Monte Carlo methods are simulation algorithms to estimate a numerical quantity in a statistical model of a real system. These algorithms are executed by computer programs. Variance reduction techniques (VRT) are needed, even though computer speed has been increasing dramatically, ever since the introduction of computers. This increased computer power has stimulated simulation analysts to develop ever more realistic models, so that the net result has not been faster execution of simulation experiments; e.g., some modern simulation models need hours or days for a single ’run’ (one replication of one scenario or combination of simulation input values). Moreover there are some simulation models that represent rare events which have extremely small probabilities of occurrence), so even modern computer would take ’for ever’ (centuries) to execute a single run - were it not that special VRT can reduce theses excessively long runtimes to practical magnitudes.