Second derivative sample path estimators for the GI/G/m queue

Article Abstract:

The derivation of second derivative sample path estimators for the GI/G/m queue is examined through the application of smoothed perturbations analysis (SPA) in a first-come, first-served (FCFS) environment. Estimators for second derivative of mean steady-state system time with respect to a service time distribution parameter open up the possibility of lessening convergence time ofgradient-based stochastic optimmization algorithms. The study illustrates the problems involved in SPA, which in general cases, requires the simulation of additional sample subpaths. An approximation procedure which obviates such simulations is proposed and is shown to have acceptable levels of accuracy. Deterministic or exponential service times result in estimator simplification and in an exact approximation process.

Models, Queuing theory

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Optimization of (s, S) inventory systems with random lead times and a service level constraint

Article Abstract:

A study was conducted to analyze the problem of optimizing periodic review inventory (s,S) systems that support order crossings and are subject to a service level constraint. Gradient-based simulation optimization techniques were utilized to carry out the analysis. A solution-based algorithm was then proposed. It supported the feature directions methodology from nonlinear programming and was implemented using different preprocessing steps that produce good starting solutions. Results indicated that the algorithm performed very well using a single calibration over the entire set of test cases. The calibration accommodated benchmark settings wherein parameters settings for a problem instance can be easily determined.

Inventory Control, Research, Management, Stochastic processes, Lead time

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Efficient design and sensitivity analysis of control charts using Monte Carlo simulation

Article Abstract:

A study was conducted to determine estimators that can be utilized in gradient-based optimization algorithms and in sensitivity evaluations when Monte Carlo simulation is used. Two gradient estimation processes were utilized, namely perturbation analysis and the likelihood ratio/score function technique. The methods were characterized on a general control chart that featured the Shewhart chart and the exponentially-weighted moving average chart as special cases. The possibility of significant variance reduction in settings of practical interest were then examined through simulation examples. Results indicated the possibility of significant variance reduction in specific settings.

Quality Control Management, Quality control, Monte Carlo method, Monte Carlo methods, Quality control charts

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