Journal ArticleDOI
(s, S) Inventory Systems with Random Lead Times: Harris Recurrence and Its Implications in Sensitivity Analysis
Michael C. Fu,Jian-Qiang Hu +1 more
TLDR
In this paper, the authors consider more general mechanisms for random lead times and derive sample path-based gradient estimates for the finite-horizon average cost per period with respect to the parameters s and S and give a sample path proof of unbiasedness.Abstract:
Most of the previous work on (s, S) inventory systems assumes that lead times for orders are such that orders never cross in time; i.e., the arrival of orders follows the same sequence as the placement of the orders. In this paper we consider more general mechanisms for random lead times. Because the introduction of a general random lead time mechanism makes the system essentially intractable for most performance measures of interest, simulation is a. natural candidate for estimating performance and/or optimizing the system. Two important issues in simulation are the stability and ergodicity of the system. Therefore, we first study some theoretical implications of the mechanism by providing conditions for which the system is stable and Harris ergodic, with the accompanying wide-sense regenerative properties. We then consider the problem of gradient estimation during simulation. Using the technique of perturbation analysis, we derive sample path-based gradient estimates for the finite-horizon average cost per period with respect to the parameters s and S and give a sample path proof of unbiasedness. We then show how stability and ergodicity can be used to simplify the estimators in the limiting infinite-horizon case and to establish strong consistency of the resulting estimators.read more
Citations
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Journal ArticleDOI
Optimization of( s, S ) inventory systems with random lead times and a service level constraint
Sridhar Bashyam,Michael C. Fu +1 more
TL;DR: This paper considers the constrained optimization problem, where orders are allowed to cross in time, and proposes a feasible directions procedure that is simulation based, and presents computational results for a large number of test cases.
Book ChapterDOI
Stochastic Gradient Estimation
TL;DR: In this paper, the authors present a review of gradient estimation methods for simulation optimization algorithms such as stochastic approximation and sample average approximation, including the simultaneous perturbation method.
Book ChapterDOI
Chapter 19 Gradient Estimation
TL;DR: This chapter considers the problem of efficiently estimating gradients from stochastic simulation with the main approaches described are finite differences, perturbation analysis, the likelihood ratio/score function method, and the use of weak derivatives.
Journal ArticleDOI
Sample Path Derivatives for (s, S) Inventory Systems
TL;DR: For ( s, S ) inventory systems, sample path derivatives of performance measures with respect to the two parameters s and S yield derivative estimators which can be estimated from a single sample path or simulation of the inventory system, in some cases not even requiring actual knowledge of the underlying demand distribution.
Proceedings ArticleDOI
Some topics for simulation optimization
TL;DR: A tutorial introduction to simulation optimization is given by classifying the problem setting according to the decision variables and constraints, putting the setting in the simulation context, and then summarize the main approaches to Simulation optimization.
References
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Book
Applied Probability And Queues
TL;DR: In this paper, a simple Markovian model for queueing theory at the Markovians level is proposed, which is based on the theory of random walks and single server queueing.
Book
Introduction to Queueing Networks
TL;DR: A comparison of G-Networks with Multiple Classes of Signals and Positive Customers and Discrete-Time Queueing Systems shows how different approaches to queue management can produce different results.
Journal ArticleDOI
Optimization via simulation: a review
TL;DR: Techniques for optimizing stochastic discrete-event systems via simulation, including perturbation analysis, the likelihood ratio method, and frequency domain experimentation are reviewed.
Journal ArticleDOI
Finding Optimal (s, S) Policies Is About As Simple As Evaluating a Single Policy
Yu-Sheng Zheng,Awi Federgruen +1 more
TL;DR: A new algorithm for computing optimal ( s , S ) policies is derived based upon a number of new properties of the infinite horizon cost function c as well as a new upper bound for optimal order-up-to levels S * and a new lower bound for ideal reorder levels s *.