Canan G. Corlu

Accounting for Parameter Uncertainty in Large-Scale Stochastic Simulations with Correlated Inputs

This paper considers large-scale stochastic simulations with correlated inputs having normal-to-anything (NORTA) distributions with arbitrary continuous marginal distributions. Examples of correlated inputs include processing times of workpieces across several workcenters in manufacturing facilities and product demands and exchange rates in global supply chains. Our goal is to obtain mean performance measures and confidence intervals for simulations with such correlated inputs by accounting for the uncertainty around the NORTA distribution parameters estimated from finite historical input data. This type of uncertainty is known as the parameter uncertainty in the discrete-event stochastic simulation literature. We demonstrate how to capture parameter uncertainty with a Bayesian model that uses Sklars marginal-copula representation and Cookes copula-vine specification for sampling the parameters of the NORTA distribution. The development of such a Bayesian model well suited for handling many correlated inputs is the primary contribution of this paper. We incorporate the Bayesian model into the simulation replication algorithm for the joint representation of stochastic uncertainty and parameter uncertainty in the mean performance estimate and the confidence interval. We show that our model improves both the consistency of the mean line-item fill-rate estimates and the coverage of the confidence intervals in multiproduct inventory simulations with correlated demands.

A subset selection procedure under input parameter uncertainty

This paper considers a stochastic system simulation with unknown input distribution parameters and assumes the availability of a limited amount of historical data for parameter estimation. We investigate how to account for parameter uncertainty - the uncertainty that is due to the estimation of the input distribution parameters from historical data of finite length - in a subset selection procedure that identifies the stochastic system designs whose sample means are within a user-specified distance of the best mean performance measure. We show that even when the number of simulation replications is large enough for the stochastic uncertainty to be negligible, the amount of parameter uncertainty in output data imposes a threshold on the user-specified distance for an effective use of the subset selection procedure for simulation. We demonstrate the significance of this effect of parameter uncertainty for a multi-item inventory system simulation in the presence of short demand histories.

Estimating the Parameters of the Generalized Lambda Distribution: Which Method Performs Best?

Generalized lambda distribution (GLD) is a flexible distribution that can represent a wide variety of distributional shapes. This property of the GLD has made it very popular in simulation input modeling in recent years, and several fitting methods for estimating the parameters of the GLD have been proposed. Nevertheless, there appears to be a lack of insights about the performances of these fitting methods in estimating the parameters of the GLD for a variety of distributional shapes and input data. Our primary goal in this article is to compare the goodness-of-fits of the popular fitting methods in estimating the parameters of the GLD introduced in Freimer et al. (1988), i.e., Freimer–Mudholkar–Kollia–Lin (FMKL) GLD, and provide guidelines to the simulation practitioner about when to use each method. We further describe the use of the genetic algorithm for the FMKL GLD, and investigate the performances of the suggested methods in modeling the daily exchange rates of eight currencies.

Modelling exchange rate returns: which flexible distribution to use?

It is well known that the normal distribution is inadequate in capturing the skewed and heavy-tailed behaviour of exchange rate returns. To this end, various flexible distributions that are capable of modelling the asymmetric and tailed behaviour of returns have been proposed. In this paper, we investigate the performance of the generalized lambda distribution (GLD) to capture the skewed and leptokurtic behaviour of exchange rate returns. We do this by conducting a comprehensive numerical study to compare the performance of the GLD against the performances of the skewed t distribution, the unbounded Johnson family of distributions and the normal inverse Gaussian (NIG) distribution. Our results suggest that in terms of the value-at-risk and expected shortfall, the GLD shows at least similar performance to the skewed t distribution and the NIG distribution. Considering the ease in GLD’s use for random variate generation in Monte Carlo simulations, we conclude that the GLD can be a good alternative in various financial applications where modelling of the heavy tail behaviour is critical.

Empirical distributions of daily equity index returns

We answer the question of which model to use to represent equity index returns.We compare performances of different distributions using KS and AD statistics.We also test the power of the models using Value-at-Risk failure rates.The generalized lambda distribution outperforms other models. The normality assumption concerning the distribution of equity returns has long been challenged both empirically and theoretically. Alternative distributions have been proposed to better capture the characteristics of equity return data. This paper investigates the ability of five alternative distributions to represent the behavior of daily equity index returns over the period 1979-2014: the skewed Student-t distribution, the generalized lambda distribution, the Johnson system of distributions, the normal inverse Gaussian distribution, and the g-and-h distribution. We find that the generalized lambda distribution is a prominent alternative for modeling the behavior of daily equity index returns.

A simulation-based support tool for data-driven decision making: operational testing for dependence modeling

Dependencies occur naturally between input processes of many manufacturing and service applications. When the dependence parameters are known with certainty, the failure to factor the dependencies into decisions is well known to waste significant resources in system management. Our focus is on the case of unknown dependence parameters that must be estimated from finite amounts of historical input data. In this case, the estimates of the unknown dependence parameters are random variables and simulations are designed to account for the dependence parameter uncertainty to better support the data-driven decision making. The premise of our paper is that there are certain cases in which the assumption of an independent input process to minimize the expected cost of input parameter uncertainty becomes preferable to accounting for the dependence parameter uncertainty in the simulation. Therefore, a fundamental question to answer before capturing the dependence parameter uncertainty in a stochastic system simulation is whether there is sufficient statistical evidence to represent the dependence, despite the uncertainty around its estimate, in the presence of limited data. We seek an answer for this question within a data-driven inventory-management context by considering an intermittent demand process with correlated demand size and number of interdemand periods. We propose two new finite-sample hypothesis tests to serve as the decision support tools determining when to ignore the correlation and when to account for the correlation together with the uncertainty around its estimate. We show that a statistical test accounting for the expected cost of correlation parameter uncertainty tends to reject the independence assumption less frequently than a statistical test which only considers the sampling distribution of the correlation-parameter estimator. The use of these tests is illustrated with examples and insights are provided into operational testing for dependence modeling.

Demand fulfillment probability in a multi-item inventory system with limited historical data

ABSTRACT In a budget-constrained multi-item inventory system with independent demands, we consider the case of unknown demand parameters that are estimated from limited amounts of historical demand data. In this situation, the probability of satisfying all item demands, as a measure of demand fulfillment, is a function of the finite-sample estimates of the unknown demand parameters; thus, the demand fulfillment probability is a random variable. First, we characterize the properties of an asymptotical approximation to the mean and variance of this random variable due to the use of limited data for demand parameter estimation. Second, we use the characterization of the variance of the demand fulfillment probability for quantifying the impact of demand parameter uncertainty on demand fulfillment via numerical experiments. Third, we propose an inventory optimization problem that minimizes the variance of the demand fulfillment probability due to demand parameter uncertainty subject to a budget constraint on the total inventory investment. Our numerical experiments demonstrate that, despite the availability of limited amounts of historical demand data, it is possible to manage inventory with significantly reduced variance in the demand fulfillment probability.

Subset selection for simulations accounting for input uncertainty

We study a subset selection procedure - one of the well-known statistical methods of ranking and selection for stochastic simulations - in the presence of input parameter uncertainty; i.e., the parameters of the input distributions are unknown and there is only a limited amount of input data available for input parameter estimation. The goal is to present a new decision rule which identifies subsets of stochastic system designs including the best (i.e., the design with the largest or smallest expected performance measure) with a probability that exceeds some user-specified value. At WSC 2013, we studied this problem by restricting focus to the method of asymptotic normality approximation to represent input parameter uncertainty. Motivated by the limitations of the asymptotic normality approximation for simulations of complex systems with large numbers of input parameters, we revisit this problem with the simulation replication algorithm as an alternative method to capture input parameter uncertainty.

Simulation of inventory systems with unknown input models: a data-driven approach

Abstract Stochastic simulation is a commonly used tool by practitioners for evaluating the performance of inventory policies. A typical inventory simulation starts with the determination of the best-fit input models (e.g. probability distribution function of the demand random variable) and then obtains a performance measure estimate under these input models. However, this sequential approach ignores the uncertainty around the input models, leading to inaccurate performance measures, especially when there is limited historical input data. In this paper, we take an alternative approach and propose a simulation replication algorithm that jointly estimates the input models and the performance measure, leading to a credible interval for the performance measure under input-model uncertainty. Our approach builds on a nonparametric Bayesian input model and frees the inventory manager from making any restrictive assumptions on the functional form of the input models. Focusing on a single-product inventory simulation, we show that the proposed method improves the estimation of the service levels when compared to the traditional practice of using the best-fit or the empirical distribution as the unknown demand distribution.

Driving inventory system simulations with limited demand data: Insights from the newsvendor problem

ABSTRACT Stochastic inventory system simulation is often the tool of choice by industry practitioners who struggle with the evaluation of the quality of proposed inventory targets using service levels. However, driving simulations with unknown input distribution parameters has its own challenges. In this paper, we focus on the newsvendor problem and quantify the amount of demand parameter uncertainty – the uncertainty around the unknown demand distribution parameters which are estimated from the limited historical demand data – in the confidence interval of the mean service level. We use this quantification to understand how the variance of the mean service level, due to the amount of the demand parameter uncertainty in the simulation output process, changes with the choice of Type-1 and Type-2 service-level criteria, the historical data length, the ratio of the unit shortage cost to the unit holding cost, and the distributional shape of the demand’s density function.