Browsing by Author "Biller, B."

Now showing 1 - 4 of 4

Open Access
Accounting for parameter uncertainty in large-scale stochastic simulations with correlated inputs
(Institute for Operations Research and the Management Sciences (I N F O R M S), 2011) Biller, B.; Corlu, C. G.
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 Sklar's marginal-copula representation and Cooke's 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.
Open Access
Near optimality guarantees for data-driven newsvendor with temporally dependent demand: A Monte Carlo approach
(IEEE, 2013) Akcay, Alp; Biller, B.; Tayur, S.
We consider a newsvendor problem with stationary and temporally dependent demand in the absence of complete information about the demand process. The objective is to compute a probabilistic guarantee such that the expected cost of an inventory-target estimate is arbitrarily close to the expected cost of the optimal critical-fractile solution. We do this by sampling dependent uniform random variates matching the underlying dependence structure of the demand process - rather than sampling the actual demand which requires the specification of a marginal distribution function - and by approximating a lower bound on the probability of the so-called near optimality. Our analysis sheds light on the role of temporal dependence in the resulting probabilistic guarantee, which has been only investigated for independent and identically distributed demand in the inventory management literature. © 2013 IEEE.
Open Access
Quantifying input uncertainty in an assemble-to-order system simulation with correlated input variables of mixed types
(IEEE, 2014) Akçay, Alp; Biller, B.
We consider an assemble-to-order production system where the product demands and the time since the last customer arrival are not independent. The simulation of this system requires a multivariate input model that generates random input vectors with correlated discrete and continuous components. In this paper, we capture the dependence between input variables in an undirected graphical model and decouple the statistical estimation of the univariate input distributions and the underlying dependence measure into separate problems. The estimation errors due to finiteness of the real-world data introduce the so-called input uncertainty in the simulation output. We propose a method that accounts for input uncertainty by sampling the univariate empirical distribution functions via bootstrapping and by maintaining a posterior distribution of the precision matrix that corresponds to the dependence structure of the graphical model. The method improves the coverages of the confidence intervals for the expected profit the per period.
Open Access
A simulation-based support tool for data-driven decision making: operational testing for dependence modeling
(IEEE, 2014) Biller, B.; Akçay, Alp; Çorlu, C.; Tayur, S.
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.