Quantifying input uncertainty in an assemble-to-order system simulation with correlated input variables of mixed types

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

Input uncertainty in stochastic simulations in the presence of dependent discrete input variables

\u3cp\u3eThis paper considers stochastic simulations with correlated input random variables having NORmal-To-Anything (NORTA) distributions. We assume that the simulation analyst does not know the marginal distribution functions and the base correlation matrix of the NORTA distribution but has access to a finite amount of input data for statistical inference. We propose a Bayesian procedure that decouples the input model estimation into two stages and overcomes the problem of inconsistently estimating the base correlation matrix of the NORTA distribution in the presence of discrete input variables. It further allows us to estimate the variability of the simulation output data that are attributable to the input uncertainty due to not knowing the NORTA distribution. Using this input uncertainty estimate, we introduce a simple yet effective method to obtain input uncertainty adjusted credible intervals. We illustrate our method in an assemble-to-order production system with a correlated demand arrival process.\u3c/p\u3

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

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 distributio

Stochastic input model selection

Input modeling is the selection of a probability distribution to capture the uncertainty in the input environment of a stochastic system. Example applications of input modeling include the representation of the randomness in the time to failure for a machining process, the time between arrivals of calls to a call center, and the demand received for a product of an inventory system. Building simulations of stochastic systems requires the development of input models that adequately represent the uncertainty in such random variables. Since there are an abundance of probability distributions that can be used for this purpose, a natural question to ask is how to identify the probability distribution that best represents the particular situation under study. For example, is the exponential distribution a reasonable choice to represent the time to failure for a machining process, or is it better to use an empirical distribution function obtained from the historical time-to-failure data? Recognizing the fact that there is no true input model waiting to be found, the goal of stochastic input modeling is to obtain an approximation that captures the key characteristics of the system inputs.\u3cbr/\u3e\u3cbr/\u3eThe development of a good input model requires the collection of as much information as possible about the relevant randomness in the system as well as the historical data consisting of the past realizations of the random variables of interest. In the presence of a data set, the input model can be identified by fitting a probability distribution to the historical data. However, it may be difficult and/or costly to collect data for the stochastic system under study; it can also be impossible to properly collect any data at all such as when the proposed system does not exist. In the absence of historical data, any relevant information (e.g., expert opinion and the conventional bounds suggested by the underlying physical situation) can be used for input modeling. This article addresses the key issues that arise in stochastic input modeling both in the presence and in the absence of historical data.\u3cbr/\u3e\u3cbr/\u3eThe first step in input modeling is to identify the sources of randomness in the input environment of the system under study. Many stochastic systems contain multiple sources of uncertainty, e.g., the completion time of an item on a particular machine, the potential breakdown of the machine, and the percentage of defective items produced by the machine might be among the sources of uncertainty in a manufacturing setting. Throughout, the random vector X = (X1, X2, …, X K )′ is used to represent the collection of K different inputs of a stochastic system, where X k is the random variable denoting the kth system input. The K components of this random vector might also be correlated with each other. Therefore, the stochastic properties of the random inputs X k , k = 1, 2, …, K, are captured in the joint probability \u3cbr/\u3

Simulation-based production planning for engineer-to-order systems with random yield

\u3cp\u3eWe consider an engineer-to-order production system with unknown yield. We model the yield as a random variable which represents the percentage output obtained from one unit of production quantity. We develop a beta-regression model in which the mean value of the yield depends on the unique attributes of the engineer-to-order product. Assuming that the beta-regression parameters are unknown by the decision maker, we investigate the problem of identifying the optimal production quantity. Adopting a Bayesian approach for modeling the uncertainty in the beta-regression parameters, we use simulation to approximate the posterior distributions of these parameters. We further quantify the increase in the expected cost due to the so-called input uncertainty as a function of the size of the historical data set, the product attributes, and economic parameters. We also introduce a sampling-based algorithm that reduces the average increase in the expected cost due to input uncertainty.\u3c/p\u3

Stochastic simulation under input uncertainty for contract manufacturer selection in pharmaceutical industry

We consider a pharmaceutical company that sources a biological product from a set of unreliable contract manufacturers. The likelihood of a manufacturer to successfully deliver the product is estimated via logistic regression as a function of the product attributes. The assignment of a product to the right contract manufacturers is of critical importance for the pharmaceutical company, and simulation-based optimization is used to identify the optimal sourcing decision. However, the input uncertainty due to the uncertain parameters of the logistic regression model often leads to poor sourcing decisions. We quantify the decrease in the expected profit due to input uncertainty as a function of the size of the historical data set, the level of dispersion in the historical data of a product attribute, and the number of products. We also introduce a sampling-based algorithm that reduces the expected decrease in the expected profit

Improved inventory targets in the presence of limited historical demand data

Most of the literature on inventory management assumes that the demand distribution and the values of its parameters are known with certainty. In this paper, we consider a repeated newsvendor setting where this is not the case and study the problem of setting inventory targets when there is a limited amount of historical demand data. Consequently, we achieve the following objectives: (1) to quantify the inaccuracy in the inventory-target estimation as a function of the length of the historical demand data, the critical fractile, and the shape parameters of the demand distribution; and (2) to determine the inventory target that minimizes the expected cost and accounts for the uncertainty around the demand parameters estimated from limited historical data. We achieve these objectives by using the concept of expected total operating cost and representing the demand distribution with the highly flexible Johnson translation system. Our procedures require no restrictive assumptions about the first four moments of the demand random variables, and they can be easily implemented in practical settings with reduced expected total operating costs

Analyzing the solutions of DEA through information visualization and data mining techniques:SmartDEA framework

Data envelopment analysis (DEA) has proven to be a useful tool for assessing efficiency or productivity of organizations, which is of vital practical importance in managerial decision making. DEA provides a significant amount of information from which analysts and managers derive insights and guidelines to promote their existing performances. Regarding to this fact, effective and methodologic analysis and interpretation of DEA results are very critical. The main objective of this study is then to develop a general decision support system (DSS) framework to analyze the results of basic DEA models. The paper formally shows how the results of DEA models should be structured so that these solutions can be examined and interpreted by analysts through information visualization and data mining techniques effectively. An innovative and convenient DEA solver, SmartDEA, is designed and developed in accordance with the proposed analysis framework. The developed software provides DEA results which are consistent with the framework and are ready-to-analyze with data mining tools, thanks to their specially designed table-based structures. The developed framework is tested and applied in a real world project for benchmarking the vendors of a leading Turkish automotive company. The results show the effectiveness and the efficacy of the proposed framework

Risk assessment in pharmaceutical supply chains under unknown input-model parameters

\u3cp\u3eWe consider a pharmaceutical supply chain where the manufacturer sources a customized product with unique attributes from a set of unreliable suppliers. We model the likelihood of a supplier to successfully deliver the product via Bayesian logistic regression and use simulation to obtain the posterior distribution of the unknown parameters of this model. We study the role of so-called input-model uncertainty in estimating the likelihood of the supply failure, which is the probability that none of the suppliers in a given supplier portfolio can successfully deliver the product. We investigate how the input-model uncertainty changes with respect to the characteristics of the historical data on the past realizations of the supplier performances and the product attributes.\u3c/p\u3

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

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 modelin