Ae Alp Akçay

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.

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.

A simulation-based approach to capturing autocorrelated demand parameter uncertainty in inventory management

We consider a repeated newsvendor setting where the parameters of the demand distribution are unknown, and we study the problem of setting inventory targets using only a limited amount of historical demand data. We assume that the demand process is autocorrelated and represented by an Autoregressive-To-Anything time series. We represent the marginal demand distribution with the highly flexible Johnson translation system that captures a wide variety of distributional shapes. Using a simulation-based sampling algorithm, we quantify the expected cost due to parameter uncertainty as a function of the length of the historical demand data, the critical fractile, the parameters of the marginal demand distribution, and the autocorrelation of the demand process. We determine the improved inventory-target estimate accounting for this parameter uncertainty via sample-path optimization.

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.

Managing Inventory with Limited History of Intermittent Demand

We consider a single-product discrete-time inventory model with intermittent demand. In every period, either zero demand or a positive demand is observed with an unknown probability. The distribution of the positive demand is assumed to be from the location-scale family with unknown mean and variance. The functional form of the optimal inventory target is available but it is a function of the unknown intermittent demand parameters that must be estimated from a limited amount of historical demand data. We first quantify the expected cost associated with implementing the optimal inventory policy using the point estimates of the unknown parameters by ignoring the uncertainty around them. We then minimize this expected cost with respect to a threshold variable that factors the statistical estimation errors of the unknown parameters into the inventory decision. We find that the use of an optimized threshold leads to a significant reduction in the a priori expected cost of the decision maker.

The benefits of state aggregation with extreme-point weighting for assemble-to-order systems

We provide a new method for solving a very general model of an assemble-to-order system: multiple products, multiple components which may be demanded in different quantities by different products, batch production, random lead times, and lost sales, modeled as a Markov decision process under the discounted cost criterion. A control policy specifies when a batch of components should be produced and whether an arriving demand for each product should be satisfied. As optimal solutions for our model are computationally intractable for even moderate sized systems, we approximate the optimal cost function by reformulating it on an aggregate state space and restricting each aggregate state to be represented by its extreme original states. Our aggregation drastically reduces the value iteration computational burden. For systems in which there is a product that has fulfillment priority over all other products at optimality, we derive error bound for our aggregate solution. This guarantees that the value iteration algorithm for the original problem initialized with the aggregate solution converges to the optimal solution. We also establish the optimality of a lattice-dependent base-stock and rationing policy in the aggregate problem when certain product and component characteristics are incorporated into the aggregation/disaggregation schemes. This enables us to further alleviate the value iteration computational burden in the aggregate problem by eliminating suboptimal actions. Leveraging all of our results, we are able to solve the aggregate problem for systems of up to 22 components, with an average distance of 11.09% from the optimal cost in systems of up to 4 components (for which we could solve the original problem to optimality).

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

We 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.

A taxonomy of supply chain innovations

In this paper, a taxonomy of supply chain and logistics innovations was developed and presented. The taxonomy was based on an extensive literature survey of both theoretical research and case studies. The primary goals are to provide guidelines for choosing the most appropriate innovations for a company, and help companies in positioning themselves in the supply of chain innovations landscape. To this end, the three dimensions of supply chain innovations, namely the goals, supply chain attributes, and innovation attributes were identified and classified. The taxonomy allows for the efficient representation of critical supply chain innovations information, and serves the mentioned goals, which are fundamental to companies in a multitude of industries.