Evaluating alternative estimators for optimal order quantities in the newsvendor model with skewed demand

This paper considers the classical Newsvendor model, also known as the Newsboy problem, with the demand to be fully observed and to follow in successive inventory cycles one of the Exponential, Rayleigh, and Log-Normal distributions. For each distribution, appropriate estimators for the optimal order quantity are considered, and their sampling distributions are derived. Then, through Monte-Carlo simulations, we evaluate the performance of corresponding exact and asymptotic confidence intervals for the true optimal order quantity. The case where normality for demand is erroneously assumed is also investigated. Asymptotic confidence intervals produce higher precision, but to attain equality between their actual and nominal confidence level, samples of at least a certain size should be available. This size depends upon the coefficients of variation, skewness and kurtosis. The paper concludes that having available data on the skewed demand for enough inventory cycles enables (i) to trace non-normality, and (ii) to use the right asymptotic confidence intervals in order the estimates for the optimal order quantity to be valid and precise.Inventory Control; Newsboy Problem; Skewed Demand; Exact and Asymptotic Confidence Intervals; Monte-Carlo Simulations

A maximum entropy approach to the newsvendor problem with partial information

In this paper, we consider the newsvendor model under partial information, i.e., where the demand distribution D is partly unknown. We focus on the classical case where the retailer only knows the expectation and variance of D. The standard approach is then to determine the order quantity using conservative rules such as minimax regret or Scarf's rule. We compute instead the most likely demand distribution in the sense of maximum entropy. We then compare the performance of the maximum entropy approach with minimax regret and Scarf's rule on large samples of randomly drawn demand distributions. We show that the average performance of the maximum entropy approach is considerably better than either alternative, and more surprisingly, that it is in most cases a better hedge against bad results.Newsvendor model; entropy; partial information

The Distribution-Free Newsboy Problem with Multiple Discounts and Upgrades

Most papers on the newsboy problem assume that excess inventory is either sold after discount or discarded. In the real world, overstocks are handled with multiple discounts, upgrades, or a combination of these measures. For example, a seller may offer a series of progressively increasing discounts for units that remain on the shelf, or the seller may use incrementally applied innovations aimed at stimulating greater product sophistication. Moreover, the normal distribution does not provide better protection than other distributions with the same mean and variance. In this paper, we find the differences between normal distribution approaches and distribution-free approaches in four scenarios with mean and variance of demand as the only available data to decision-makers. First, we solve the newsboy problem by considering multiple discounts. Second, we formulate and solve the newsboy problem by considering multiple upgrades. Third, we formulate and solve a mixed newsboy problem characterized with multiple discounts and upgrades. Finally, we extend the model to solve a multiproduct newsboy problem with a storage or a budget constraint and develop an algorithm to find the solutions of the models. Concavity of the models is proved analytically. Extensive computational experiments are presented to verify the robustness of the distribution-free approach. The results show that the distribution-free approach is robust

Evaluating alternative estimators for optimal order quantities in the newsvendor model with skewed demand

This paper considers the classical Newsvendor model, also known as the Newsboy problem, with the demand to be fully observed and to follow in successive inventory cycles one of the Exponential, Rayleigh, and Log-Normal distributions. For each distribution, appropriate estimators for the optimal order quantity are considered, and their sampling distributions are derived. Then, through Monte-Carlo simulations, we evaluate the performance of corresponding exact and asymptotic confidence intervals for the true optimal order quantity. The case where normality for demand is erroneously assumed is also investigated. Asymptotic confidence intervals produce higher precision, but to attain equality between their actual and nominal confidence level, samples of at least a certain size should be available. This size depends upon the coefficients of variation, skewness and kurtosis. The paper concludes that having available data on the skewed demand for enough inventory cycles enables (i) to trace non-normality, and (ii) to use the right asymptotic confidence intervals in order the estimates for the optimal order quantity to be valid and precise

Evaluating alternative estimators for optimal order quantities in the newsvendor model with skewed demand

This paper considers the classical Newsvendor model, also known as the Newsboy problem, with the demand to be fully observed and to follow in successive inventory cycles one of the Exponential, Rayleigh, and Log-Normal distributions. For each distribution, appropriate estimators for the optimal order quantity are considered, and their sampling distributions are derived. Then, through Monte-Carlo simulations, we evaluate the performance of corresponding exact and asymptotic confidence intervals for the true optimal order quantity. The case where normality for demand is erroneously assumed is also investigated. Asymptotic confidence intervals produce higher precision, but to attain equality between their actual and nominal confidence level, samples of at least a certain size should be available. This size depends upon the coefficients of variation, skewness and kurtosis. The paper concludes that having available data on the skewed demand for enough inventory cycles enables (i) to trace non-normality, and (ii) to use the right asymptotic confidence intervals in order the estimates for the optimal order quantity to be valid and precise

REVENUE AND ORDER MANAGEMENT UNDER DEMAND UNCERTAINTY

We consider a firm that delivers its products across several customers or markets, each with unique revenue and uncertain demand size for a single selling season. Given that the firm experiences a long procurement lead time, the firm must decide, far in advance of the selling season not only the markets to be pursued but also the procurement quantity. In this dissertation, we present several operational scenarios in which the firm must decide which customer demands to satisfy, at what level to satisfy each customer demand, and how much to produce (or order) in total. Traditionally, a newsvendor approach to the single period problem assumes the use of an expected profit objective. However, maximizing expected profit would not be appropriate for firms that cannot afford successive losses or negligible profits over several consecutive selling seasons. Such a setting would most likely require minimizing the downside risk of accepting uncertain demands into the production plan. We consider the implications of such competing objectives. We also investigate the impact that various forms of demand can have on the flexibility of a firm in their customer/market selection process. a firm may face a small set of unconfirmed orders, and each order will often either come in at a predefined level, or it will not come in at all. We explore optimization solution methods for this all-or-nothing demand case with risk-averse objective utilizing conditional value at risk (CVaR) concept from portfolio management. Finally, in this research, we explore extensions of the market selection problem. First, we consider the impact of incorporating market-specific expediting costs into the demand selection and procurement decisions. Using a lost sales assumption instead of an expediting assumption, we perform a similar analysis using market-specific lost sales costs. For each extension we investigate two different approaches: i) Greedy approach: here we allocate order quantity to market with lowest expediting cost (lowest expected revenue) first. ii) Rationing approach: here we find the shortage (lost sale) then ration it across all the markets. We present ideas and approaches for each of these extensions to the selective newsvendor problem

On the design for flexibility of manufacturing systems : a stochiastic approach

Flexibility has emerged as one of the most strategic imperatives for company viability in today\u27s fast paced economy. This realization has stimulated extensive research efforts in this area most of which have focused mainly on defining flexibility and its attributes, the need for flexibility and how to measure it. Nevertheless, despite the considerable amount of publications regarding flexibility and its related subjects, insufficient attention has been given to the optimality of the design for flexibility and the inherent needs to meet uncertainty. Bridging this gap is the intent of this work. In this dissertation, developed analytical models are for the optimum design of flexible systems. The models introduced are based on extensions of the single period stochastic inventory model and real option theory to determine the optimum level of the various flexibility attributes that are required to meet the needs of a concern in an uncertain environment. Our premise stems from the fact that flexibility does not come at no cost. That is, when designing a system, the more flexibility built in it, the more the cost that will be incurred to maintain it. On the other hand, if the system is designed with low levels of flexibility, it may not be able to meet the uncertain demand, therefore causing loss of future revenue. The developed models, then, are applied to examples where data are obtained from machine tool manufacturers to show how to strike a balance between the two conflicting scenarios of over and under-flexible designs

Distribution-free Inventory Risk Pooling in a Multi-location Newsvendor

With rapidly increasing e-commerce sales, firms are leveraging the virtual pooling of online demands across customer locations in deciding the amount of inventory to be placed in each node in a fulfillment network. Such solutions require knowledge of the joint distribution of demands; however, in reality, only partial information about the joint distribution may be reliably estimated. We propose a distributionally robust multi-location newsvendor model for network inventory optimization where the worst-case expected cost is minimized over the set of demand distributions satisfying the known mean and covariance information. For the special case of two homogeneous customer locations with correlated demands, we show that a six-point distribution achieves the worst-case expected cost, and derive a closed-form expression for the optimal inventory decision. The general multi-location problem can be shown to be NP-hard. We develop a computationally tractable upper bound through the solution of a semidefinite program (SDP), which also yields heuristic inventory levels, for a special class of fulfillment cost structures, namely nested fulfillment structures. We also develop an algorithm to convert any general distance-based fulfillment cost structure into a nested fulfillment structure which tightly approximates the expected total fulfillment cost.https://deepblue.lib.umich.edu/bitstream/2027.42/146785/1/1389_Govindarajan.pd

Demand Estimation at Manufacturer-Retailer Duo: A Macro-Micro Approach

This dissertation is divided into two phases. The main objective of this phase is to use Bayesian MCMC technique, to attain (1) estimates, (2) predictions and (3) posterior probability of sales greater than certain amount for sampled regions and any random region selected from the population or sample. These regions are served by a single product manufacturer who is considered to be similar to newsvendor. The optimal estimates, predictions and posterior probabilities are obtained in presence of advertising expenditure set by the manufacturer, past historical sales data that contains both censored and exact observations and finally stochastic regional effects that cannot be quantified but are believed to strongly influence future demand. Knowledge of these optimal values is useful in eliminating stock-out and excess inventory holding situations while increasing the profitability across the entire supply chain. Subsequently, the second phase, examines the impact of Cournot and Stackelberg games in a supply-chain on shelf space allocation and pricing decisions. In particular, we consider two scenarios: (1) two manufacturers competing for shelf space allocation at a single retailer, and (2) two manufacturers competing for shelf space allocation at two competing retailers, whose pricing decisions influence their demand which in turn influences their shelf-space allocation. We obtain the optimal pricing and shelf-space allocation in these two scenarios by optimizing the profit functions for each of the players in the game. Our numerical results indicate that (1) Cournot games to be the most profitable along the whole supply chain whereas Stackelberg games and mixed games turn out to be least profitable, and (2) higher the shelf space elasticity, lower the wholesale price of the product; conversely, lower the retail price of the product, greater the shelf space allocated for that product