The Dynamic Newsvendor Model with Correlated Demand

The classic newsvendor model was developed under the assumption that period‐to‐period demand is independent over time. In real‐life applications, the notion of independent demand is often challenged. In this article, we examine the newsvendor model in the presence of correlated demands. Specifically under a stationary AR(1) demand, we study the performance of the traditional newsvendor implementation versus a dynamic forecast‐based implementation. We demonstrate theoretically that implementing a minimum mean square error (MSE) forecast model will always have improved performance relative to the traditional implementation in terms of cost savings. In light of the widespread usage of all‐purpose models like the moving‐average method and exponential smoothing method, we compare the performance of these popular alternative forecasting methods against both the MSE‐optimal implementation and the traditional newsvendor implementation. If only alternative forecasting methods are being considered, we find that under certain conditions it is best to ignore the correlation and opt out of forecasting and to simply implement the traditional newsvendor model.      

A Newsvendor Problem with Revenue Sharing and Channel Coordination*

Increasingly manufacturers and retailers are implementing revenue‐sharing policies to coordinate distribution channels more effectively. This article considers a standard newsvendor problem in a single manufacturer–retailer channel and compares the expected profits that each party receives in a traditional ordering environment with those that can be achieved under a revenue‐sharing policy designed to completely eliminate double marginalization. It is shown that the retailer always benefits from the transition to revenue sharing by capturing a portion of the incremental channel profit generated by the complete elimination of double marginalization. A necessary demand‐distribution‐dependent condition is derived under which the transition to revenue sharing benefits the manufacturer as well. The findings of this research are illustrated in a numerical example for the uniform demand distribution.     

On Core Sorting in RMTS and RMTO Systems: A Newsvendor Framework

Variation in core condition and uncertainty in market demand pose great challenges for remanufacturers to match supply with demand. This article investigates a firm that acquires and remanufactures cores of multiple quality conditions to satisfy demand. Both remanufacturing‐to‐stock (RMTS) and remanufacturing‐to‐order (RMTO) systems are considered. In each system, a sorting operation that resolves the core conditions before remanufacturing may or may not be adopted, leading to four possible sorting/remanufacturing strategies: (1) no sorting in RMTS; (2) sorting in RMTS; (3) no sorting in RMTO; and (4) sorting in RMTO. Under each strategy, we derive the optimal decisions on the acquisition and remanufacturing quantities, in two scenarios, respectively: (i) all acquired cores are remanufacturable and (ii) some cores are non‐remanufacturable. We find that sorting can be completely useless to RMTS system, and thus should never be adopted regardless of the sorting cost. We provide the analytical condition under which this ineffectiveness of sorting occurs. Nevertheless, sorting is always useful to RMTO system and should be adopted when the sorting cost is below a threshold value. We also conduct an extensive numerical study and show that the effects of sorting to RMTO system are more significant than that to RMTS system.     

Improving Revenue Management Decision Making for Airlines by Evaluating Analyst‐Adjusted Passenger Demand Forecasts*

To maximize revenue, airline revenue management analysts (RMAs) attempt to protect the right number of seats for late‐booking, high‐revenue‐generating passengers from low‐valued leisure passengers. Simulation results in the past showed that a major airline can generate approximately $500 million per year through efficient RM operations. Accurate passenger demand forecasts are required, because reduced forecast error significantly improves revenue. RMAs often adjust the system forecasts to improve revenue opportunity. Analysis of system forecast performance and analyst adjustment is complex, because one must account for all unseen demands throughout the life of a flight. This article proposes a method to account for unseen demand and evaluate forecast performance (adjusted or unadjusted) through a forecast monitoring system. Initial results from one major airline's origin‐destination market data justify the value of RMA forecasting adjustments.     

Lowering Inventory Systems Costs by Using Regression-Derived Estimators of Demand Variability*

Scientific techniques for inventory management typically are applied to systems containing many items. Such techniques require an estimation of the demand variance (and mean) of each item from historical data. This research demonstrates a significant potential for improvement in system cost performance from using least-squares regression fits of a variance-to-mean functional relation instead of the standard statistical variance estimate. Even when there is a moderate degree of heterogeneity among items and when the form of the variance-to-mean relation is misspecified, substantial cost savings may be realized. The cost of statistical uncertainty may be reduced by half. The research also provides evidence that system cost is fairly insensitive to the number of items used to fit the regression. This paper provides the underlying reason why a regression-derived variance estimator yields lower cost: it is less variable than the usual individual item variance estimator.     

An Inventory Model with Planned Shortages and Price Dependent Demand

Previous research has yielded a procedure for a retailer to determine the optimal lot size and selling price when a supplier offers all-unit quantity discounts and demand is a decreasing function of price. In this paper, we extend that research by allowing for shortages. An algorithm is presented that determines the optimal lot size, order level, and selling price for a class of demand functions, including the constant price-elasticity and linear demand functions.     

Retailer's Response to Alternate Manufacturer's Incentives Under a Single‐Period,Price‐Dependent,Stochastic‐Demand Framework*

This article considers the joint development of the optimal pricing and ordering policies of a profit‐maximizing retailer, faced with (i) a manufacturer trade incentive in the form of a price discount for itself or a rebate directly to the end customer; (ii) a stochastic consumer demand dependent upon the magnitude of the selling price and of the trade incentive, that is contrasted with a riskless demand, which is the expected value of the stochastic demand; and (iii) a single‐period newsvendor‐type framework. Additional analysis includes the development of equal profit policies in either form of trade incentive, an assessment of the conditions under which a one‐dollar discount is more profitable than a one‐dollar rebate, and an evaluation of the impact upon the retailer‐expected profits of changes in either incentive or in the degree of demand uncertainty. A numerical example highlights the main features of the model. The analytical and numerical results clearly show that, as compared to the results for the riskless demand, dealing with uncertainty through a stochastic demand leads to (i) (lower) higher retail prices if additive (multiplicative) error, (ii) lower (higher) pass throughs if additive (multiplicative) error, (iii) higher claw backs in both error structures wherever applicable, and (iv) higher rebates to achieve equivalent profits in both error structures.     

Single-Stage and Serial Production Line Systems with Unreliable Machines and General Probability Distributions

This paper presents stochastic models for analyzing production to stock and production on demand systems with arbitrary demand, production, machine breakdown and repair processes, and a finite buffer. Expressions are developed for the transition probabilities among the different states, the proportion of transitions that take the process to a particular state, the probabilities that the process is at a particular state, and the expected state residence times. Also, expressions are developed for some quantities of interest, like average inventory, percentage of lost sales, and expected waiting time. Applications are discussed for various demand, production, machine breakdown, and repair processes and numerical examples are presented. Guidelines are given for utilizing the models in evaluating the economic performance of production systems. Using an approximation procedure, the models are used for modeling multi-stage serial production to stock and production on demand lines. Simulation results indicated that the quality of the approximation is very good. The multi-stage models are useful in practical situations, because they allow the use of different probability distributions for the various processes (production, machine failure, etc.) of each stage.     

An Entropy‐Based Methodology for Valuation of Demand Uncertainty Reduction

We propose a distribution‐free entropy‐based methodology to calculate the expected value of an uncertainty reduction effort and present our results within the context of reducing demand uncertainty. In contrast to existing techniques, the methodology does not require a priori assumptions regarding the underlying demand distribution, does not require sampled observations to be the mechanism by which uncertainty is reduced, and provides an expectation of information value as opposed to an upper bound. In our methodology, a decision maker uses his existing knowledge combined with the maximum entropy principle to model both his present and potential future states of uncertainty as probability densities over all possible demand distributions. Modeling uncertainty in this way provides for a theoretically justified and intuitively satisfying method of valuing an uncertainty reduction effort without knowing the information to be revealed. We demonstrate the methodology's use in three different settings: (i) a newsvendor valuing knowledge of expected demand, (ii) a short life cycle product supply manager considering the adoption of a quick response strategy, and (iii) a revenue manager making a pricing decision with limited knowledge of the market potential for his product.     

Economic Inventory/Transport Lot,Sizing with Quantity and Freight Rate Discounts

Discounts are a primary marketing mechanism for inducing customers to increase the size of their purchases. Quantity discounts from suppliers and freight discounts from shippers are commonly encountered by organizations. This paper structures quantity and freight discounts into the order size decision in a deterministic economic order quantity system. Optimum lot-sizing algorithms are derived for the dual discount situations of all-units or incremental quantity discounts and all-weight or incremental freight discounts.     

Economic Production Lot Sizing with Periodic Costs and Overtime*

Traditional approaches for modeling economic production lot‐sizing problems assume that a single, fixed equipment setup cost is incurred each time a product is run, regardless of the quantity manufactured. This permits multiple days of production from one production setup. In this paper, we extend the model to consider additional fixed charges, such as cleanup or inspection costs, that are associated with each time period's production. This manufacturing cost structure is common in the food, chemical, and pharmaceutical industries, where process equipment must be sanitized between item changeovers and at the end of each day's production. We propose two mathematical problem formulations and optimization algorithms. The models' unique features include regular time production constraints, a fixed charge for each time period's production, and the availability of overtime production capacity. Experimental results indicate the conditions under which our algorithms' performance is superior to traditional approaches. We also test the procedures on a set of lot‐sizing problems facing a national food processor and document their potential economic benefit.     

Utility‐consistent Brand Demand Systems with Endogenous Category Consumption: Principles and Marketing Applications*

This paper introduces the design and implementation of utility‐consistent, brand, and category demand systems. It extends formal demand analysis to the area of brand and category demand, which directly concerns marketing researchers and managers. The proposed brand demand system is a set of interrelated demand functions that are derived explicitly from a utility function describing consumer preferences. The model generalizes by the integration of category expenditures, which are determined endogenously. The theoretical plausibility of the proposed demand model is demonstrated first and, subsequently, brand and category level systems are derived. Econometric methods for estimating the systems are also developed and illustrated in empirical data. The results yield empirically determined, quantitative insights into the structure of consumer demand for brands and product categories. The proposed approach has the attractive feature of structuring the interdependencies of consumer decisions and ensuring an explicit role for theory in applied research.