Nils Rudi

Centralized and Competitive Inventory Models with Demand Substitution

A standard problem in operations literature is optimal stocking of substitutable products. We consider a consumer-driven substitution problem with an arbitrary number of products under both centralized inventory management and competition. Substitution is modeled by letting the unsatisfied demand for a product flow to other products in deterministic proportions. We obtain analytically tractable solutions that facilitate comparisons between centralized and competitive inventory management under substitution. For the centralized problem we show that, when demand is multivariate normal, the total profit is decreasing in demand correlation.

A Two-Location Inventory Model with Transshipment and Local Decision Making

In situations where a seller has surplus stock and another seller is stocked out, it may be desirable to transfer surplus stock from the former to the latter. We examine how the possibility of such transshipments between two independent locations affects the optimal inventory orders at each location. If each location aims to maximize its own profits--we call this local decision making--their inventory choices will not, in general, maximize joint profits. We find transshipment prices which induce the locations to choose inventory levels consistent with joint-profit maximization.

Resource Flexibility with Responsive Pricing

This article studies two types of flexibility used by firms to better respond to uncertain market conditions: resource flexibility and responsive pricing. We consider a situation in which a single flexible resource can be used to satisfy two distinct demand classes. While the resource capacity must be decided based on uncertain demand functions, the resource allocation as well as the pricing decision are made based on the realized demand functions.We characterize the effects of two key drivers of flexibility: demand variability and demand correlation, assuming normally distributed demand curve intercepts. Demand variability creates opportunity costs and, with fixed prices, decreases the firms profit. We show that with the additional flexibility gained from responsive pricing, the firm can maximize the benefits of favorable demand conditions and mitigate the effects of poor demand conditions, ultimately profiting from variability. Positive demand correlation, on the other hand, remains undesirable under responsive pricing. The optimal capacity of the flexible resource is always increasing in both demand variability and demand correlation. This contrasts with the scenarios based on fixed prices, highlighting the crucial difference that responsive pricing makes in the management of flexible resources. We further quantify the value of flexibility for the firm and its customers by considering, as a benchmark, a firm relying on two dedicated resources. The value of flexibility is most significant if the demand levels are highly variable and negatively correlated. In such cases, the firm benefits from demand variability due to responsive pricing, while facing limited demand risk due to resource flexibility. Finally, we endogenize the input price of the flexible resource by considering the pricing decision of the resource supplier.

Supply Chain Choice on the Internet

Internet companies extensively use the practice of drop-shipping, where the wholesaler stocks and owns the inventory and ships products directly to customers at retailers request. Under the drop-shipping arrangement, the supply chain benefits from risk pooling because the inventory for multiple retailers is stocked at the same location, the wholesalers. Another more traditional channel alternative on the Internet is one in which retailers stock and own the inventory. These two supply chain structures, which predominate on the Internet, result in different inventory risk allocation, stocking decisions, and profits for channel members. Moreover, the two channel alternatives can be combined into a dual strategy whereby the retailer uses local inventory as a primary source and relies on drop-shipping as a backup. We model the dual strategy as a noncooperative game among the retailers and the wholesaler, analyze it, and obtain insights into the structural properties of the equilibrium solution to facilitate development of recommendations for practicing managers. Finally, we characterize situations in which each of three channels is preferable by specifying appropriate ranges of critical parameters, including demand variability, the number of retailers in the channel, wholesale prices, and transportation costs.

Operational Flexibility and Financial Hedging: Complements or Substitutes?

We consider a firm that invests in capacity under demand uncertainty and thus faces two related but distinct types of risk: mismatch between capacity and demand and profit variability. Whereas mismatch risk can be mitigated with greater operational flexibility, profit variability can be reduced through financial hedging. We show that the relationship between these two risk mitigating strategies depends on the type of flexibility: Product flexibility and financial hedging tend to be complements (substitutes)---i.e., product flexibility tends to increase (decrease) the value of financial hedging, and, vice versa, financial hedging tends to increase (decrease) the value of product flexibility---when product demands are positively (negatively) correlated. In contrast to product flexibility, postponement flexibility is a substitute to financial hedging as intuitively expected. Although our analytical results assume perfect flexibility and perfect hedging and rely on a linear approximation of the value of hedging, we validate their robustness in an extensive numerical study.

An Empirical Examination of the Decision to Invest in Fulfillment Capabilities: A Study of Internet Retailers

Internet technology has allowed for a higher degree of decoupling between the information-intensive sales process and the physical process of inventory management than its brick-and-mortar counterpart. As a result, some Internet retailers choose to outsource inventory and back-end operations to focus on the sales/marketing aspects of e-commerce. Nonetheless, many retailers keep fulfillment capabilities in-house. In this paper, we identify and empirically test factors that persuade firms to integrate inventory and fulfillment capabilities with virtual storefronts. Based on the extant literature and previous research in e-commerce, we formulate nine theoretical predictions. We then use data from a sample of over 50 public Internet retailers to test whether empirical data are consistent with these hypotheses. Finally, given the strategic importance and financial magnitude of the inventory investment decision, we analyze the effect of this decision on the economic success of Internet retailers during the period of study. We find that there are many circumstances in which it is prudent to own fulfillment capabilities and inventory. Empirical data are consistent with hypotheses that this tendency is higher for older firms selling small, high-margin products, offering lower levels of product variety, and facing lower demand uncertainty. We also discover that firms making inventory ownership decisions that are consistent with an empirical benchmark derived from environmental and strategic factors are less likely to go bankrupt than those making inconsistent inventory choices.

Observation Bias: The Impact of Demand Censoring on Newsvendor Level and Adjustment Behavior

In an experimental newsvendor setting, we investigate three phenomena: level behavior---the decision makers average ordering tendency; adjustment behavior---the tendency to adjust period-to-period order quantities; and observation bias---the tendency to let the degree of demand feedback influence order quantities. We find that, in three of four conditions, the portion of mismatch cost that results from adjustment behavior exceeds the portion of mismatch cost caused by level behavior. Observation bias is studied through censored demand feedback, a situation that arguably represents most newsvendor settings. When demands are uncensored, subjects tend to order below the normative quantity when they face high margin and above the normative quantity when they face low margin, but in neither case do they order beyond mean demand the pull-to-center effect. Censoring in general leads to lower quantities, magnifying the below-normative-level behavior when they face high margin but partially counterbalancing the above-normative-level behavior when they face low margin, violating the pull-to-center effect in both cases. Data, as supplemental material, are available at http://dx.doi.org/10.1287/mnsc.2013.1825 . This paper was accepted by Christian Terwiesch, operations management.

Product Recovery at the Norwegian National Insurance Administration

Technical aid centers (TACs) in Norway supply devices, such as wheelchairs and hearing aids, to people with handicaps. When a device is returned to a TAC, the TAC staff must decide whether to scrap it or to refurbish it so that it can be used again. The Norwegian National Insurance Administration (NNIA) found that decision makers were scrapping units too frequently, basing their decisions mainly on the hours of labor required to refurbish. We developed a more complete decision-support-system model that accounts for the full cost of sending a unit to the landfill, the cost of refurbishing, the value of parts that can be used elsewhere, the benefits of refurbishing, and so on. Our model is quite simple and visual. Early results suggest that acceptance has been widespread and that decisions have changed, leading to fewer units being scrapped and more being refurbished for redistribution.

Continuous Review Inventory Model with Dynamic Choice of Two Freight Modes with Fixed Costs

We analyze a continuous review (Q, r) stochastic inventory model in which orders placed with a make-to-order manufacturer can be shipped via two alternative freight modes differing in lead time and costs. The costs of placing an order and using each freight mode consist of fixed components and hence exhibit economies of scale. We derive an optimal policy for using the two freight modes for shipping each order. This freight-mode decision is delayed until manufacturing is complete and the optimal policy uses information about the demand incurred in the meantime. Furthermore, given that the two freight modes are used optimally for shipping each order, we solve our model for reorder point and order quantity that minimizes cost. We analyze the cost savings achieved from postponing the freight-mode decision and provide analytical and numerical comparisons between the solutions to our two-freight model and single-freight models. Finally, we illustrate the properties of the solution to our model using an extensive set of numerical examples.

Demand Estimation and Ordering Under Censoring: Stock-Out Timing Is Almost All You Need

Retailers facing uncertain demand can use observed sales to update demand estimates. However, such learning is limited by the amount of inventory carried; when demand exceeds inventory i.e., when a stock-out event occurs, a retailer in general cannot observe actual demand. We propose using observations on the timing of sales occurrences in a Bayesian fashion to learn about demand, and we analyze this learning method for a multiperiod newsvendor setting. We find that, as previously shown with the use of only stock-out event observations, the optimal order quantity with timing observations is greater than the optimal order quantity with full demand observations. We prove this result using a novel methodology from the statistics literature on comparison of experiments. Although the optimal over-ordering with timing observations tends to be less than that with only stock-out event observations in most cases, we do observe cases where the opposite is true. Such cases correspond to high demand uncertainty and low margins, where marginal learning from timing observations is significantly higher than using only a stock-out event. In an extensive numerical study we find that, on average and with respect to uncensored demand observations, the use of timing observations eliminates 76.1% of the loss in expected profit from using only stock-out event observations. We show that, for Poisson and normal demand with unknown mean, the proposed learning method is tractable as well as intuitively appealing: the information contained in the timing of sales occurrences is fully captured by a single number-the timing of stock-out. We also investigate checkpoint models in which the newsvendor can make observations only at predetermined times in a period, and illustrate its convergence to the models with timing and stock-out event observations.