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.Transshipments, Newsvendor Model, Nash Equilibrium

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.

This paper studies how transshipments affect manufacturers and retailers, considering both exogenous and endogenous wholesale prices. For a distribution system where a single manufacturer sells to multiple identical-cost retailers, we consider both the manufacturer being a price taker and the manufacturer being a price setter in a single-period setup under multivariate normal demand distribution. In the case of the manufacturer being a price taker, we provide several analytical results regarding the effects of key parameters on order quantities and profits. In the case of the manufacturer being a price setter, we characterize the Stackelberg game that arises, and provide several insights into how the game dynamics are affected by transshipments. Specifically, we find that risk pooling makes retailers' order quantities less sensitive to the wholesale price set by the manufacturer; hence, in general, the manufacturer benefits from retailers' transshipments by charging a higher wholesale price, while retailers are often worse off. The paper captures the effect of demand correlation and the effect of the number of retailers throughout, and it illustrates the findings by a numerical example. We also provide an interactive Web page for numerical experiments.transshipment, multivariate normal distribution, demand correlation, Stackelberg equilibrium

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 firm’s 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.

W e introduce a class of models, called newsvendor networks, that allow for multiple products and multiple processing and storage points and investigate how their single-period properties extend to dynamic settings. Such models provide a parsimonious framework to study various problems of stochastic capacity investment and inventory management, including assembly, commonality, distribution, flexibility, substitution and transshipment. Newsvendor networks are stochastic models with recourse that are characterized by linear revenue and cost structures and a linear input-output transformation. While capacity and inventory decisions are locked in before uncertainty is resolved, some managerial discretion remains via ex-post inputoutput activity decisions. Ex-post decisions involve both the choice of activities and their levels and can result in subtle benefits. This discretion in choice is captured through alternate or ''nonbasic'' activities that can redeploy inputs and resources to best respond to resolved uncertain events. Nonbasic activities are never used in a deterministic environment; their value stems from discretionary flexibility to meet stochastic demand deviations from the operating point.The optimal capacity and inventory decisions balance overages with underages. Continuing the classic newsvendor analogy, the optimal balancing conditions can be interpreted as specifying multiple ''critical fractiles'' of the multivariate demand distribution; they also suggest appropriate measures for and trade-offs between product service levels. This paper shows that the properties of optimal newsvendor network solutions extend to a dynamic setting under plausible conditions. Indeed, we establish dynamic optimality of inventory and capacity policies for the lost sales case. Depending on the nonbasic activities, this also extends to the backordering case. Analytic-and simulation-based solution techniques and graphical interpretations are presented and illustrated by a comprehensive example that features discretionary input commonality and a flexible processing resource.