Information and Inventory Recourse for a Two-Market, Price-Setting Retailer

We analyze the problem of determining inventory and pricing decisions in a two-period retail setting when an opportunity to refine information about uncertain demand is available. The model extends the newsvendor problem with pricing by allowing for multiple suppliers, the pooling of procurement resources, and more general informational dynamics. One contribution is the solution procedure: we show that all decisions (up to seven in all, including recourse decisions) can be determined uniquely as a function of a surrogate first-period decision called the stocking factor. Hence, the two-period decision problem with recourse reduces to a search for one .decision variable. A second contribution is the policy implications: we find that the cost of learning is (I) a consequence of censored information because, on the margin, learning is free if full information is guaranteed; (2) measured in the form of an increased stocking factor; and (3) shared with the consumer in. the form of a higher selling price when demand uncertainty is additive. A third contribution is the application of the results to three motivating examples: A market research problem in which a product is introduced in a test market prior to a widespread launch; a global newsvendor problem in which a seasonal product is sold in two different countries with non-overlapping selling seasons; and a minimum-quantity commitment problem in which procurement resources for multiple purchases may be pooled

Capacity Investment under Demand Uncertainty: Price vs. Quantity Competition

This article shows that under uncertainty, a firm's capacity investment decision crucially depends on the mode of market approach (price-setting vs. quantity-setting) and competition that follows investment. We model an industry in which firms have to make capacity investment decisions when demand is uncertain. First each firm must decide on its capacity investment level. Then, industry capacity levels are observed and firms engage in quantity or price competition. Finally, demand and revenues are realized. We begin by considering a monopoly and show that the monopoly price given an uncertain demand curve can be higher or lower than the reference price when the demand curve is known at the start. Moreover price and firm value may fall or rise with increasing uncertainty. We compare thses results with a setting where a monopolist sets quantity instead of price. The resulting investment fundamentally differs from the price-setting investment. Moreover, the investment strategy under quantity-setting is significantly less sensitive to variability and more profitable than under price-setting. Under quantity competition, these results extend to a duopoly, oligopoly and perfect competition. In addition, entry dettering investments are possible yet more difficult as variability increases and credible only at low investment costs. Under price competition, no pure equilibria exist if there is demand uncertainty. Key Words: pricing, quantity, capacity, competition, strategy, game theory, demand uncertainty.

Dynamic Learning, Pricing, and Ordering by a Censored Newsvendor

We address the problem of determining optimal ordering and pricing policies in a finite-horizon newsvendor model with unobservable lost sales. The demand distribution is price-dependent and involves unknown parameters. We consider both the cases of perishable and non-perishable inventory. A very general class of demand functions is studied in this paper. We derive the optimal ordering and pricing policies as unique functions of the stocking factor (which is a linear transformation of the safety factor). An important expression is obtained for the marginal expected value of information. As a consequence, we show when lost sales are unobservable, with perishable inventory the optimal stocking factor is always at least as large as the one given by the single-period model; whereas, if inventory is non-perishable, this result holds only under a strong condition. This expression also helps to explain why the optimal stocking factor of a period may not increase with the length of the problem. We compare this behavior with that of a full information model. We further examine the implications of the results to the special cases when demand uncertainty is described by additive and multiplicative models. For the additive case, we show that if demand is censored, the optimal policy is to order more as well as charge higher retail prices when compared to the policies in the single-period model and the full information model. We also compare optimal and myopic policies for the additive and multiplicative models

Inventory and Pricing in Global Operations: Learning From Observed Demands

We develop a two-period model applicable to global sourcing by considering a firm that operates in two markets: one is located in the U.S. and the second is in a country having a selling season that does not overlap with the U.S. selling season. Demand for each market depends linearly on the selling price and includes an unknown scale parameter. We assume that the firm learns from sales in the first market to assist decision making in the second. We also assume a single procurement opportunity, but allow the firm to ship leftovers from the first market to the second if doing so is profitable. Our results include the characterization of the optimal recourse policy, which represents the firm\u27s decisions made at the beginning of the second selling season after it observes both sales in the first market and a realized value of the foreign exchange rate. Additionally, we provide a sufficient condition for reducing the optimization problem to a maximization over a single variable that we interpret as the safety stock for the first market. Further, we provide evidence that the sufficient condition is a rather mild one, likely to be satisfied in practical applications. We also establish a lower bound on the optimal value of the first-market safety stock, thereby truncating the search region of the last decision variable. This lower bound represents the optimal safety stock for the first market if that decision were made myopically, without regard to its effect on the profit associated with the second market

Global Production Planning under Exchange-Rate Uncertainty

Motivated by a production planning problem in an actual global manufacturing network, we examine the impact of exchange-rate uncertainty ... namely the volatility in and correlations among exchange rates ... on the choice of various optimal production policies and the conditions which lead to them. A two-stage stochastic program with recourse is developed that provides opportunities to hedge financial risk by allowing for some production planning decisions to be deferred until exchange rates are realized. The proposed model and analysis yield the following results: (1) Under significant exchange-rate uncertainty it may be optimal to hedge production by producing less than total demand, (2) production hedging is more likely an optimal policy when either the profit margin is small and/or the exchange rates are highly volatile, (3) the probability of following a production hedging policy decreases as the correlations between exchange rates monotonically increase in a positive direction, (4) after exchange rates are realized it may be optimal to hedge allocation by not allocating all production to some of the markets, and (5) given production and/or allocation hedging, our model identifies the value of financial hedging for each firm rather than a single option price for all firms. This guarantees that all markets are served and that each firm gets an option price that is commensurate with its exchange-rate risk. These findings and implications are illustrated with examples adapted from data provided by IBM

A Periodic Review Base Stock Inventory System with Sales

We consider a system in which an order is placed every T periods to bring the inventory position up to the base stock S. We accept demand until the inventory position reaches a sales rejection threshold M. Our objective is to find the optimal values of S and M which minimize the long-run average cost per period. We establish the stationary distribution of our system and develop structural properties of the optimal solution that facilitate computation. In particular, we show that in an optimal solution, the optimal value of M is non-negative under some reasonable conditions. Hence, in our model a mixture of backorders and lost sales may occur. Additionally, we compare our system against traditional systems in which demand during stockouts is either fully backordered or lost

An Inventory Allocation System with Backorders and Sales Rejection

We consider a variant of the periodic review system with a virtual warehouse that is due to Eppen and Schrage (1981). Depending on the realized pattern of demand during the delivery leadtime, this inventory is dynamically allocated or rationed to each of the retailers. While Eppen and Schrage (1981) assume that all unfilled demand is backordered, we allow some demand to be rejected to keep inventories in balance. This results in an exact analysis of the system. We develop conditions for the unique solution in a two retailer model and discuss the implications for the multi-retailer systems. Our analysis works for both discrete and continuous demands. Illustrative numerical examples suggest that, with our policy, only a very small fraction of demand would be rejected. The scope of our policy for general distribution and transshipment models has been explained

A Two-Echelon Inventory System with Priority Shipments

A two-echelon system for spare parts is analyzed. The system allows the use of priority inventory pooling to expedite service when a stock-out occurs. First, a tractable aggregate model is derived. This model is then disaggregated to approximate the performance of the exact system. Results of computer tests are also presented.inventory, multi-echelon systems, spare parts