Guillermo Gallego

A Multiproduct Dynamic Pricing Problem and Its Applications to Network Yield Management

A firm has inventories of a set of components that are used to produce a set of products. There is a finite horizon over which the firm can sell its products. Demand for each product is a stochastic point process with an intensity that is a function of the vector of prices for the products and the time at which these prices are offered. The problem is to price the finished products so as to maximize total expected revenue over the finite sales horizon. An upper bound on the optimal expected revenue is established by analyzing a deterministic version of the problem. The solution to the deterministic problem suggests two heuristics for the stochastic problem that are shown to be asymptotically optimal as the expected sales volume tends to infinity. Several applications of the model to network yield management are given. Numerical examples illustrate both the range of problems that can be modeled under this framework and the effectiveness of the proposed heuristics. The results provide several fundamental insights into the performance of yield management systems.

Integrating Replenishment Decisions with Advance Demand Information

There is a growing consensus that a portfolio of customers with different demand lead times can lead to higher, more regular revenues and better capacity utilization. Customers with positive demand lead times place orders in advance of their needs, resulting inadvance demand information. This gives rise to the problem of finding effective inventory control policies under advance demand information. We show that state-dependent ( s, S) and base-stock policies are optimal for stochastic inventory systems with and without fixed costs. The state of the system reflects our knowledge of advance demand information. We also determine conditions under which advance demand information has no operational value. A numerical study allows us to obtain additional insights and to evaluate strategies to induce advance demand information.

Coordinating pricing and inventory replenishment policies for one wholesaler and one or more geographically dispersed retailers

Abstract We analyze coordination issues in a supply chain consisting of one wholesaler and one or more retailers under deterministic price-sensitive customer demand. Operating costs include purchasing, setup, order processing, and inventory costs. We consider both pricing and lot sizing decisions and take special care to correctly account for the impact of transfer prices and ownership of retail-inventory. We show that a solution that maximizes channel profits can be interpreted as consignment selling. We also show that separating pricing and lot sizing decisions is near optimal when the demand rate is sufficiently large.

Revenue Management of Flexible Products

Aflexible product is a menu of two or more alternative, typically substitute, products offered by a constrained supplier using a sales or booking process. The supplier reserves the right to assign customers who purchase a flexible product to one of the alternatives at a time near the end of the booking process. An example would be an airline offering a morning flight consisting of specific flights serving the same market. Flexible products are currently offered by a number of industries including air cargo, tour operators, and Internet advertising. Flexible products have the advantage of increasing overall demand and enabling better capacity utilization at the cost of potentially cannibalizing high-fare demand for specific products. This paper introduces the concept of flexible products and derives conditions and algorithms for the management of a single flexible product consisting of two specific products. We use numerical simulation to illustrate the benefits from offering flexible products and discuss extension of the approach to more general settings.

How to avoid stockouts when producing several items on a single facility? What to do if you can't?

This paper considers the Multiple Product Single Facility Stockout Avoidance Problem (SAP). That is the problem of determining, given initial inventories, whether there is a multiple product single facility production schedule that avoids stockouts over a given time horizon. The optimization version of the SAP where stockouts are penalized linearly is also studied. We call this problem the Weighted Stockout Problem (WSP). Both problems are NP-hard in the strong sense. Mixed Integer Linear Programming (MIP) formulations for both the SAP and the WSP are developed. We show that there exist polynomial algorithms for some special cases of the SAP and the WSP. We have also developed heuristics and computational results.

Dynamic Pricing of Perishable Assets Under Competition

We study dynamic price competition in an oligopolistic market with a mix of substitutable and complementary perishable assets. Each firm has a fixed initial stock of items and competes in setting prices to sell them over a finite sales horizon. Customers sequentially arrive at the market, make a purchase choice, and then leave immediately with some likelihood of no purchase. The purchase likelihood depends on the time of purchase, product attributes, and current prices. The demand structure includes time-variant linear and multinomial logit demand models as special cases. Assuming deterministic customer arrival rates, we show that any equilibrium strategy has a simple structure, involving a finite set of shadow prices measuring capacity externalities that firms exert on each other: equilibrium prices can be solved from a one-shot price competition game under the current-time demand structure, taking into account capacity externalities through the time-invariant shadow prices. The former reflects the transient demand side at every moment, and the latter captures the aggregate supply constraints over the sales horizon. This simple structure sheds light on dynamic revenue management problems under competition, which helps capture the essence of the problems under demand uncertainty. We show that the equilibrium solutions from the deterministic game provide precommitted and contingent heuristic policies that are asymptotic equilibria for its stochastic counterpart, when demand and supply are sufficiently large. This paper was accepted by Yossi Aviv, operations management.

Stock Positioning and Performance Estimation in Serial Production-Transportation Systems

This paper considers serial production-transportation systems. In recent years, researchers have developed a fairly simple functional equation that characterizes optimal system behavior, under the assumption of constant leadtimes. We show that the equation covers a variety of stochastic-leadtime systems as well. Still, many basic managerial issues remain obscure: When should stock be held at upstream stages? Which system attributes drive overall performance, and how? To address these questions, we develop and analyze several heuristic methods, inspired by observation of common practice and numerical experiments. One of these heuristics yields a bound on the optimal average cost. We also study a set of numerical examples, to gain insight into the nature of the optimal solution and to evaluate the heuristics.

A minmax distribution free procedure for the (Q, R ) inventory model

We are concerned with the continuous review (Q, R) model with backorder costs when only the mean and the variance of the distribution of the lead time demand are known. For each (Q, R) the minmax approach consist of finding the most unfavorable distribution fitting these two moments and then minimizing over (Q, R). The most unfavorable distribution turns out to have positive mass at only two points. This allows a closed form expression for the expected number of backorders per cycle. Given this closed form expression, the optimal (Q, R) pair is easy to find.

Capacitated inventory problems with fixed order costs: Some optimal policy structure

Abstract Almost 40 years ago, H. Scarf (The optimality of (s,S) policies in dynamic inventory problems, in: K. Arrow, S. Karlin, P. Suppes (Eds.), Mathematical Models in the Social Sciences, Stanford University Press, Stanford, 1960) established the optimal (s,S) policy structure for the periodic review inventory problem with fixed ordering costs and no capacity constraint. Since then, the capacitated problem has resisted characterization. In the present paper we partially bridge this gap; using a generalization of Scarfs K-convexity we show that the optimal capacitated policy has an (s,S)-like structure. To do so we divide the parameter space into four regions: In two of these regions the optimal policy is completely specified, while in the other two, it is partially specified. We complement these findings with a computational study. This study suggests that a still simpler optimal policy structure exists.

Optimal Replenishment Policies for Multiechelon Inventory Problems Under Advance Demand Information

Customers and downstream supply chain partners often place, or can be induced to place, orders in advance of future requirements. We show how to optimally incorporate advance demand information into periodic-review, multiechelon, inventory systems in series. While the state space for series systems appears to be formidably large, we decompose the problem across locations, as in Clark and Scarf (1960), and reduce the state space at each location by using modified echelon inventory positions (that nets known requirements). We prove the optimality of state-dependent, echelon base-stock policies for finite and infinite horizon problems. We also show that myopic policies are optimal and very easy to compute when costs and demands are stationary. We provide managerial insights into the value of advance demand information through a numerical study.