计量经济分析 = Econometric analysis

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Convex Analysisの二,三の進展について

Many companies have embarked on initiatives that enable more demand information sharing between retailers and their upstream suppliers. While the literature on such initiatives in the business press is proliferating, it is not clear how one can quantify the benefits of these initiatives and how one can identify the drivers of the magnitudes of these benefits. Using analytical models, this paper aims at addressing these questions for a simple two-level supply chain with nonstationary end demands. Our analysis suggests that the value of demand information sharing can be quite high, especially when demands are significantly correlated over time.

The Value of Information Sharing in a Two-Level Supply Chain

There are two broad categories of risk affecting supply chain design and management: (1) risks arising from the problems of coordinating supply and demand, and (2) risks arising from disruptions to normal activities. This paper is concerned with the second category of risks, which may arise from natural disasters, from strikes and economic disruptions, and from acts of purposeful agents, including terrorists. The paper provides a conceptual framework that reflects the joint activities of risk assessment and risk mitigation that are fundamental to disruption risk management in supply chains. We then consider empirical results from a rich data set covering the period 1995–2000 on accidents in the U. S. Chemical Industry. Based on these results and other literature, we discuss the implications for the design of management systems intended to cope with supply chain disruption risks.

Managing Disruption Risks in Supply Chains

In the newsvendor problem, a decision maker facing random demand for a perishable product decides how much of it to stock for a single selling period. This simple problem with its intuitively appealing solution is a crucial building block of stochastic inventory theory, which comprises a vast literature focusing on operational efficiency. Typically in this literature, market parameters such as demand and selling price are exogenous. However, incorporating these factors into the mode l can provide an excellent vehicle for examining how operational problems interact with marketing issues to influence decision making at the firm level. In this paper we examine an extension of the newsvendor problem in which stocking quantity and selling price are set simultaneously. We provide a comprehensive review that synthesizes existing results for the single period problem and develop additional results to enrich the existing knowledge base. We also review and develop insight into a dynamic inventory extension of this problem, and motivate the applicability of such models.

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Pricing and the News Vendor Problem: a Review with Extensions

In many industries, managers face the problem of selling a given stock of items by a deadline We investigate the problem of dynamically pricing such inventories when demand is price sensitive and stochastic and the firm's objective is to maximize expected revenues Examples that fit this framework include retailers selling fashion and seasonal goods and the travel and leisure industry, which markets space such as seats on airline flights, cabins on vacation cruises, and rooms in hotels that become worthless if not sold by a specific time

We formulate this problem using intensity control and obtain structural monotonicity results for the optimal intensity resp, price as a function of the stock level and the length of the horizon For a particular exponential family of demand functions, we find the optimal pricing policy in closed form For general demand functions, we find an upper bound on the expected revenue based on analyzing the deterministic version of the problem and use this bound to prove that simple, fixed price policies are asymptotically optimal as the volume of expected sales tends to infinity Finally, we extend our results to the case where demand is compound Poisson; only a finite number of prices is allowed; the demand rate is time varying; holding costs are incurred and cash flows are discounted; the initial stock is a decision variable; and reordering, overbooking, and random cancellations are allowed

https://www0.gsb.columbia.edu/mygsb/faculty/research/pubfiles/3943/vanryzin_optimal_dynamic_pricing.pdf

Optimal dynamic pricing of inventories with stochastic demand over finite horizons

We present here a new, very compact, proof of the optimality of Scarf's ordering rule for the newsboy problem where only the mean and the variance of the demand are known. We then extend the analysis to the recourse case, where there is a second purchasing opportunity; to the fixed ordering cost case, where a fixed cost is charged for placing an order; to the case of random yields; and to the multi-item case, where multiple items compete for a scarce resource.

http://scm.snu.ac.kr/publication/paper/04.pdf

The Distribution Free Newsboy Problem: Review and Extensions

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.

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

Many industries face the problem of selling a fixed stock of items over a finite horizon. These industries include airlines selling seats before planes depart, hotels renting rooms before midnight, theaters selling seats before curtain time, and retailers selling seasonal goods such as air-conditioners or winter coats before the end of the season. Given a fixed number of seats, rooms, or coats, the objective for these industries is to maximize revenues in excess of salvage value. When demand is price sensitive and stochastic, pricing is an effective tool to maximize revenues. In this paper we address the problem of deciding the optimal timing of a single price change from a given initial price to either a given lower or higher second price. Under mild conditions, we show that it is optimal to decrease resp., to increase the initial price as soon as the time-to-go falls below resp., above a time threshold that depends on the number of yet unsold items.

Optimal starting times for end-of-season sales and optimal stopping times for promotional fares

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.

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Guillermo Gallego

Papers

Optimal dynamic pricing of inventories with stochastic demand over finite horizons

The Distribution Free Newsboy Problem: Review and Extensions

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

Optimal starting times for end-of-season sales and optimal stopping times for promotional fares

Integrating Replenishment Decisions with Advance Demand Information