Multiproduct Dynamic Pricing with Reference Effects Under Logit Demand

Optimal peak load pricing with time-additive consumer preferences

It is common for a firm to make use of multiple suppliers of different delivery lead times, reliabilities, and costs. In this study, we are concerned with the joint pricing and inventory control problem for such a firm that has a quick‐response supplier and a regular supplier that both suffer random disruptions, and faces price‐sensitive random demands. We aim at characterizing the optimal ordering and pricing policies in each period over a planning horizon, and analyzing the impacts of supply source diversification. We show that, when both suppliers are unreliable, the optimal inventory policy in each period is a reorder point policy and the optimal price is decreasing in the starting inventory level in that period. In addition, we show that having supply source diversification or higher supplier reliability increases the firm's optimal profit and lowers the optimal selling price. We also demonstrate that, with the selling price as a decision, a supplier may receive even more orders from the firm after an additional supplier is introduced. For the special case where the quick‐response supplier is perfectly reliable, we further show that the optimal inventory policy is of a base‐stock type and the optimal pricing policy is a list‐price policy with markdowns.

This article considers the dynamic pricing of two substitutable products over a predetermined, finite selling season. The initial inventory levels of the products are fixed exogenously and there are no replenishment opportunities during the season. It is assumed that each arriving customer chooses from available products based on the multinomial logit choice model, which captures the effect of prices on consumer choice. Every time a product runs out of stock, the set of choices shrinks, capturing the effect of stockouts on consumer choice. It is shown that, under the optimal pricing policy, the marginal value of an item is increasing in the remaining time and decreasing in its own stock level and the other product's stock level. Despite such non-surprising behavior on the part of marginal values, the optimal price itself is not simply monotonic in the remaining time or the other product's stock level. For example, a product's optimal price may increase if the remaining time decreases or if the total inventory grows. It is shown that such optimal behavior can be understood through alternative gauges such as the optimal price difference between the two products and the optimal purchase probabilities.

Wait Time Based Pricing for Queues with Customer-Chosen Service Times

The Journal of FinanceVolume 41, Issue 5 p. 1141-1148 Note A Note on Optimal Credit and Pricing Policy under Uncertainty: A Contingent-Claims Approach CHUN H. LAM, CHUN H. LAMSearch for more papers by this authorANDREW H. CHEN, ANDREW H. CHEN Both authors from Edwin L. Cox School of Business, Southern Methodist University. We are indebted to the comments and suggestions of Chris Barry, Sam Dennis, and two anonymous referees on earlier versions of the paper. The authors also acknowledge the financial support from the Center for the Study of Financial Institutions and Markets at Southern Methodist University.Search for more papers by this author CHUN H. LAM, CHUN H. LAMSearch for more papers by this authorANDREW H. CHEN, ANDREW H. CHEN Both authors from Edwin L. Cox School of Business, Southern Methodist University. We are indebted to the comments and suggestions of Chris Barry, Sam Dennis, and two anonymous referees on earlier versions of the paper. The authors also acknowledge the financial support from the Center for the Study of Financial Institutions and Markets at Southern Methodist University.Search for more papers by this author First published: December 1986 https://doi.org/10.1111/j.1540-6261.1986.tb02536.xCitations: 3 Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Citing Literature Volume41, Issue5December 1986Pages 1141-1148 RelatedInformation

We consider a dynamic pricing model for selling a given stock of a perishable product over a finite time horizon. Customers, whose reservation price distribution changes over time, arrive according to a nonhomogeneous Poisson process. We show that at any given time, the optimal price decreases with inventory. We also identify a sufficient condition under which the optimal price decreases over time for a given inventory level. This sufficient condition requires that the willingness of a customer to pay a premium for the product does not increase over time. In addition to shedding managerial insight, these structural properties enable efficient computation of the optimal policy. Numerical studies are conducted to show the revenue impact of dynamic price policies. Price changes are set to compensate for statistical fluctuations of demand and to respond to shifts of the reservation price. For the former, our examples show that using optimal dynamic optimal policies achieves 2.4–7.3% revenue improvement over the optimal single price policy. For the latter, the revenue increase can be as high as 100%. These results explain why yield management has become so essential to fashion retailing and travel service industries.

Designing Shipping Policies with Top-up Options to Qualify for Free Delivery

Dynamic Pricing of Relocating Resources in Large Networks

We describe aggregate inflation as a stochastic process in which the rate of change of the price level can be positive or zero, where the times spent in each state are of random duration. This class of processes includes Two-State Markov Chains and Renewal Processes as special cases. It is shown that the optimal pricing policy of a monopolistic firm with non-convex costs of price adjustment is (S, s) in its real-price, i.e. its nominal price relative to the price level. A basic certainty-equivalence result is proved: i.e. the firm behaves as if it faces a certain and fixed rate of inflation, higher than the actual expected rate, the difference between the two rates being a risk premium which depends on the real interest rate and the parameters of the stochastic process. One can thus apply previous results from the case of certainty (Sheshinski and Weiss, Review of Economic Studies, 1977) to obtain comparative static results. In particular, one finds that an increase in the variance of expected inflation leads firms to choose a pricing policy with larger amplitude in real price. The paper also addresses the question of consistency in firms' expectations when the price level is determined by the firms' actions. In this paper we consider pricing policies of individual firms in an inflationary environment. Each firm expects the general price level to increase and must determine the rate of increase of its own price. It is assumed that the firm incurs an adjustment cost when it changes its nominal price. Consequently, firms choose to change prices occasionally rather than continuously.

We consider a robust version of the classic problem of optimal monopoly pricing with incomplete information. In the robust version, the seller faces model uncertainty and only knows that the true demand distribution is in the neighborhood of a given model distribution. We characterize the optimal pricing policy under two distinct, but related, decision criteria with multiple priors: (i) maximin expected utility and (ii) minimax expected regret. The resulting optimal pricing policy under either criterion yields a robust policy to the model uncertainty. While the classic monopoly policy and the maximin criterion yield a single deterministic price, minimax regret always prescribes a random pricing policy, or equivalently, a multi-item menu policy. Distinct implications of how a monopolist responds to an increase in uncertainty emerge under the two criteria.

Pricing and replenishment policies in dual-channel supply chain under continuous unit cost decrease

In this paper we study the effect of dynamic behavior of the market on the optimum pricing policy for a revenue maximizing firm in both monopoly and duopoly cases. We show that the optimum pricing policy in the dynamic market can be very different from the static one, and the most important contributing factors for this difference are: consumer response time, planning period and the discount rate. Furthermore we show that for the linear model that we use, in the limit of infinite planning horizon or market equilibrium the optimum price for the dynamic market reduces to the optimum price for the static market.

This paper explores the optimal road pricing policy when a new elevated road is constructed in a corridor that suffers from traffic congestion before the elevated road is built. Due to the extra construction/maintenance expenditure for this new elevated road and the need to lessen congestion situation, the government decides to apply a road-pricing mechanism on the transportation system. Three pricing policies are discussed in this paper: (a) charging the travelers who live after the entrance of the new elevated road by a flat toll; (b) charging the travelers who live after the entrance of the new elevated road but the new elevated road users and original road users would pay different toll; and (c) charging all the travelers with different congestion toll depending on which path they use. The numerical result shows the existence of the social optimal corresponding toll. The best pricing policy among these three alternatives is also discussed.

PurposeThis study aims to examine the value of the call option contract in hedging the risks in the supply chain. The decentralized supply chain without call option contract is first studied as the criterion model for evaluations. This paper addresses several questions: What will be the optimal manufacturer’s production quantity, retailer’s ordering and pricing policies in the presence of random demand and random yield by applying the downconversion approach? How will the call option contract influence the optimal decisions for the members of the supply chain? Can the risk from randomness be divided among the members in the supply chain through the call option contract?Design/methodology/approachThis paper considers a two-level decentralized supply chain under random yield and random demand in which the manufacturer takes advantage of the downconversion approach with two scenarios, with and without option contract. To the best of the authors’ knowledge, no article or study uses the downconversion approach in a supply chain regarding random yield and random demand. Furthermore, the paper considers pricing with option contract in the supply chain, which makes this article stands out significantly from other articles in the literature.FindingsThis study shows that the downconversion approach would reduce the risk caused by the random yield, which appears to be the appropriate method for the environmental goal of the supply chains. Moreover, adopting a call option contract can increase flexibility and mitigate risks, resulting in more expected members’ profits.Research limitations/implicationsTo simplify the model, the authors assume one manufacturer and one retailer, so extending the model to consider multiple retailers instead of one retailer and inventory sharing between them would be interesting. Considering the option and exercise prices as decision variables would be important future research topics. Put option and bidirectional option contracts could be investigated in the future. Another extension is modeling asymmetry of information in supply chain.Originality/valueThis paper provides managerial insights on dealing with both demand and yield risks in a manufacturer–retailer supply chain. The manufacturer has a random yield production and produces two types of vertical products: low-end and high-end. To reduce waste caused by the random yield, the manufacturer uses a downconversion approach in which low-end products are made by converting the defective high-end products. The manufacturer purchased a shortage of high-end products from the secondary market (i.e. emergency sourcing). High-end products are sold through the retailer, and low-end products are sold directly by the manufacturer. The customer demand for high-end products in the end market is random and depends on the selling price, and the customer demand for the low-end products in the secondary market is independent and random. The retailer contracts the manufacturer with the call option to obtain high-end products to meet a random demand; in fact, by using the call option contract, the authors try to balance the risks between two members. Two scenarios of with and without call option contract are proposed. After the high-end product demand is observed, the retailer would exercise the option order quantity in the call option contract scenario and then place an instant order with the manufacturer if necessary. In each scenario, the manufacturer and the retailer make their decisions simultaneously (static game) to determine the retailer’s optimal ordering and pricing policies and the optimal production quantity of the manufacturer (Nash equilibrium) by maximizing their expected profits. Finally, the impact of the model parameters on the supply chain is expressed through numerical examples. The numerical analysis shows that the call option contract provides greater profit than the wholesale price contract.

Game-theoretic analysis of a two-echelon supply chain with option contract under fairness concerns