Impact of demand uncertainty on supply chain cooperation of single-period products

Cooperation is an approach of improving competitive advantages of a supply chain. A two-echelon supply chain consisting of a manufacturer and a retailer for a single-period product is studied, and retail-market demand uncertainty is described by coefficient of variation. We develop a cooperation mechanism to address the cooperation and its implementation between the manufacturer and the retailer, two market situations are considered: (i) the wholesale price and the order quantity are decision variables, (ii) the wholesale and the retail prices as well as the order quantity are decision variables. In both market situations, our research shows that: (1) the cooperation mechanism can improve the overall channel profits and the supply chain members’ allocated profits, (2) the described cooperation is conditional on retail-market demand uncertainty: it can be implemented if, and only if, the fluctuation of retail-market demand is relatively small and coefficient of variation of retail-market demand does not exceed an upper bound. Impacts of retail-market demand uncertainty on wholesale price, order quantity and/or retail price have also been investigated through analytical and numerical analyses. Although our research is based on the assumption that the manufacturer dominates the supply chain in the non-cooperative situation, which is not the case for most retailer-driven supply chains, this research is still significant on providing guidelines for practitioners in current China mid-level car market that is similar to situations described in the paper.     

Sequential price and quantity decisions under supply and demand risks

Firms need to deal with not only risks from stochastic demand but also risks from supply side. The supply side risk may be due to parts/service outsourcing, third party logistics, or random yield in production processes. In this paper, we study how firms sequentially make price and quantity decisions under these two risks. The first question we try to answer is how these two risks affect the decisions and profits of the firm. We find that increased supply risk usually causes increased quantity/stocking decision, however, there exists a threshold level of supply risk above which the firm reduces quantity/stocking amount as supply risk increases. This observation may be used in a supply chain setting, where reduction of the supply risk can cause higher delivered quantity and improve supply chain performance. This observation also provides support and insights on prioritizing the risk reduction efforts from marketing and operations to achieve better coordination. At the same time, reduction of the risks help not only firms but also consumers as the optimal price decreases. To further improve decision making process under both uncertainties, we study the impact from information revelation and postponement of decisions. We compare results from different sequential decision making cases. As illustrated in the paper, firms gain competing advantage when decision postponement is available and this advantage becomes further significant as the risks increase. Our numerical examples also indicate that price postponement strategy is usually preferred but the relative profit difference between price postponement and quantity postponement become smaller as consumers become more sensitive to the price.     

Predatory intent under uncertainty

Current analyses of predatory behavior neglect uncertainty. Its presence complicates a firm's evaluation of profits and risks associated with various pricing strategies. Using a price leadership model (with the supply of the competitive fringe not known in advance), we show that a risk averse dominant firm will price lower than the price which maximizes expected profits. Such behavior could be misconstrued as being predatory if marginal and average variable cost rules are used for establishing the proof of predation.     

Inflation,Taxes, and the Demand For Housing*

Inflation affects homeownership and housing adversely through the “real-payment tilt” of the conventional mortgage. Expectations of additional housing price appreciation, however, may induce households to invest in housing. This paper uses household data to estimate the demand for homeownership and housing, and it takes explicit notice of expectations of housing price appreciation. The results indicate for each 1% increase in the inflation rate that the conditional probability of purchase falls by 3%. Interest rate effects outweigh appreciation and tax effects. Given the decision to purchase, housing appreciation expectations do not have large effects on the amount purchased.     

Investments in next generation access infrastructures under regulatory uncertainty

This article studies the impact of regulatory uncertainty on an incumbent’s incentives to undertake the socially optimal investments in NGA networks. Thus, a regulatory non-commitment setting in which the regulator sets the access price after the deployment of the NGA network is used. In particular, it is assumed that the regulator sets the access price at the marginal cost of providing the access with some probability and gives an access markup, which equals the average cost of the investments, with the complementary probability. It is found that when the slope of the marginal investment cost function is not particularly steep in relation to the impact of investments on demand, the incumbent underinvests compared to the socially optimal investment level. On the contrary, in a more realistic case when the impact of investments on demand is low in relation to the slope of the marginal investment cost function, the incumbent may overinvest or underinvest depending on the probability of incorporating an access markup into the access price.     

Unimodality of price-setting newsvendor's objective function with multiplicative demand and its applications

We present a general solution framework for the price-setting newsvendor problem with a multiplicative stochastic demand. Under mild assumptions, such as increasing price elasticity on the mean demand function and increasing generalized failure rate on the distribution of the random factor, we first prove that both the profit function with respect to price and its derived function with respect to order quantity are quasi-concave. Three applications are then studied under our solution framework: (1) We consider a wholesale price only contract by which a manufacturer sets a wholesale price and a newsvendor determines an order quantity and the retail price, and show that the manufacturer's profit function is unimodal with respect to retailing price or stocking factor under certain conditions. (2) We consider a newsvendor problem in which the demand depends on both the retail price and the level of sales effort, and the cost exerting the sales effort is proportional to the order quantity; we prove that there exists a unique pair of price and sales-effort levels that maximize the total profit. This result is established under a set of mild assumptions on the demand and cost functions. (3) We identify a property in the single-period profit function that satisfies Condition 1 of Huh and Janakiraman (2008), which in turn guarantees the optimality of (s, S) policy for an infinite stationary dynamic inventory-price control system with lost sales and fixed order costs. Finally, the unimodality of the newsvendor problem with a general stochastic and price-sensitive demand is studied.     

企业营销中的量价决策初探

结合具体案例介绍了在运用概率的方法定量预测市场价格的基础上，按照利润最佳、产销均衡、库存合理的原则进行量价决策的方法。     

Pricing in revenue management for multiple firms competing for customers

We consider the pricing strategies of multiple firms providing the same service in competition for a common pool of customers in a revenue management context. The firms have finite capacity and the demand at each firm depends on the selling prices charged by all firms, each of which satisfies demand up to a given capacity limit. We use game theory to analyze the systems when firms face either a deterministic demand or a general stochastic demand. The existence and uniqueness conditions of a Nash equilibrium are derived, and we calculate the explicit Nash equilibrium point when the demand at each firm is a linear function of price. We also conduct sensitivity analysis of the equilibrium prices with respect to cost and capacity parameters.     

Incorporating uncertainty into a supplier selection problem

Supplier selection is an important strategic supply chain design decision. Incorporating uncertainty of demand and supplier capacity into the optimization model results in a robust selection of suppliers. A two-stage stochastic programming (SP) model and a chance-constrained programming (CCP) model are developed to determine a minimal set of suppliers and optimal order quantities with consideration of business volume discounts. Both models include several objectives and strive to balance a small number of suppliers with the risk of not being able to meet demand. The SP model is scenario-based and uses penalty coefficients whereas the CCP model assumes a probability distribution and constrains the probability of not meeting demand. Both formulations improve on a deterministic mixed integer linear program and give the decision maker a more complete picture of tradeoffs between cost, system reliability and other factors. We present Pareto-optimal solutions for a sample problem to demonstrate the benefits of the SP and CCP models. In order to describe the tradeoffs between costs and risks in an analytical form, we use multi-parametric programming techniques to more completely analyze the alternative Pareto-optimal supplier selection solutions in the CCP model. This analysis gives insights into the robustness of the solutions with respect to number of suppliers, costs and probability of not meeting demand.     

Optimal pricing and order quantity for the newsvendor problem with free shipping

To attract and keep customers, companies, especially those in e-business, are increasingly offering free shipping to buyers whose order sizes exceed the free shipping quantity. In this paper, given the supplier offers free shipping and the retailer faces stochastic demand, we determine the retailer's (i.e., the newsvendor's) optimal order quantity and the optimal selling price simultaneously. We consider two different ways in which price affects the demand distribution, namely price only affects the location or scale of the demand distribution. We explicitly incorporate the supplier's quantity discount and transportation cost into the models. The transportation cost function is very general, which includes those most commonly used in the literature. We numerically examine the impacts of free shipping, quantity discount, transportation cost, and demand variance on the retailer's optimal order quantity and pricing decisions. We find that even though the retailer faces uncertain demand, free shipping can effectively encourage the retailer to order more of the good and can benefit the supplier, the retailer, and the end customers. An increase in transportation cost or a decrease in purchase price will induce the retailer to order more of the good and decrease the retail price. With increasing demand variance, the retailer should order more of the good. We also find that the newsvendor can cope with demand variance by taking advantage of free shipping.     

Optimal pricing and advertising strategy for introducing a new business product with threat of competitive entry

The problem of optimal joint pricing and advertising decision making for a new product facing potential competitive entry has received inadequate attention. We propose a model that attempts to find the optimal price-advertising frontier in the face of potential competitive entry that maximizes total discounted profits for pre- and post-entry periods. We find that a firm would charge the price that equates price elasticity to marginal revenue product of advertising (as predicted by [Dorfman, R. and Steiner, P.O. (1954), Optimal Advertising and Optimal Quality, American Economic Review, 44(5), 826-836.]) only when the potential effects of pricing and advertising on its market share are not considered. Under optimal conditions, aware that market share is subject to erosion, the firm charges a somewhat lower price than the profit maximizing price, and sets an advertisement expense that is somewhat higher than the profit-maximizing advertising level as predicted by Cournot's monopolistic setting. We illustrate the applicability of our model using business product examples taken from several industries including operating systems, software, pharmaceutical, and telephone switching. Directions for future research with implications for B2B managers (for example, the possible effects of preannouncement to forestall competitive entry) are discussed.     

Optimal Pricing and Order-Up-To S Inventory Policy with Expected Utility of the Present Value Criterion

The article determines pricing and order-up-to level S inventory decisions over an infinite planning horizon from the point of view of a risk-averse decision maker. The demand is assumed to be stochastic but influenced by the selling price which is a decision variable. Shortages are allowed and backordered partially. We calculate the present value of the cash flow over the entire planning horizon and incorporate the notion of risk aversion into the model using a concave utility function. We numerically demonstrate the model and investigate the impact of different model-parameters on the optimal decisions. It is observed that the optimal selling price for a risk-averse decision maker is not less than the optimal selling price of a risk-neutral decision maker while the optimal order level for the risk-averse decision maker is always less than that of the risk-neutral decision maker.     

Inventory decisions for substitutable products with stock-dependent demand

We study a retailer’s inventory policy for two products. The products are substitutable and have inventory dependent demand, so a higher inventory level of a product increases its sales. We model the joint effect of demand stimulation and product substitution on inventory decisions by considering a single-period, stochastic demand setting. We provide the first order optimality conditions for the profit maximizing order quantities and interpret them using marginal analysis. We also consider two heuristic solutions that separately account for either demand stimulation or product substitution. Our numerical analysis reveals that the optimal policy by appropriately using sales information that quantifies substitution and demand stimulation can produce significantly higher profits. The profit benefits are lessened under certain circumstances, such as when the two products have similar critical fractile values, suggesting that in such instances the heuristics may be used effectively.     

回收数量受价格和随机因素影响的定价模型

假设在再制造闭环供应链中,集中决策者、第三方和制造商分别从最终客户那里回收废旧品,其回收数量受回收价格和随机因素影响,制造商对获得的旧部件进行再制造,如果旧部件不能满足生产需求,制造商将从新部件供应商那里以高价格采购新部件来补充短缺。本文按照废旧品回收的供应链成员不同,建立了3个定价决策模型,证明了每个模型最优解的存在性和唯一性,然后在特殊情形下进一步求得各模型最优解的解析式,最后用具体算例对模型进行了验证。     

Collusion Under Risk Aversion and Fixed Costs

We analyze collusion under demand uncertainty by risk‐averse cartels that care about the utility derived from profits. With sufficient risk aversion and non‐trivial fixed operating costs, it becomes difficult for cartels to collusively restrict output both when demand is low and marginal dollars are highly valued, and when demand is high and potential defection profits are high: output relative to monopoly levels becomes a U‐shaped function of demand. Greater risk aversion or higher fixed operating costs make collusion more difficult to support in recessions, but easier to support in booms.     

Legal unbundling can be a golden mean between vertical integration and ownership separation

We study an industry in which an upstream monopolist supplies an essential input at a regulated price to several downstream firms. Legal unbundling means in our model that a downstream firm owns the upstream firm, but this upstream firm is legally independent and maximizes its own upstream profits. We allow for non-tariff discrimination by the upstream firm and show that under quite general conditions legal unbundling never yields lower quantities in the downstream market than ownership separation and integration. Therefore, typically, consumer surplus will be largest under legal unbundling. Outcomes under legal unbundling are still advantageous when we allow for discriminatory capacity investments, investments into marginal cost reduction and investments into network reliability. If access prices are unregulated, however, legal unbundling may be quite undesirable.     

Solving the Winner Determination Problem in a Divisible-Object Auction

In an auction of a divisible object, bidders' demand functions are often assumed to be nonincreasing, meaning that bidders are willing to pay less or the same price for every additional unit. Under this assumption, the optimal allocation that maximizes the auctioneer's revenue can be found using a greedy-based procedure. This article argues that situations may arise where a bidder may need to express her preferences through a nondecreasing demand function; when such a bidder is present in the auction, the greedy-based procedure does not guarantee the optimal allocation. Thus, this article proposes a mixed integer program that finds the optimal allocation in a divisible-object auction at which bidders submit their bids as arbitrary stepwise demand functions. The practical aspect of the mathematical program is presented by means of a simple yet illustrative example in a treasury bond auction setting. The results of the auctioneer's revenue are reported as a function of the number of bidders with nonincreasing and nondecreasing demand functions.     

Joint pricing and inventory control for non-instantaneous deteriorating items with partial backlogging and time and price dependent demand

In this paper, a joint pricing and inventory control for non-instantaneous deteriorating items is developed. We adopt a price and time dependent demand function. Shortages is allowed and partially backlogged. The major objective is to determine the optimal selling price, the optimal replenishment schedule and the optimal order quantity simultaneously such that, the total profit is maximized. We first show that for any given selling price, optimal replenishment schedule exists and unique. Then, we show that the total profit is a concave function of price. Next, we present a simple algorithm to find the optimal solution. Finally, we solve a numerical example to illustrate the solution procedure and the algorithm.     

A Search Model Where Consumers Choose Quantity Based on Expected Price

I describe a price game in which consumers face search costs and base their quantity decision on the expected price. Because of search costs, the choice of the firm they will buy from is described by a random process. I show that the expected equilibrium price is above the monopoly price. This result does not change if demand comes from a small share of perfectly informed consumers with zero search costs.     

A theory of hub-and-spoke collusion

We develop a model of hub-and-spoke collusion between a manufacturer and two retailers. Demand is stochastic, and collusion between retailers is difficult; the best collusive equilibrium is inefficient (Rotemberg and Saloner (1986)). In the hub-and-spoke collusive agreement, retailers transmit their information about the state of demand to the supplier. The supplier uses this information to adjust the wholesale price. By organizing the collusion, the supplier increases profits of the vertical chain. We show that, surprisingly, this type of collusive agreement can under some conditions improve consumer welfare.