A note on the classification of consumer demand functions with respect to retailer pass-through rates

Tyagi (1999) derived conditions on the curvature of consumer demand functions which make it optimal for a profit-maximizing retailer to pass-through greater (less) than 100% of a manufacturer trade deal amount. Since the pass-through is customarily evaluated at the optimal wholesale price, then additional sufficient conditions are needed to ensure the existence of an optimal wholesale price. The purpose of this note is to derive the additional required conditions on the curvature of the consumer demand functions for the existence of a greater (less) than 100% retailer pass-through rate at the optimal wholesale price.     

The effects of demand uncertainty on channel structure

Motivated by the business practice whereby some manufacturers open their own retail stores despite the existence of more efficient independent retailers, this paper examines the distribution channel choice of competing manufacturers under demand uncertainty and resale price maintenance. We characterize the conditions for the equilibrium channel structures. We find that (1) manufacturers tend to distribute products with more design attributes through their own retail stores, (2) manufacturers with highly substitutable products are more likely to use independent retailers, and (3) at least one manufacturer has more incentive to open its own retail stores when facing an increase of the market size asymmetry.     

Optimal inventory policy with supply uncertainty and demand cancellation

We consider a periodic review model where the firm manages its inventory under supply uncertainty and demand cancellation. We show that because of supply uncertainty, the optimal inventory policy has the structure of re-order point type. That is, we order if the initial inventory falls below this re-order point, otherwise we do not order. This is in contrast to the work of Yuan and Cheung (2003) who prove the optimality of an order up to policy in the absence of supply uncertainty. We also investigate the impact of supply uncertainty and demand cancellation on the performance of the supply chain. Using our model, we are able to quantify the importance of reducing the variance of either the distribution of yield or the distribution of demand cancellation. The single, multiple periods and the infinite horizon models are studied.     

Impact of sourcing flexibility on the outsourcing of services under demand uncertainty

This paper investigates the relationship between market conditions and the value and use of sourcing flexibility for service processes. We develop and analyze a series of models, and we derive expressions for the optimal switching decision, the value of the option to outsource, the value of the option to backsource, and the probability and timing of switches between the alternative sources.     

The effect of demand uncertainty in a price-setting newsvendor model

We study the effects of demand uncertainty on optimal decisions and the expected profit of a price-setting newsvendor who faces either additive or multiplicative stochastic demand. Our key findings are as follows. (1) A stochastically larger demand may even lead to a smaller order size and a lower profit when price is endogenous. (2) A stochastically larger demand will lead to a higher selling price in general for the additive demand case but to a lower selling price under certain mild conditions for the multiplicative demand case. Moreover, if the larger demand can be represented by a transformation of the lower one, it will lead to a higher expected profit for both demand cases. However, except for the setting with a zero shortage cost, a larger demand may not necessarily result in a higher expected profit in general. (3) Under mild conditions, a less variable demand will lead to a higher and lower selling price for the additive and multiplicative demand case, respectively, and a higher expected profit for both cases.     

Buyback contracts with price-dependent demands: Effects of demand uncertainty

We explore buyback contracts in a supplier–retailer supply chain where the retailer faces a price-dependent downward-sloping demand curve subject to uncertainty. Differentiated from the existing literature, this work focuses on analytically examining how the uncertainty level embedded in market demand affects the applicability of buyback contracts in supply chain management. To this end, we seek to characterize the buyback model in terms of only the demand uncertainty level (DUL). With this new research perspective, we have obtained some interesting new findings for buyback. For example, we find that (1) even though the supply chain’s efficiency will change over the DUL with a wholesale price-only contract, it will be maintained constantly at that of the corresponding deterministic demand setting with buyback, regardless of the DUL; (2) in the practice of buyback, the buyback issuer should adjust only the buyback price in reaction to different DULs while leave the wholesale price unchanged as that in the corresponding deterministic demand setting; (3) only in the demand setting with an intermediate level of the uncertainty (which is identified quantitatively in Theorem 5), buyback provision is beneficial simultaneously for the supplier, the retailer, and the supply chain system, while this is not the case in the other demand settings. This work reveals that DUL can be a critical factor affecting the applicability of supply chain contracts.     

Flexible capacity strategy with multiple market periods under demand uncertainty and investment constraint

We establish a flexible capacity strategy model with multiple market periods under demand uncertainty and investment constraints. In the model, a firm makes its capacity decision under a financial budget constraint at the beginning of the planning horizon which embraces n market periods. In each market period, the firm goes through three decision-making stages: the safety production stage, the additional production stage and the optimal sales stage. We formulate the problem and obtain the optimal capacity, the optimal safety production, the optimal additional production and the optimal sales of each market period under different situations. We find that there are two thresholds for the unit capacity cost. When the capacity cost is very low, the optimal capacity is determined by its financial budget; when the capacity cost is very high, the firm keeps its optimal capacity at its safety production level; and when the cost is in between of the two thresholds, the optimal capacity is determined by the capacity cost, the number of market periods and the unit cost of additional production. Further, we explore the endogenous safety production level. We verify the conditions under which the firm has different optimal safety production levels. Finally, we prove that the firm can benefit from the investment only when the designed planning horizon is longer than a threshold. Moreover, we also derive the formulae for the above three thresholds.     

Capacity allocation,ordering, and pricing decisions in a supply chain with demand and supply uncertainties

This paper studies coordinated decisions in a decentralized supply chain that consists of one Original Equipment Manufacturer (OEM), one manufacturer, and one distributor, and possesses uncertainties at both demand and supply sides. These uncertainties emerge, respectively, from random demand the distributor faces and randomness of capacity with which the OEM processes the manufacturer’s outsourced quantity. Sharing supply and demand uncertainty information along the supply chain enables us to develop three models with different coordination efforts—the OEM and manufacturer coordination, the manufacturer and distributor coordination, and the OEM, manufacturer, and distributor coordination—and quantify the coordinated decisions in these three models. Our analysis of these coordination models suggests that coordinating with the OEM improves the manufacturer’s probability of meeting downstream demand and his expected profit, yet coordinating with the manufacturer is not necessarily beneficial to the OEM when downstream coordination is lacking.     

用Mathcad2001进行希克斯和斯勒茨基价格效应分析(二)

利用 Mathcad2 0 0 1 ,据实例条件在上文作出了价格效应分析的基础上 ,求出了三条具有重要意义的非线性的马歇尔需求曲线、希克斯需求曲线和斯勒茨基需求曲线的方程 ,并画出了两种价格效应分析和三条需求曲线的准确图形 ,展示了 Mathcad在经济学理论中的用途 ,以期引起同仁对 Mathcad在经济学乃至其它社会科学中应用价值的高度重视     

A note on testing symmetry with estimated parameters

A simple yet general technique is presented for the problem of assessing symmetry about an unknown point with linear rank statistics.     

Tool capacity planning for semiconductor fabrication facilities under demand uncertainty

This research is motivated by issues faced by a large manufacturer of semiconductor devices. Semiconductor manufacturing companies allocate millions of dollars every year for new types of machine tools for their facilities. Typically these are special purpose machine tools which are made to order. The rate of change in products and technology makes it difficult for manufacturers to have a good estimate of future tool requirements. Further, manufacturers experience a long lead time while procuring these tools. In this paper, we model the tool capacity planning problem under uncertainty in demand. The number of tools required in a facility is sufficiently large (nearly hundred or more tools) to make it nearly impossible to obtain efficient exact algorithms. We provide heuristics to find efficient tool procurement plans and test their quality using lower bounds on the formulation.     

A note on uncertainty principle

Weighted form of uncertainty principle is proved.     

Softness of MALL proof-structures and a correctness criterion with Mix

We show that every MALL proof-structure [9] satisfies the property of softness, originally a categorical notion introduced by Joyal. Furthermore, we show that the notion of hereditary softness precisely captures Girards algebraic restriction of the technical condition on proof-structures. Relying on this characterization, we prove a MALL+Mix sequentialization theorem by a proof-theoretical method, using Girards notion of jump. Our MALL+Mix correctness criterion subsumes the Danos/Fleury-Retoré criterion [6] for MLL+Mix.This work was supported by Grant-in-Aid for Young Scientists of Ministry of Education, Science and Culture of Japan.Mathematics Subject Classification (2000):03F52, 03F07, 03F03Revised version: 9 August 2003     

A qualitative uncertainty principle for functions generating a Gabor frame on LCA groups

Let G be a locally compact Abelian group. In this paper we study in which way the qualitative uncertainty principle is modified when we consider only functions f∈L²(G) which generate a Gabor frame associated with a uniform lattice K in G. This provides us with sharp lower bounds for the measure of the support of such functions and their Plancherel transforms.     

A note on sequential auctions with multi-unit demand

Within the independent private value paradigm, this note first analyzes two-round sequential first-price auctions with multi-unit demand. We show that the expected price in the first round is strictly lower than that in the second round due to the “extraction effect”. We then compare the revenues for the sequential auctions and the simultaneous auctions. We show that the discriminatory auction, the Vickrey auction, and the sequential second-price auctions generate the same revenue for the seller, followed in order by the sequential first-price auctions, and by the uniform-price auction.     

Combined pricing and supply chain operations under price-dependent stochastic demand

In this study, we determined product prices and designed an integrated supply chain operations plan that maximized a manufacturer’s expected profit. The computational results of this study revealed that as the variance of the demand distribution increases, a manufacturer will increase its inventory to levels that are greater than the anticipated demand to prevent the potential loss of sales and will simultaneously raise product prices to obtain a greater profit. In the cost minimization approach, the manufacturer may earn the highest possible profits, as determined by the profit optimization approach, only if this firm precisely forecasts the mean market demand for its products. Greater inaccuracies in this forecast will produce lower levels of expected profit.     

Production decisions under joint price and production uncertainty

While production decisions in the presence of price uncertainty have been extensively studied, this is not so for the case in which the level of production is itself uncertain. In this paper,we provide a decision analysis under multiplicative production uncertainty, both with and without price uncertainty. We depict equilibrium and obtain comparative statics results with the aid of a diagram based on the difference between expected price and marginal cost. Comparative statics results are obtained for the model with production uncertainty alone and also for simultaneous price and production uncertainty (including two special cases). We first derive results based on the Arrow–Pratt coefficients of risk aversion, and then supplement these with the Ross measure of relative risk aversion, since this proves useful in the presence of multiple sources of uncertainty. We find that increases in risk (both price and production) or input prices reduce expected output. However, expected output supply is an increasing function of (expected) price only for “low” levels of risk aversion, and in general the relationship is ambiguous.     

A weak Brun—Titchmarsh theorem for multiplicative functions

An important theorem of Shiu gives a (precise) bound for the average of values of multiplicative functions, of a certain class, over ‘short’ intervals. Here we obtain, by simple means, the above result of same qualitative order.     

A note on polyharmonic functions

In this note we prove the following theorem:Suppose 0<p<∞ and α>−1. Then there is a constant C=C(p,m,n,α) such that

     

A note on W-I-continuous functions

In [1], Aç?kgöz et al. introduced and investigated the notions of w-I-continuous and w*-I-continuous functions in ideal topological spaces. In this paper, we investigate their relationships with continuous and θ-continuous functions.