Fubini Type Products for Densities and Liftings

In our former paper (Fund. Math. 166, 281–303, 2000) we discussed densities and liftings in the product of two probability spaces with good section properties analogous to that for measures and measurable sets in the Fubini Theorem. In the present paper we investigate the following more delicate problem: Let (Ω,Σ,μ) and (Θ,T,ν) be two probability spaces endowed with densities υ and τ, respectively. Can we define a density on the product space by means of a Fubini type formula \((\upsilon\odot\tau)(E)=\{(\omega,\theta):\omega\in\upsilon(\{\bar {\omega}:\theta\in\tau(E_{\bar{\omega}}\})\}\), for E measurable in the product, and the same for liftings instead of densities? We single out classes of marginal densities υ and τ which admit a positive solution in case of densities, where we have sometimes to replace the Fubini type product by its upper hull, which we call box product. For liftings the answer is in general negative, but our analysis of the above problem leads to a new method, which allows us to find a positive solution. In this way we solved one of the main problems of Musia?, Strauss and Macheras (Fund. Math. 166, 281–303, 2000).     

Product variety, pricing and differentiation in a supply chain

Manufacturers typically sell consumer products through retailers and the presence of intermediaries has interesting ramifications for their product variety and pricing decisions. Retailers may want higher variety to help reduce price competition but the costs of variety are borne by the manufacturer. The increased variety may increase demand and profits for the manufacturer too but this depends on market-specific factors as well as costs. We explore these interactions through a model wherein a manufacturer sells multiple product variants at a wholesale price to two retailers who in turn compete for consumers. Consumers choose between the retailers based on the price and variety offered by each retailer and the search or transportation cost incurred by the consumer, equivalent to the level of retailer differentiation in our model. Several insights emerge from the analysis. The manufacturer offers the same variety to both retailers and this variety increases with market size and consumer sensitivity to variety. We find that some retailer differentiation benefits the retailers (not the manufacturer) but too much differentiation hurts both the retailers and the manufacturer. If the market is fully covered, then the channel is coordinated even with a simple wholesale pricing contract. If the retailers incur costs to sell the product, the manufacturer surprisingly loses out more than the retailers and in fact absorbs some or all of the retailer costs. Finally, asymmetry between retailers has some unexpected consequences. For example, variety is not impacted by asymmetry in consumer preferences for a retailer and the manufacturer offers the same variety to both retailers.     

Matching product architecture with supply chain design

Product architecture is typically established in the early stages of the product development (PD) cycle. Depending on the type of architecture selected, product design, manufacturing processes, and ultimately supply chain configuration are all significantly affected. Therefore, it is important to integrate product architecture decisions with manufacturing and supply chain decisions during the early stage of the product development. In this paper, we present a multi-objective optimization framework for matching product architecture strategy to supply chain design. In contrast to the existing operations management literature, we incorporate the compatibility between the supply chain partners into our model to ensure the long term viability of the supply chain. Since much of the supplier related information may be very subjective in nature during the early stages of PD, we use fuzzy logic to compute the compatibility index of a supplier. The optimization model is formulated as a weighted goal programming (GP) model with two objectives: minimization of total supply chain costs, and maximization of total supply chain compatibility index. The GP model is solved by using genetic algorithm. We present case examples for two different products to demonstrate the model’s efficacy, and present several managerial implications that evolved from this study.     

A note on the class of paracompact spaces whose product with every paracompact space is paracompact

We prove that if X is a paracompact space which has a neighborhood assignment x→Hx such that for each y∈X the closure of the set is compact then the products T×X, for every paracompact space T, and Xω are paracompact. The first result answers a problem of H. Junnila.     

SUBMANIFOLDS OF PRODUCT RIEMANNIAN MANIFOLD

1IntroductionLetUandVbeRiemannianmanffolds,withthedimensionn1andn2respectively.UxVistheRiemannianproductofUandV.WedenotebyPandQtheprojectionmappingsofT(UxV)toTUaildTVrespectively.ThenwehaveWeputJ=P-Q.ItiseasytoseethatJ~=I.WedefineaRiemannianmetricofUxVbyg(X,Y)==g1(PX,PY) g2(QX,QY),wllereg1andg2areRiemannia11metricofUandVrespectively.ItfollowsthatBy7wedellotetheg'sLevi-Civitaconnection.ThenwecaneasilyseethatInfact,Frollltlledefillitiollofg,wecangetthatUalldVareallgeodesicsub…     

On the product line selection problem under attraction choice models of consumer behavior

Product line design (PLD) involves important decisions at the interface of operations and marketing that are very costly to implement and change, and, simultaneously, determinant for market success. To evaluate the financial performance of a product line, a number of mathematical programming approaches have been proposed. Problem formulations are typically mixed or pure integer non-linear optimization models that are intractable for exact solution - in particular when empirically supported consumer choice models are incorporated.     

两个图的积的S-不可收缩性(英)

本文从组合角度明确给出了两个图的积是S-不可收缩的特征．     

On product form tandem structures

This paper is written in honour to A. Hordijk. It establishes product form results for a generic and instructive multi-class tandem queue with blocking, to which A. Hordijk has directly and indirectly contributed. First, a sufficient and necessary product form characterization is provided. Next, three special cases are briefly presented. These illustrate the possibility of product forms despite finite capacity constraints (blocking), unproportional processor sharing mechanisms and resource contentions (such as for access control). The results are partially new and of interest for present-day applications. In essence these rely upon the pioneering work by A. Hordijk     

REGULAR FUNCTIONS ON A PRODUCT OF AFFINE VARIETIES

ABSTRACT

Assume that f:X×Y→Z is a map from the product of two affine varieties into another affine variety such that f is a regular map when one variable is fixed. We show that f is a regular map if the underlying field is not countably infinite. The condition is indispensable.     

Product safety for a monopolist under strict liability

This paper views strict producer liability as essentially requiring the producer to provide a tie-in sale of full coverage insurance to its customers. The output and safety levels under strict producer liability are compared to those that would exist when the consumer retains all liability. The risk averseness of the producer and the availability of commercial liability coverage are shown to affect the producer's output and safety decision. In general, a shift from consumer to producer liability might not encourage the production of safer products, either with or without the availability of commercial liability insurance to the producer.