STOCHASTIC COMPARISONS IN A PRICE-QUANTITY SETTING FIRM WITH UNCERTAIN DEMAND AND EMERGENCY PROCUREMENT

We consider a newsvendor problem with price-dependent demand, in either additive or multiplicative format. The newsvendor has two modes of purchasing： regular ordering at the beginning of the selling season and emergency ordering （if the realized demand exceeds the initial order quantity） at the end of the selling season. By stochastic comparisons, we systematically investigate the effects of demand magnitude and demand randomness on pricing and ordering quantity decisions as well as expected profit of the newsvendor, under both usual stochastic order （first order stochastic dominance） and convex order （less variable）. Our key findings include： （i） in contrary to the case where price is exogenous, a stochastically larger demand shock may even lead to a lower order quantity; （ii） a stochastically larger demand shock leads to a higher price for the additive demand case, but may lead to a lower price for the multiplicative demand case; （iii） a stochastically larger demand shock leads to a higher expected profit for both demand models; （iv） in general, a less variable demand leads to a higher expected profit for both demand models; and furthermore, a less variable demand shock has no effect on price for the additive demand model, but leads to a higher price for the multiplicative demand model. The implications of all these findings for pricing and order quantity are discussed in detail.

An Identity for Expectations and Characteristic Function of Matrix Variate Skew-normal Distribution with Applications to Associated Stochastic Orderings

We establish an identity for E f(Y)-E f(X),when X and Y both have matrix variate skew-normal distributions and the function f satisfies some weak conditions.The characteristic function of matrix variate skew normal distribution is then derived.We then make use of it to derive some necessary and sufficient conditions for the comparison of matrix variate skew-normal distributions under six different orders,such as usual stochastic order,convex order,increasing convex order,upper orthant order,directionally convex order and supermodular order.

Stochastic Comparison and Preservation of Positive Correlations for Lévy-type Processes

The stochastic comparison and preservation of positive correlations for Levy-type processes on R^d are studied under the condition that Levy measure v satisfies f{0〈｜z｜≤1）｜z｜｜v（x, dz） - v（x, d（-z））｜ 〈 ∞, x∈ R^d, while the sufficient conditions and necessary ones for them are obtained. In some cases the conditions for stochastic comparison are not only sufficient but also necessary.

GROUP SIZE AND PARALLELISM EFFECTS IN TASKS WITH HETEROGENEOUS LEVELS OF DIFFICULTY:A STOCHASTIC ORDER APPROACH

We consider tasks where in order to perform them it is sufficient that one member of a group will know how to do it. We are interested in the effect of task difficulty, and variability of that difficulty, on group performance, and in particular on the marginal contribution of an additional number to the performance of groups of different size. We explore the implications of various stochastic orders over task difficulty and variability. Some intuitive conjectures are shown to be false.

SOME RESULTS ON COMPARISON OF MAINTENANCE POLICIES

In this paper, we study the stochastic comparisons of minimal repair replacement policies in repairable case. We give some results on comparisons of the same unit for different policies and on comparisons of the same policies for different units.

APPROXIMATING ANALYSIS OF A KIND OF REPAIRABLE STANDBY SYSTEMS

In this paper, some approximating analyses are considered in a class of repairable systems.By using the properties and the techniques of partial orderings for random variables, we find some conditions under which some reliability indices of a system are less (or larger) than the corresponding indices of another system; and then, we obtain the bounds of the main reliability indices of a general system.

The Additive Hazard Mixing Models

This paper is concerned with the aging and dependence properties in the additive hazard mixing models including some stochastic comparisons. Further, some useful bounds of reliability functions in additive hazard mixing models are obtained.

SOME RESULTS ON THE RESIDUAL LIFE AT RANDOM TIME

In this paper, we consider the residual life at random time, i.e. XY=X-Y|X>Y, where X and Y are non-negative random variables. We establish a number of stochastic comparison properties for XY under various assumptions of X and Y. Under the assumption that Y has decreasing reverse hazard rate (DAHR), we show that if X is in any one of the classes IFR, DFR, DMRL or IMRL then XY is in the same class as X. We also obtain some useful bounds for the distribution and the moment of XY. Because the idle time in classical GI/G/1 queuing system can be regarded as the residual life at random time, the results obtained in this paper have applications in the study of such system.