Optimal Ordering Policies for Inventory Systems with Emergency Ordering

This paper considers dynamic single- and multi-product inventory problems in which the demands in each period are independent and identically distributed random variables. The problems considered have the following common characteristics. At the beginning of each period two order quantities are determined for each product. A “normal order” quantity with a constant positive lead time of λ _n periods and an “emergency order” quantity with a lead time of λ _e periods, where λ _e = λ _n - 1. The ordering decisions are based on linear procurement costs for both methods of ordering and convex holding and penalty costs. The emergency ordering costs are assumed to be higher than the normal ordering costs. In addition, future costs are discounted.For the single-product problem the optimal ordering policy is shown to be the same for all periods with the exception of the last period in the N-period problem. For the multi-product problem the one- and N-period optimal ordering policy is characterized where it is assumed that there are resource constraints on the total amount that can be ordered or produced in each period.     

Ordering groups constructively

The existence of a linear order on a group that is compatible with the group structure generally requires transfinite methods. However, this can be circumvented by concentrating on the consistency of a suitable propositional theory. To this end, we work with Scott’s multiple-conclusion entailment relations to describe the positive cones of a group. The commutative case then leads to a constructive version of Levi’s theorem that an Abelian group be orderable if and only if it is torsion-free. Subsequently, Cederquist and Coquand’s fundamental theorem of entailment relations prompts a finitary version of Sikora’s theorem.     

Comparing and Ordering Integers

<正>When am I ever going to use this?WEATHER The Wind Chill Temperature Index table shows how cold air feels on human skin.1.What is the wind chill if there is a wind at 20miles per hour and the temperature is 5°?     

树按Balaban指标的排序(英文)

连通图G的Balaban指标(也称J指标)定义为J=J(G)=(|E(G)|)/μ+1∑_(uυ∈E(G)),其中σ_G(u)=∑(w∈V(G)d_G(u,w)此处μ是基圈数.Balaban指标常用于各种QSAR和QSPR的研究.本文根据Balaban指标的计算公式及文中提到的变换方式,我们得到了一些序关系.基于这些序关系,我们确定了n个顶点的树中具有最小Balaban指标的前21个树.     

Ordering sequences by permutation transducers

To extend a natural concept of equivalence of sequences to two-sided infinite sequences, the notion of permutation transducer is introduced. Requiring the underlying automaton to be deterministic in two directions, it provides the means to rewrite bi-infinite sequences. The first steps in studying the ensuing hierarchy of equivalence classes of bi-infinite sequences are taken, by describing the classes of ultimately periodic two-sided infinite sequences. It is important to make a distinction between unpointed and pointed sequences, that is, whether or not sequences are considered equivalent up to shifts. While one-sided ultimately periodic sequences form a single equivalence class under ordinary transductions, which is shown to split into two under permutation transductions, in the two-sided case there are three unpointed and seven pointed equivalence classes under permutation transduction.     

Ordering events in Minkowski space

Let p₁,…,p_k be k points (events) in (n+1)-dimensional Minkowski space . Using the theory of hyperplane arrangements and chromatic polynomials, we obtain information on the number of different orders in which the events can occur in different reference frames if the events are sufficiently generic. We consider the question of what sets of orderings of the points are possible and show a connection with sphere orders and the allowable sequences of Goodman and Pollack.     

Ordering free products of groups

A method of constructing orders on free products of groups is given, based on work of Botto Mura and Rhemtulla, and of Holland and Medvedev.     

Ordering trees by algebraic connectivity

LetG be a graph onn vertices. Denote byL(G) the difference between the diagonal matrix of vertex degrees and the adjacency matrix. It is not hard to see thatL(G) is positive semidefinite symmetric and that its second smallest eigenvalue,a(G) > 0, if and only ifG is connected. This observation led M. Fiedler to calla(G) thealgebraic connectivity ofG. Given two trees,T ₁ andT ₂, the authors explore a graph theoretic interpretation for the difference betweena(T ₁) anda(T ₂).Research supported by ONR contract 85K0335     

Back Ordering in Inventory Control

An approach to determining the empirical relationship between time out of stock and back ordering is outlined. Using this relationship the expected lost sales in a reorder level system of inventory control are derived for continuous and block demand depletion, fixed and variable lead times. Their applicability to a generalized inventory model is discussed.     

Ordering trees by their spectral radii

Let T be a tree with n vertices and let A（T） be the adjacency matrix of T. Spectral radius of T is the largest eigenvalue of A（T）. Wu et al. [Wu, B.F., Yuan, X.Y, and Xiao, E.L. On the spectral radii of trees, Journal of East China Normal University （Natural Science）, 3：22-28 （2004）] determined the first seven trees of order n with the smallest spectral radius. In this paper, we extend this ordering by determining the trees with the eighth to the tenth smallest spectral radius among all trees with n vertices.     

Probability,Defectives and Mail Ordering

Probabilistic methods are applied to the problems facing the customer attempting to order items from a distributor where the probability of any item being faulty is a constant, q. The model involves only faulty items being returned by the customer in each round, and it is suggested that the situation being analysed is fairly general, conferming, for example, to that of the mail order customer exemplified by the record collector. Calculations are provided showing the extent of benefit from delaying purchase until a large order has accumulated.     

含参Schur型排序不等式

本文类比经典的Schur不等式,建立了几个含参Schur型排序不等式,并将其应用于基本Schur型的含参推广.     

Linear Codes and Their Coordinate Ordering

A necessary and sufficientcondition for a q-ary code to satisfy the two-waychain condition (TCC) is found. A known construction of q-arycodes is shown to yield codes satisfying the TCC. Some q-arycodes of dimension k 6 meeting the Griesmerbound are proved to satisfy the TCC.     

Ordering of risks: a review

In this review we will consider and discuss the most important partial orderings of riks, namely consistent partial ordering and net-stop-loss ordering. More especially we will study the consequencies of ordering of risks for the compound risk: S = X₁+X₂+···+X_N.The impact of orderings of claim size distributions (F_X) and claim intensities (F_N) on orderings of claim amounts (F_S) is examined. The consequencies of these kind of orderings on orderings of risks by means of premium calculation principles is also discussed.In this framework the influence of the dangerousness of distributions on orderings of risks is given.In analogy with the notion of stochastic dominance appearing in the theory of finance, the notion of stop-loss dominance is introduced.     

Ordering trees by the Laplacian coefficients

Motivated by a Mohar’s paper proposing “how to order trees by the Laplacian coefficients”, we investigate a partial ordering of trees with diameters 3 and 4 by the Laplacian coefficients. These results are used to determine several orderings of trees by the Laplacian coefficients.     

管道订购和运输

在对图形一分析的基础之上 ,首先建立了问题一的非线性规划的模型 .然后采用了两种方法分别对问题一求解