摘要:

AbstractIt is pointed out that in many cases statistical assumptions, such as the assumption of a normal population, really cannot be known to be true with the absolute certainty that the word “assumption” has come to imply. In fact, in some instances data collected for purposes other than testing the assumptions cast serious doubt on the validity of the assumptions. A simple safety or hedging device is proposed, and illustrated for the case where the problem is to estimate the qthquantile (m, say) of a distribution assumed to be normal with given standard deviation σ. LetX, R denote the sample mean and the qthsample quantile, respectively. Under the assumption, the best estimate of m isX+ t σ, where t is a properly chosen constant, while R is a reasonable estimate of m even if the assumption is not true. The hedging device is to useX+ t σ as the estimate if |X+ t σ – R| ≤ d, and to use R as the estimate if || + t σ – R|>d, where d is a preassigned value. In order to choose d to reflect our faith in the validity of the assumption, and to obtain the operating characteristics of our estimation rule, it is necessary to know the joint distribution ofXand R. This is shown to approach a bivariate normal distribution as the sample size increases, for any population satisfying mild regular

ISSN:0028-1441    

DOI:10.1002/nav.3800080302

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1961

数据来源: WILEY

摘要:

AbstractIn application of operations research models in the area of logistics, important constraints are typically encountered in the form of limitations on the funds appropriated. A supply system must be operated within whatever budgeted funds are appropriated by Congress. In the present article, various possible types of budget constraints are discussed as well as their impact on certain types of operations research models. The possible misallocations that can result from the setting of specific budgets designated for particular purposes are discussed. The confusion existing in the literature concerning the type of constraints that are actually encountered versus those that are imposed upon the mathematical models is pointed out as well as the typical inconsistency of budget constraints and steady‐state models. The difference between a steady‐state budget and a transition‐phase budget is clar

ISSN:0028-1441    

DOI:10.1002/nav.3800080303

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1961

数据来源: WILEY

摘要:

AbstractIn this paper we analyze the inventory model in which the disposal of surplus items is taken into consideration as well as the purchase of stock in anticipation of future demand. Our main concern is to formulate the optimal ordering and disposal policy in a simple form, and it is assumed that the decision to be made at the beginning of each period is always one of the following: (1) ordering, (2) disposal, (3) no ordering and no disposal. The multiple installation model is treated by the method of implied penalty described by Clark and Scarf. The simple optimal policies are explicitly determined under various sets of assumptions on the cost structure of the inventory model.

ISSN:0028-1441    

DOI:10.1002/nav.3800080304

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1961

数据来源: WILEY

摘要:

AbstractThis paper gives a method by which economic retention quantity of a material having a known shelf‐life and following a normal probability law of obsolescence and deterioration has been calculated. The relevant equations are solved by trial and error metho

ISSN:0028-1441    

DOI:10.1002/nav.3800080305

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1961

数据来源: WILEY

ISSN:0028-1441    

DOI:10.1002/nav.3800080306

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1961

数据来源: WILEY

摘要:

AbstractIf Y1≤ … ≤ Ynare ordered observations from a population with cumulative distribution function\documentclass{article}\pagestyle{empty}\begin{document}${\rm G}\left( {{\textstyle{{{\rm X - B}} \over {\rm C}}}} \right)$\end{document}, probability density function\documentclass{article}\pagestyle{empty}\begin{document}$ {\rm (1/C)g}\left( {{\textstyle{{{\rm X - B}} \over {\rm C}}}} \right) $\end{document}, where B and C are unknown parameters with C>0, and the function G(x) is known, it is shown that under mild restrictions on G(x),\documentclass{article}\pagestyle{empty}\begin{document}$ \frac{{{\rm n + 1}}}{{{\rm n - 1}}}\sum\limits_{{\rm j = 1}}^{{\rm n - 1}} {{\rm g[G}^{{\rm - 1}} {\rm (j/n)](Y}_{{\rm j + 1}} {\rm - Y}_{\rm j} {\rm)}} $\end{document}is a consistent estimate of C. In certain important cases, this estimate has a structure similar to that of estimates known to be op

ISSN:0028-1441    

DOI:10.1002/nav.3800080307

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1961

数据来源: WILEY

摘要:

AbstractA FORTRAN II transportation code, using Kuhn's Hungarian Method, was reported upon at the RAND Symposium on Mathematical Programming in March 1959. The algorithm was based upon a proof of the König‐Egervary theorem, presented by the present author at the 1958 Symposium on Combinatorial Problems sponsored by the American Mathematical Society. The code was entirely rewritten (in FORTRAN II), during the 1959 IBM Summer Institute on Combinatorial Problems, and several problems were run at the IBM Research Center to obtain data regarding computing times and frequencies of various internal loops. A CLOCK Subroutine yields readings, in hundredths of minutes, for each time through selected portions of the computing run. The version reported upon at RAND solved a 29 × 116 pseudorandom transportation problem in 8.01 min, as compared with 3.17 min using the fastest competing code (SHARE 464) then available. The present version solved this same problem in 2.87 min, and another 29 × 116 problem in 1.89 min. This paper presents the algorithm and reports upon computing experi

ISSN:0028-1441    

DOI:10.1002/nav.3800080308

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1961

数据来源: WILEY

摘要:

AbstractConsider a model in which there are N neighboring cells in one of which there is an object that it is required to find. The a priori probabilities of the object being in cells 1, …, N are p1, …, pNrespectively, and the costs of examination of these cells are tl, …,tN respectively; the search policy is considered to be optimal when the statistical expectation of the total cost of the search is minimized. For the case in which the ti†s are constant throughout the search, an optimal policy solution has previously been found by Bellman and by Smith. In the present paper it is assumed that the costs comprise a travel cost dependent upon the distance from the last cell examined, in addition to a fixed examination cost: initially, assuming that the searcher is next to cell 1, ti= i + t, where t is constant; and from then onwards, assuming that the jthcell has just been examined, ti= | i ‐ j | + t. An optimal search strategy is found in the case where the pi† s are all equal, and approximately optimal strategies in the case where piis proportional to i. The latter case has application to defense situations where complete searches occur at successive intervals of time, and hence the enemy objects are thinned out the nearer they come to the d

ISSN:0028-1441    

DOI:10.1002/nav.3800080309

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1961

数据来源: WILEY

ISSN:0028-1441    

DOI:10.1002/nav.3800080310

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1961

数据来源: WILEY

ISSN:0028-1441    

DOI:10.1002/nav.3800080311

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1961

数据来源: WILEY