However,for medium-and fastmovingitems it is not a tenabledistribution. The negativeexponentialdistributionis definedonly for non-negativevaluesĪnd is monotonicdecreasing.It thus fulfilsthe generalrequirementsfor representing the demand of slow-movingitems. (ii) Becauseit is symmetricalit is only adequatefor representingthe demand Of customerreturns.Truncatingthe distributionat zero to removethisĭifficultygreatly increasesthe mathematicalcomplexityin subsequent Unrealisticfor inventorycontrolwork-the only interpretationwould be (i) It is definedfor - oo x Koo.The conceptof negativedemandis, we think, The disadvantageof the normal distributionwith regard to the desired
The requirementis then to find a statisticalfrequencydistributionhavingtheseĪ survey of literatureon inventorycontrol shows that, of the continuousįrequencydistributions,the two most usuallyused are the normaland negative (c) normaltype distributions(truncatedat zero) (b) unimodaldistributionsheavilyskewedto the right,and finallyto (ii) as the meandemandof itemsincreasesthe observeddistributionschange (i) they exist only for non-negativevaluesof demand In the field of inventorycontrol of finishedgoods we find that the observedįrequencydistributionsof demandhave the followinggeneralcharacteristics: That will adequatelyrepresentthe observedfrequencydistributionof demand Oneof the basicproblemsin inventorycontrolis to finda frequencydistribution 3, iĬalculationsimpliedby the formulaeto be incorporatedinto inventorycontrol The particularapplicabilityof the gammadistributionto inventorycontrolmayīe more widely recognizedand to provide sufficientdetail for the numerical The aim of this paperis to cover all these points underone headingso that Appropriatemethods ofĬalculationare describedto give the requiredinversionof the integraldefining Stock out, the re-orderlevel which will achievethis.
In certain circumstanceswe wish to determine,for a given probabilityof With which it may be used to deal with fixed lead times and how this can beĮxtendedto situationswhere the lead time is distributed.Again methods of It is shownthat a particularadvantageof the gammadistributionis the ease Statedapproximationsto facilitatecalculation. The sales lost (under the assumptionof no back-ordering).The appropriateįormulaeare developedand methods of calculationgiven.įor certain areas of calculationthe formulae may be replacedwith the Additionally,when a stock out does occur we may wish to estimate So extensiveas to be unsuitablefor computer-operatedĬontrol. Stock out may be determinedas a mathematicalformula and a method ofĬalculatingthis for specificvalues of the distributionparameters,the methodīeing particularlysuitablefor computeruse since the tables of Pearson2are Justify its applicability.Leadingfrom this we show how the probabilityof a Lead time) which may be fixed or distributed.Ī variety of statisticaldistributionsare availableto describethe demandĭistribution.In this paper we consider the gamma distributionand aim to This pr obabilitywill depend upon the distribution ofĭemandfor the item and the time elapsingbetweenorderingand receipt(the Algorithms forĪ CENTRAL problemin inventorycontrolis to determine,for stock re-orderedĪt a certainlevelor pointin time,the probabilityof a stockout (see,for example,īurgin and Wild'). The paper aims to justify the applicabilityof the gamma distributionto inventoryĬontrol and to collect under one heading the properties of the distribution andĪssociated formulae arising from inventory control theory. Printed in Great Britainĭunlop Limited, Fort Dunlop, Birmingham,England This content downloaded from 146.201.208.22 on Fri, 01:47:38 UTCĪll use subject to JSTOR Terms and Conditions We use information technology and tools to increase productivity and facilitate new forms of scholarship.įor more information about JSTOR, please contact Research Society and Palgrave Macmillan Journals are collaborating with JSTOR to digitize, preserve and extendĪccess to Operational Research Quarterly (1970-1977). JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content
Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at You may need to log in to JSTOR to access the linked references. Linked references are available on JSTOR for this article: Published by: Palgrave Macmillan Journals on behalf of the Operational Research Society Source: Operational Research Quarterly (1970-1977), Vol. The Gamma Distribution and Inventory Control