OR FORUMFORD WHITMAN HARRIS AND THE ECONOMIC ORDERQUANTITY MODELDONALD ERLENKOTTERUniversity of California, Los Angeles, California(Received January 1990; revision received May 1990; accepted May 1990)Ford Whitman Harris first presented the familiar economic order quantity (EOQ) model in a paper published in 1913.Even though Harris's original paper was disseminated widely, it apparently was unnoticed for many years before itsrediscovery in 1988. During this period much confusion developed over the origin of the EOQ model. This paperexplores the early literature on this model and traces the evolution of the confusion. \\ also sketches the remaikaWe lifeof Harris, who made contributions as an engineer, inventor, author and patent attorney, even though he received noformal education beyond high school. Harris's original 1913 essay is reprinted following this paper.PART I. AN EARLY CLASSIC OBSCURED:FORD WH\TMAN HARR\S'S ECONO^A^CORDER OUANTITY MODEL OF 1913While by the present methods of teaching, a knowledge ofscience in its present state of advancement is imparted verysuccessfully, eminent and farsighted men have repeatedlybeen obliged to point out a defect which too often attachesto the present scientific education ... it is the absence of thehistorical sense and the want of knowledge of the greatresearchers upon which the edifice of science rests.Cajori(1899),as quoted byJafre(1957, p. ;c).Although this quotation was directed toward the fieldof physics at the turn of the century, recent discussionsby Miser (1989a, b) and others suggest that it mayapply equally well to our own field of OperationsResearch at the present time. The origins of an ideaand the original context in which it was developedmay be obscured over time, and then historical viewsof the idea can become distorted. I believe that thefamiliar square-root formula for the economic orderquantity (EOQ) provides a remarkable example of thiskind of historical distortion. Other reviews have dis-cussed a number of the early EOQ papers (Raymond1931, Whitin 1954, Mennell 1961), but much of thehistory of the development and dissemination of thismodel and formula has been left untouched. As weexplore this history further, we shall see that theopening quote, which is taken from the preface to thebiography of the eminent management engineer, LeonPratt Alford, provides an unintended irony, for Alfordhimself played a prominent role in obscuring theorigin of the EOQ formula.Harris's 1913 EOQ PaperThe EOQ model and formula were presented origi-nally by Ford Whitman Harris in a paper publishedin 1913 in Factory, The Magazine of Management.This paper (Harris 1913a) was disseminated widely:Factory had a readership of 10,000 at that time, witha target audience of manufacturing managers. Thepublisher of Factory, A. W. Shaw, was closely associ-ated with the Harvard Business School during its earlyyears, and was the first there to use actual business"cases" in teaching (Copeland 1958a, b, Ingham 1983,Cruikshank 1987). In 1911, a special gift from Shawfinanced the establishment of the school's Bureau ofBusiness Research. The A. W. Shaw Company wasthe first publisher of the Harvard Business Review,under an agreement by which all profits were returnedto the school to support research activities. Shaw'scompany also published business books and othermagazines, including System, The Magazine of Busi-ness, which became Business Week after McGraw-Hill acquired the Shaw publishing interests. Even withthis seemingly auspicious origin, Harris's originalSubject dassifications: Inventory/Production: EOQ model. Professional: history of OR/MS; obituaries.Operations ResearchVol. 38, No. 6, November-December 19909370030-364X/90/3806-0937 $01.25© \990 Operations Reae-atch SocietV of Avi938 / ERLENKOTTEREOQ paper was lost from sight for many years untilits rediscovery in 1988 (Erlenkotter 1989).Today the EOQ model is so well known that weaccept its basic structure as obvious. In 1913, however,it was a modeling achievement of classical elegance.The simple square-root formula for the optimal orderquantity followed directly from Harris's assumptionof a continuous constant rate for demand and hisrecognition of the need to balance intangible inven-tory costs against the tangible costs for ordering. Ver-sions of his depiction of cost tradeoffs in the"manufacturing quantities curves" have appeared inall standard works on the subject. Even his originalpresentation of the model, which defines costs on aper item basis, is easier to interpret than the standardtextbook development, which expresses costs as anaverage per unit of time. Harris's basic EOQ modelbecame the dominant paradigm for order-quantityanalysis for at least the next 40 years.In his paper, Harris emphasized that the EOQ for-mula was intended as a practical tool to be usedintelligently, and not as a panacea to be applied indis-criminately. His second paper on inventories (Harris1913b), which displays a broad view of the functionsof inventory systems, shows that the calculation ofEOQs was just one aspect of the overall managementof the systems with which he was concerned.A revision of Harris's original EOQ paper becamea chapter in The Library of Factory Management,published by the A. W. Shaw Company in 1915(Harris 1915). This six-volume work provides anextraordinary view of the field of factory managementat the time of the First World War. It also was distrib-uted widely, and is listed either as a set or by individualvolume in several key, early bibliographies of manage-ment literature (Cannons 1920, Atkins 1923, Berg1931). Sources for the chapters in these volumes werenot cited, and the existence of the earlier paper (Harris1913a) is not readily apparent from Harris's EOQchapter. But, in the first volume, it is mentioned thatmuch of the material was drawn from Factory andSystem.Early Development of the EOQ LiteratureGiven the widespread circulation of Harris's EOQformula, in both article and chapter versions, thedegree of confusion about its origin is surprising.Although the original article may have been unknownfor many years, the chapter version has been cited,albeit erroneously, since 1931 (Raymond 1931,Erlenkotter 1989). But some still date the originof this formula to the mid-1920s (Baumol and Tobin1989). Others call it the "Wilson lot size formula"(Morse 1958, Wagner 1980, p. 450), while to manyEuropeans it is known as "Camp's formula" (Eilon1962). I shall trace the history behind this