36 JOHN D. c. LITTLE

JOHN R. HAUSER AND GLEN L. URBAN

The de,•eloprnent of operations research (OR) after World War II (WWII) was greatly influenced by OR pioneers who applied their knowledge and experiences to the problems of business and

industl")'. In parallel, they brought OR methods and practices into academia, and created the environment for the development and training of a new cadre of OR practitioners and researchers. In the forefront of this new !lJ'OUp, we find John D. C. Littk From b~ing the first tt> receive a Ph.D. in OR, John went on to leave his own hlsting imprint on the field as a progenitor of the field of marketing science and its applications. the person behind I.he eponymous Little's Lav .. for queues, an influential acadernic leader, and a highly successful OR researcher, practitioner. and entrepreneur.

For his innovative and scn1inal research in rnarketing> John received the American Marketing Association (AJ'1A) Charles Parlin Award for contributions to the practice of marketing research ( 1979), the AMA's Paul D. Converse Award for lifetime achievement (1992), and MIT's Buck Weaver Award for outstanding contributions to marketing (2003). He was president of the Operations Research Society of America (ORSA) in 1979, The Institute of Management Sciences (TIMS) in 1984-1985, and first president (1995) of the lnstitut~ for Operations Research and the Management Sciences (INFORMS). one of onlj• two individuals who have served as president of the three organiwtions.

A.A. Assad. SJ. Gass {e<ls.). Profiles 111 Operations R£.searcl1, lnternational Series in 659 Operations Rt'St'aJX'.h & Manag.:mcnt Science 147. DOJ 10.1007/978- 1-4119·628 1·2_36, ©Springer &ie-i1ct"+Business l\<ft'tlia, U.C 201 1

660 Plt0FllF$ IN 0f>ERATIONS RESEARCH

BOS'fON BORN, MASSAC:HUS>TJ'S Bun, ANl> ON TO MIT

John D. C. Little was born in Boston, Massachusetts, on February 1, 1928, the son of Jolrn D. and Margare1 J. Utile, and grew up in Andover, Massachusetts. Both his futher and mother were natives of Massachusetts, he was born in Malden and she in Gloucester. Margaret graduated from Smith College and, afler her three children had grown up, became an English le•chcr and 1hen the principal of a private school in Andover. John D. attended Malden public schools and Dartmouth C-Ollege, bul left 1>ithout graduating to become an ambulance driver in France during World War l. Laler, he held · various pos11mns including reporter for the Boston Herald; editor for a financial journal in Washington, D.C.; bond salesman for a Boston brokerage firm; writer for the Ofnce tlf War Jnformalion in Washington during WWII; and a :.I credit manager.

John (D. C.) lived in the West Parish part of Andover, which was then quite rural, an exurbia from which his father commuted 10 Bnstoo by train. John attended Andover's elementary and middle public schools and was a good student. especially in mathematics and science. For high school, he obtained a scholarship to the independent Phillips Academy in Andover and won most of the science-related prizes. He graduated Andover in I 945 and started college at the Massachusetts Institute of Technology (M IT). Due to the wartime acceleration of MIT's academic program. his freshman year began in the sununer. He decided 10 major in physics, which appealed to him as a worthy intellectual challenge. John did more than s1udy-he became editor-in-chief of \loo Doo, the MIT humor magazine. He also "took a minor in hitchhiking to Wellesle)' [a women's college)" (Little 2008). He graduated in J years, receiving an S.B. degree in 1948. Tired of school and nol ye! wanting lo enter the working world, John hitchhiked around the country for JO months. This brought him 10 the point where work seeme.d bener than poverty, so he joined the General Eleclric Company as an engineer. In 1951. he went back to MIT, enrolling as a

CHAPTER. 36: JOHN D. C. LITTLE 661

graduate student in physics. Although he passed his general exams in physics, his intellectual curiosity caused him to search out other areas-a research assistantship (RA) on an unclassified air defense project with the psychologist J.C.R. Licklider, and a course in the new field of OR taught by George Wadsworth of the mathematics department.

John, inspired by the challenges offered by the embryonic field of OR, obtained an RA working for the physicist Philip Morse. Morse, a WWII pioneer in OR, is recognized as the founder of OR in tlie U.S.-he had established the fust U.S. OR group for the Navy in 1942. After W'Wf!, Morse founded and dir.cted MIT's inter-departmental Operations Research Center. John's RA was for a Navy-sponsored project, 'Machine Methods of Computation and Numerical Methods.'

Machine computation meant Whirlwind, one of the earliest digital computers-it had been built in the late 1940s by MIT personnel to support the l\avy's research program. John's task was to learn about Whirh,fad, how to program it, and to compute a book of tables for spheroidal wave fonciions-rather esoteric functions used for calculations in theoretical physics. John did not think the resulting book was going to be a big seller, but, in assuming the task. he thought ·an RA is an RA'; one usually does not question the professor, especially when the job belps pay your tuition. More importantly, John became one of the few people in the W(>rld with access to a digital computer. The knowledge of what a computer could accomplish was central to his future research and consulting activities. He felt that "computers are cool' and be can often be found "pla}illg' witlt the latest technological devices (Little 2008) .

• When John asked Morse about possible thesis topics, Morse

mentioned a few from physics and then wondered if John would be interested in an OR topic. Physics or OR? john fa<:Aed the decision and concluded, •physics is fine, but look at it this way. Bohr solved the hydrogen atom and it's beautiful. Then somebody named Hylleraas solved the helium atom. It took him 7 years on a hand-crank calculator and it's ugly. Beyond helium there arc another 100 or so clements •Nith bad prognoses. I'm searching for a field with a lot of unsolved hydrogen atoms. OR looks good' (Little 2007, 3).

John's dissertation research dealt with the study of mtcr-flow management in a hydroelectric rt>servoir and dam system (Little 1955). In particular, his analysis dealt with Washington State's section of the Colwnbia

662 PRO~ILES IN OPLKArlONS IUSEARCH

River, its Grand Oml"" hydroelectric plant. and the Franklin Oclnno Roosevelt Lake (the reservoir that formed behind Grand Coulee Dam).

The probl~m was how best to schedule the amount of water flow~ 10 generate eleclriciry. The system is naturally dynamic wi1h the 3\'llilablc ""'ter to generate power a function of seasonal rainfall and the runoff from snow melting in the mountains during the spring and summer. In the foll nnd \1tinter, \Vhen precipitation falls as !>flO\V in the n1ountains, the natural river flow drops drastically. Water leaves the reservoir from spiU-over (wasted energy) and when the water is drawn down to generate electricity. The problem is interesllng because the power is proportional to the head, the height of the water behind the dam rdative to the wa1er below the dam, and to the rate of waler flow. A greater Oow generates more electricity, hut also redu~s the head at a faster rate.

The tradeolT was challenging. As John notes, decisions have to be made: • ... in the spring and summer. the right decisions about water use are obvious-indeed they arc hardly decisions-whereas in the fall and winter such decisions rtquire a balancing of the benefits of future againsl immediate water use in the face of uncertain future flow• (Little 1955, 188).

John formulated the problem as a dynamic program, although, al the time, be did not know it was a dynamic progr•m. John faced the dynamic-programming ·curse of dimensionality; the rapid increase in computing time with the number of state ,..,riablcs (Bellman 1957, ix). The simplest credible formulation required two slate variable<: one for the amoun1 of water in the reservoir (which determines the head) and the other for the current river flow. Thanks to Whirlwind, John was able to finish his Jhesis before his RA ran out (Little 2007, 4).

The thesis was ''cry likcly the first non-defense application of dynamic programming to a problem of practical importance. Real data were used for the historical stream '1ows. Tile models of Grand Coulee and its reservoir were simplified to save computing time, but were based on actual physical dimensions (Little 1955).

John received his Ph.D. in OR in 1955, the fust person in the world to rtecivc such a degree-his dissertation title was the ·u,.. of Storage Water in a Hydroelectric System." and his advisor "'as Philip Morse. John, to be precise, describes his Ph.D. as being in physics and OR, since his general exams were in physics and his thesis in OR (Litt le 2008).

CHAPTER 36: JOHN 0. C. Ll'ITLE 663

In 1953, John married Elizabeth (Betty) Alden, an MIT physics graduate student who worked on ferroelectrics under Professor Arthur von Hippe!, a pione<:r in dielectrics. especially ferromagnetic and ferroelectric materials. She received her Ph.D. in physics from MIT in 1954, one of very few women to do so at the time. After their marriage. Betty and John moved to Marlborough Street in Boston's Back Bay. The rent was high "but not too bad and we could split it" (Little 2007. 4). Beginning a lifetime of exercise {John jogs and bicycles daily at age 80), they had to walk up five flights to reach their tiny, top floor, two-room apartment. It had sloping ceilings to conform to the roof, but it suited their purposes admirably.

A•MV, CASE INSTITUTE, AND LAVING DowN THE LAw

In early 1955, 3 months after completing his thesis, John was drafted into the Army. He was stationed for 2 years at Ft. Monroe, Hampton, Virginia, where he served as an operations analyst working on military OR problems that included probabilistic models of land mine warfare. As an antidote to the Army, John and Betty bought a sailboat and had a wonderful time getting in and out of trouble on the Chesapeake Bay. Their first child, John N. Little. was born in the Ft. Monroe Army hospital. Upon his discharge from 1he Army in 1957, John began his academic career as an assistant professor at Case Institute of Technology (now Case Western Reserve Universi·ty) in Cleveland, Ohio. There he had his first experiences working on industrial OR projects.

A project with M&M Candies introduced him to advertising problems, and a project with Cummins Engine, Inc. introduced him to the issues of conflict between a manufucturer and its independent distributors. At M&M, the president had deliberately stopped all advertising after a long period of operating at a high level to see what would happen. The Case team analyzed the resulting sales over time. At first, sales changed very Uttle and the:n started into a serious decline. With their response analysis and further data, the team caUbrated a model which led it to recommend a new policy for buying TV spot advertising. At Cummins, top management was dismayed that, when the company provided extra sales support to its independent distributors. the latter rather quickly reduced their own. Jolnn devised a graphical profit analysis showing that such behavior by the distributors was entirely rational. With

664 PROFI LES IN OPUtATIONS RESEARCH

his accumulation of such real-world experiences, he developed and taught a graduate course- OR in Marketing- that may have been the fi rst such marketing science course.

Although not a problem in marketing, John also worked on the traveling salesman problem (TSP), whose solution procedures for finding the minimum TSP route were computationally challenging. In addressing the problem, he and his coauthors introduced and popularized the term branch and bound as a technique for solving the TSP, as weU as other combinatorial optimization problems (Little et al 1963, 972). For a while, the authors held "the indoor record for size of problem solved, 40 cities on the fastest machine at MIT at the lime, an IBM 7090' (Uttle 2008). Ct turns out, over four decades later, that the TSP is relevant to modern marketing science. With automatic tracking of supermarket shopping caits and recorded chockout data, researchers are using optimal traveling salesman solutions as reference routes for studying how shoppers actually move around in stores.

John's research at Case (and later work) was clearly influenced by his mentor Philip Morse, who hqian his career as a theoretical physicist but, in the course of his OR actMties. became both an experimentalist and a theoretician. John was guided by the definition of OR promulgated by Morse and George Kimball in their book, Methods of Operations Research (Morse and Kimball 1951. 1) •o]><'rations Research is a scientific method of providing executive departments with a quantitative basis for decisions regarding operations under their control.' John, in his retrospective review, "Philip M. Morse and the beginnings• (Little 2002) notes: "The definition leaves room for the tremendous development of methodology that we have witnessed in the past 50 years, but it keeps our foet on the ground with the requirement for data, models. and decisions. I like that, and I am sure it is what Morse intended' (Little 2002, l<IS).

Being true to this paradigm.John, in a study of a real-world problem, wot~d often meet with managers to karn how they perceive the problem. Then he would formulate tentative hypotheses about underlying processes that, if w1derstood, might permit improvement in operations. After that, he would look for relevant data and/ or design and execute a plan for collecting it. Whenever feasible, he would do chis with students. Often, iteration was required between the observed and modeled worlds until the model was right for the job at hand. This style marked his professional behavior in such disparate subfields of OR as hydroelectric systems, traffic signal synchronization, the process of managing. and eventually marketing.

CHAPTER 36: JOHN D. C. LITTLE 665

An exception to the paradigm is the paper underlying Little's Law. This paper, written while John was at Case, established him in OR history. He published the first general proof of the famous queueing fommla, L ~ 2 W (Little I 96 la). Assuming steady state operation, the formula says that the 3\'erage number of customers in a queueing system over time (!.) equals the average arrival rate of customers to the system(,\) multiplied by the average time that each customer spends waiting in the system ( W). A customer can be anything from a consumer waiting for a teller in a bank, to an aircraft waiting to land, toa packet of data waiting to be processed in a computer network. Little's Law allows an analyst to obtain all three of these fundamental performance measures of a queue by calculating (or measuring) on!)' lwo of them. This is useful because the analytic methods used to calculate Land Ware usually quite different and, often, one is much easier to carry out than the other.

John taught a queueing course at Case and, among other so\lrces, used Morse's pioneering book on queueing theory for OR applications, Qtmies, Inventory and Maintenance (Morse 1958). ln one of John's lectures, be pointed out Morse's observation that the curious formula L " AW always seemed to apply to queues whose operational beha\1or Morse had solved the long, hard probabilistic way, that is, by making specific assumptions about arrival processes, service time distributions, and queue disciplines (Morse 1958, 75). John went on to sketch a figure on the blackboard, similar to the one that appears in his paper (Little 1961a, 385). He used the figure to give a heuristic argument why the formula should hold in great generality for steady state queues. In discussion after class, one of the students wondered how ~ifficult it would be to prove the general case. John oblib~ngly answered, •it shouldn't be too hard." "Then you should do it!" was the response (Llltle and Graves 2008, 99).

The disC\lssion stuck in John's mind and he started to think about how he might turn his heuristic proof into a formal one. He bought and read some books on general stochastic processes. In those years, he and Betty would pile themselves, their children, their summer clothes, and a stack of books for John's research projects into their Ford Falcon station wagon and head for Nantucket (Island), Massachusens to •1'end the summer. This particular year (1960) he took his new books and worked on L =A-Was one of his major projects. The books did not have any magic formulas, but they gave him important ideas- the outcome was his paper, •A proof of the queuing fomrnla L =AW' (Little 196la). John decided then and there not to make a career out of being a measure-theoretic stochastic

l'l\OFILES IN OPERATION\ RESEARCH

process mathematician-he has never regretted it. Little's I.aw has entered OR folklore. At an ORSA conference in New Orleans, T ·Shirts were sold to raise money for ORSA. A best seller wa> the one that proclaimed: 'It may be Little, but it's the Law."

\\"}IA]"") I!'; ''>AMP Til.UWHICH \IE CALLA R°'-f

There ha. l>ecn moch tW"IO'lt)' about...., h•t Jnhn's D. C. n1lddlt 1n1l1ili 3-Und for-~ ha& bet"n bktd ofttn. An o-IH'nle ca~ u( curlos1t)' occurred \\·hen an OR (t:acher 11'1 Oklaho1na ('II)' d1aUcngcd h.h: OR class lo fln,I out tht exact mlddte namo of tht picrson afk.r "-·hom Llldt's law~ n•nltc.l-thc tITT.t 111..Ji::nt who d.icl-"" "'-ould get a fl'"'•rd. rh.b mu! tcJ if1 John rtet'!\1ll@'. r:'l\io<. l'I ttn.a.il from OUahoma C:th. Out of curios.it)·. John drdCed io pruwe the c.h:aHen~ ind .c-udttd tht \\.cb tor the: am.•cr. He wu .surpnt.itd io fwd ho"' dillkul11he task was. Ht "'--u ab1e to Jo 11, bu1 2dnub h" "''Ii atdtd b)' kno"'·ing th.at the name. t..rC ill IWO pla«S On ihe f\otIT' \\1cb ~lie

Man)' pt0ple ha\'e gu<.'!1"00 1ha1 0. C.. cal'l\.t trom dirrxl cu1rtnl l:Nkd on fohn'l <arly worlc on h)·dn.ltl«tricity. whk.h. by the "''l w.:iuld be A. C (.tltcTnating currcnl) Othm hJ.vtgut:S$C'd ~of Q:llumbsa fromjohn',u;int:nbonoru to OR in tht U.S II KIK>I DC ~ although man)· pc<tpi(' consli<kr John a SLlpn ·hc-ro. nor DC S·otlCS (oir lklteoboud.J.-Jnhn jog), ti i.. ft01 Donhl\gn Q>11ege Of tht l)ublln C.Ore, nor "'n D. C. United, the Otpattmc:nt of Correctioni., dc~C:l't crul1b11,t, or dJg1tol cameni.

'l'hc an\\\t>r b Dutton <.:;o1\an1. His father, "''ho was John Ovuon Utt!e1 did nn1 want John to tlf ai!.cd junior and '«) adJ<d a.nothtr middk namf'_ tli'f b.thtt wu d~ to his grandmu4 n<t whost: maickn 11•mt ... -u Con.tnt Thus. John be..~ John O. C l 1<tlt lohn. tu.s ooced tr.at, .Jthough 1hc-rc att man) ~"f'k' named JoM Unlc. :ie has nnrt found .inoL1'a who \\'lS John O. C. Uule He finds thl• helpful m iotlNhmg for hJn\~df in \\' tb documcntll (I ht it 2008),

REn;RN ro MIT, EvoLv-rtON O• THE Sarna o• MARKETING

In 1962, John interviewed for a faculty position al MIT in the School of lndU$trial Management, now the MIT Sloan School He had been a tenured associale professor at Case and, without any qualms, he accepted MIT's offer as an untcnured associate professor. John viewed the S<:Ope of OR broadly and was attracted hack to MIT by the promise of new problems and new research directions. IYUT w-as an excellent base of oper.uions with good colleagues and great students-he has never left!

John, perhaps frustrated by Boston dtivers, who are alleged to be the worst in the U.S., fust continued his work on traffic Oow and 1rnfllc signal control, a problem he had begun at Case- traffic delays due to additional time to travel over a route as a result of traffic and traffic lights (Little J961b). He had also worked with a master's student, John Morgan. who programme,l 1he synchronization of 1raffic signals on a 1wo-wny street on

CHAPTER 36: JOHN 0. C. LITTLE 667

t]1c Case computer. This was the first time the problem had ever been approached in this manner. Pre,iously, it had been done graphically by baud. ll is trivial to syncnronize lhe SigJlalS on a one way street so that cars traveling at an average speed can traverse the lcmgth of lhe street without slopping. The problem becomes c.ombinatorial and quite difficult on a two· way street when it is desired lo have the c.irs in both directions be able to do lhe same. The fraction of the signal cycle time for which cars in both directions can travel without slopping is known as the bandwidth of the street (Morgan and Little, 1964). Finding the maximum bandwidth (MAXllAND) is a challenging optimization problem.

At MIT, John extended this work lo complete street networks, seeking to maximize a linear combination of the bandwidths of the various arteries in the network (Little l 966a}. The methodology was based on mixed-integer linear programming. He was joiJ1ed by colleagues and research assistants and supported by the Federal Highway Administration to produce the software package, MAXBAND- it was distributed lo municipaliUes so they could optimize their street systems (Gartner et aL 1981; Little and Cohen 1982). This stream of research defined a new state of the art in the field of synchronizing traffic signals on arteries and networks.

In a quite different direction, Jolin, now in a business school, had the vision to perceive marketing as source of interesting and relevant unexplored opportunities for OR and management science (MS}. As an example, the effectiveness ofa company's advertising is likely to vary over time. No man er how good the response function used to calculate an optimal advertising rate at one point in time, it is like!)' to drift to something different. \\That to do?­run an experiment to re-measure effectiveness and update the advertising response function. For example, take five medium-sized markets and sel them at higher than the currently presumed optimal advertisil1g rate and set another 6\•e markets lower. The resulting measurement can be used to reset the advertising response function and obtain a more profitable advertising rate for use nationally. But the 10 experimental markets are being deliberately operated differently from the perceived best rate, thereby incurring a calculable cost. Tbe adaptive system optimization, however, takes the next step by setting the number oi experimental markets so as to maximize total system profit, including the cost of the experiment. John thus became the first scholar to develop adaptive c.ontrol methods for the field of marketing. He was particular!)' pleased that his model c.ould be applied readily (Little 1966b). For John, it was not enough to develop a nice mathematical solution- he wanted somebody to use it. He also published

668 PROFILES IN OPERATIOl'!i RfSEARCll

a generaliled version of the mathematics in terms of optimal adapth"e control (Ultle 1977).

During this period, John became increasingly interested in advertising budgeting and media selection. He and Leonard Lodish, one of his Ph.D. students, developed an on-line. computer-based system for selecting and scheduling advertising media. They described it as a media planning calculus and named it MEDIAC (Lillie and Lodish 1969). MEDIAC replaced heuristic anal)•ses "ith the optimization of a measure more dosely related to sales and profits.

In 1968, while he was conducting an MIT summer session on OR in marketing, John was approached by allendees from l'\abisco (fom1erly the National Biscuit Company) who asked him to develop a model to set advertising s~nding levels for Oreo cookies. John realized that Nabisco had some explicit, hard data, but !hat other key data were buried in managers' heads. Managers with experience in this area had implicil knowledge of how sales would respond to ad\'crtisi ng. The challenge was how to unl<11:k that information in a manner that could augment rather than replace the hard data. From lhis challenge, John developed the concept or a decision calculus as described in •Models and managers: The concept or a decision calculus• (Little t 970).

This revolutionary paper st.orts out .,;th the sentence: "The big problem with management science models is that managefi practically never use them" (Little 1970, B166). But it was not a negative paper-John wanted to impro\'e matters. First, it broke with standard practice for empirical models that all constants be estimated at once on a single data set. If data were not available on, say, ad,erlising. then advertising could not be in the model. John's paper took rhe view of those who wanted 10 apply management science models nnd set forth guidelines that would be critical to implement.at Ion. John def1ned a decision calculus as •• model-based set or procedures for processing data and judgments to assist a manager in his decision malking. •and proposed that models, to be useful to managers, should be "simple, robust, easy lo control, adaptive, complere on important issues, and easy to communicate with" (Little 1970, B-469, B483). John's insight was that for managers to use a model, they musl understand th• model well enough that they could control it. His Iheme was: ·1 daim that the model builder should try to design his models to be given away. In other words, as much as possible, the models should become the property of the manager, not the technical people•

CHAPTER. 36: IOI IND. C. LITTLE 669

(Little 1970, B-483). The decision calculus paper was cited as one of the ten most influential papers published in the first so rears of the journal Mcmagemc11t Science.

John demonstrated the relevance of the decision calculus by applying it to the complex problem of selecting the entire marketing mix. He espoused eclectic calibration. Some submodels, like manufacturer advertising and its effect on brand share, are almost sure to include time Jags and be dynamic. Others, like S<'3Sonality and trend, may be straightforward and standard. Still others, like coupons, premiums, and production capacity constraints might be handled by simple indices based on data anal)'sis or the product manager's prior experience. The resulting model-ADBUOG (AdYertising Budget)-is given in Little (1970). This model was later expanded into BRANOAID, which is a more complete on-line marketillg-mix model that provides AID for the BRAND manager by permitting the evaluation of new strategies with respect to price, advertising. promotion, and related variables (Little 1975a, b). The latter paper describes a case study for a well-established brand of packaged goods sold ihrough grocery stores.

Ttt1! MARl(llTlNG DATA EXJ>LOS(ON

John, in his paper, 'Aggregate ad\•ertising models: The state of the art,' (Little 1979), summarized and critiqued the previous decade's modeling knowledge a.nd advances in modeling advertising phenomena. After posing a set of modeling questions. he r~iewed the published empirical data and studies that bore on them. He then listed five phenomena that a dynamic model of advertising response should, at a minimum, be able to incorporate: assist annual budget setting, geographic a1location of fundc.;, allocation over time, and illcorporate media and copy effects.

One of John's concerns was that available data to test and calibrate such models were aggregate in nature, for example, historical time series at a national or market level. He observed (Little 1979, 629): 'Although many models have been built, they frequently contradict each other and considerable doubt exists as to which models best represent advertising processes .... Future work must join better models with more powerful calibration methods.' Central to this objective was the need for accurate data at the point-of-sale (local) level. John noted that such a data revolution was on its way (Little 1979, 663).

670 PROfllES IN OPERATI ON~ R£~~ARCH

Products had begun to be labeled •-'ith computer readable Universal Product Codes (t;PC), supermarket scanners were being installed that could read such codes, and computer technology was becoming distributed-no longer just mainframes-to collect, organize, and nnal)'te those dula. The marketing field would soon be inundated with data.

To addres.' the new issues in using such data, John and Pe1er Guadagni, one of his master students, built a disaggregated model- a logll model of brand choice calibrated on scanner dala- that predicted actions at the level or the indn'idual consumer maldng indi\idual purchase. (GuadllgJli and Llnle 1983). A novel aspect of the model was that it included what John termed a loyalty variable; an exponentially smoothed history of past

purchases treated as 0- 1 \'ariables and, thus, a measure of the cusiomer's past propensity to purchase the product, weighted most for recent purchases. This paper is one of the most dted papers In Marketing Science and has been republ.ishcd as one of that journal's eight classic papers. The logit model has heen Improved, reanalyzed, expanded, kicked, and modifled. New phenomena have been added and new data have been analrted. llui the ba•ic slructure (and the power of the loyalty variable) remai.n. An entire generation or marketing science academics and students have been influenced by the original and extended UPC logit models.

The logit models are powerful, but could be intimidating to mangers who, according to John's deci!.ion calculus theme, should be able to understand the model well enough that Lhey could control it. Managers wanlcd answers in a form they could digest. More importantly. computer technology had gotten to the polnl where the logit models could work behind Lite scenes to create automated reports in the form that managers could use. This thinklng led to a decision support (expert) system termed CoverStory that was developed for Ocea11 Spray Cranberries, a fruit-processing cooperative. Oczln Spray track> •al<> and assesses the effecth·eness of its marketing program using large data bases coUce1cd through bar-code scanners in supermarkets (Schmitz et al. 1990).

For a brand manager, CoverStory rapidly and automatically computes and swnmari'es a large amount of output generated by the system's models. The output-structured as a memorandum to the manager- includes a single page of charts and a series of descriptive lines customized for the markets in which the brand competes, showing performance \iS-a-\'iS competitors brands. The number or brands, individual products, and regions make it infeasible to do such an analysis

CHArTER 36: IOHN D. C. UTILE 671

manually. Modem computers, artificial intelligence, and advanced marketing scienc. models fom1 the CovcrStory system-thq· are combined in such a way as to have a direct, po•itive impact on marketing practices, as weU as managerial efficiency ruid effectiveness. John had come a long way from Whirlwind.

EoUCA 1'0R, WDER, E.l."TREPREl'EUR, AND SERVIC6

John is an innovative and demted educator across all programs of the university und•rgraduate, !I.IBA. and Ph.D. Since 1990, he has bttn chair of the Undergraduate Program Committee of the !I.UT Sloan School. As such, he is involved in policy matters. but he always has a group of undergraduate advisees. !\'UT undergraduates who major at MIT Sloan receive an S,B, degree in Management Science, which John calls an MIT-style busln_.s degree (Little 2008),

From Lhe time hedevdopcd a course on OR in marketing at Case, John bas bttn interested in teaching master students how to solve marketing science problems. At MIT, he developed MIT's first course in marketing model<- • course that was a staple fixture in the marketing group untU marl:cting model$ ultimately invaded almost all marketing courses. In the 1970s. he pioneered a new specialty program at the MIT Sloan School called Fast Track. John would read all the files for admitted students and, if they had very strong quantitative skills, he would invite them to join the Fast Track program, He found that the students thrived in the challenging advanct-d courses in mathematical pro.gnurnning, information technology. and statistics. John has serwd MIT in many capacities. At MIT, he was director of the Operations Research C'..entcr from 1969 to 1975, succeeding Philip Mon;.,. For the MIT Sloan School, be headed the marketing group and eve11tually the Management Science Area (MSA) from 1972 to 1982. During this period, he was instrumental in making

A l liOMl. vm1i 1 D.C.t.

Johri ofttn ln,1tcd !lluckJ'l' 10 hi' ~ for .o..Nl tuncrions ""'' osuolJy tnduded •q1ud 1..ung. A spooal tun< ...., T~UlA 0.J ~ John •IXllJ tn\it.e foreign studtnu ind that Eam.tlic. foe- d&nner at hi;; boox in t....na.irl John Lso ~e U a sinctJCeto inrte new &cu:t) to ~ann1.dcc1 du.tlng Uie hl'rU'nU 10 er1ioy L1t 1W.J 11nd bit tXpNtd to Ntw Cngl.ind culture. A ~ll'f \n John'• Li111t c1tb1n and 6shing for bluefish olt Miac:ontCI Rip h.avt pR)vultd partinllarl)' vi ... ld nH?mori« (vr n>any fohn lm:e.<i 5cafood and clainl'( th•t "anyth.iiJg from the sea "'·as good ti> e.11 urn ii pl'U\-cn otbcrw».e • Se3 urclt.ln roe pb1.a lj a 1.Jttte •r•<i.•ltr (utd< 2008).

672 PROflLFS 1:-1 OPERAllO'lS RESEARCH

the MSA cohesive and interdisciplinary. In 1982. John was asked Lo work his magic again-the Behavioral and Policy Science Arca (BPS) at MIT Sloan was formed after a major reorganu.ation. It was not a cohesive group and, surprisingly, did not include anyone who might be labeled either an o~rations researcher or management scientist It was primarily a collection of fucuh)• from lhc less quantiltllive fields of organizational studies, research and development management, human relations, and strategy. John led the group for 6 years and his legacy was the e<tablishmenl of a sound foundation for the area and a potent BPS faculty. In 1989, John was appointed an MIT lnstirutt Professor-a special rank and honor reserved for a very few faculty al lhe universil)'. In this capacity, John has undertaken some sensitive and important MIT-wide projects. He reporL• directly to the Provost.

JOHN'S PA ~llLY John's wUr .inJ former fellow rh>'lta gradualt 'tb\kr.:t, a.my. ~ an lmptCSSJ\e

W.~ Ill htt ""-n nP,L F0< hn PhD. ih...J. sh< •cud...! 11\e di.,_ b<hmor of domain ~'llla .. '-""'-"" ritultt"-thc fin i~ her thaas before John 6nhhtd htt and ruWbhcd • paf""' oo i1 m the JJftrrc.aJ Rh;r-. ti. L111le J 95S). She did n~ pursue • full- time caron, l)('lng lhc one who agrted to stay al home u they raised 1nt1r chddrm. John N. Oack). Sllrnh A., Thoma~ D. C. (Tom), and Rud 0. Betty becamt a tta ... ha'.s aide during the 1lnl( her chi!drtn ~·e:l'(I In pubtk school, ia11d later, in I 9fl5 at Ajt:t 58, ha\ing become UUftrstcd ln Nantuckt hl4-1\lf)' .inJ its rtathc-Nmncan archaeok>g)" rccei\'Ul an \1 A m Anthropology, \ltath COl'ICC1'tnltioOS in tt~ and !to&og)·. from the Uni\'CTSit}' of ~iaq,a,,:huiefu; Am.\cn1. lktly cuntmucd Mr t.11:h11CO:op:.l ~r!:h :aod "''nttngs for m&n)' mort )"tan. Alter~ 2·)'e&r Nttk "·1th (.illl<1.-lt'.f", i...1':- cbrd i.n l:OOJ.

Their childrtll OOllld OOC ~.ape \heir r3rt1u~· );OC'Dtifi..:. tngin«ring, and L'fUtepN>neudal inOuences.. Jade Unle gradu.tlcd frofn ~flT tn ela.-irical cnglnt't'ring and re:cth'td an '-tS. ln l:il.o:uic:al FJlgJnt.Ulng from Stan(Otd Unh"<!Sily. In 19tW be co-foundtd M.1th\\'Ofk.s, •

lc>d;ng de.'"""' ol uduUcal """l'llllng '°"""' "" engjn«n and "'""""' "' indusu), r-•· ..nd ocl>aoon. Sanh Ut<L p-admced - ...Woo! in ph)"" and lh<n jOincd m. .\!IT "°""' H"" °""'°Snl-hl: in ...... Ph.D. rrosnm. ~llng"' ~- •ith • ~ tba:t lnvoh'td nlakatlg ~ in the detp-octan 11.lbn'ltl'll-'e A./..'" and coll«ttng data on h)·drothem)al vcn1-1n the Pad&. ·r<1n1 Unit graduated frM\ Rt~acr l'olrlcehnic Jnsti1ute in biologKal englJtttrlng. and atrn"-1 a P.h.O. in o.'n)pulll"r tn¢flmrulg fm1n S}'r.teust Unl\'eNity. He: b n<.>w a profes6()( In lhe Dc:panmtnt (If Computer F.ngir'itl"r'IAg. ~on UnL.-.rJllY SdlOOI of Enginem"l Will> • fi>nner <1ud<n1 ht co-fcwia.d • -d>-ue and '""'"king &nn. MolmUr, Inc.. ~l\Jdl ch<y tu.•~ told. Jt"'1 U."°' "'° • B.A in rh>"'-' 1i<>n1 (ohru Hori,."' l:nl>-cy ...S tn S.M • ., ~ ~ &uln \tn Ali« ~,,rklngfu< many)'tAn for !<W cmrgy~ ho hclr<d l<>1md Gn=Ray. • ool&r ""'1ll startup tha1 ~ dc\.dorinN ?abor saV1ng tt<hnolog.)' tha1 simpllllb construction 11-d ln~taDation of solar modWe$ for delivering cloclrlcit)' lUrC!C'!ly into IH\fn( 11ppbanc~ and Ugtulng.

As a gnu'Mt.h1lher, lohn anflfff1 t() tigtll grand.:-h1ldrtn

CHAPTER 36: )OHN [). C. LITTLE 673

John's interest in modeling real-world probkms led him, in 1967, to co-found Management Decision Systems. Inc. (MDS). a company 1A1hose objective \•:as to create and commercialize marketing models and marketing decision -support software. MDS grew to over 200 employees. In t985, MOS merged with Information Resources. Inc. (IRI) with John serving on the llU board until 2003. John continued his entrepreneurial activities by investing and serving on the board of a start-up company, lnSitc Marketing Technology. lnSite provided a new class of e-business applications that identify the buying style of the customer and the selling style o f the company, and dynamically integrate them to help the customer through the buying process. In 2000, lnSite merged with the Kana Corporation. a multichannel c.usto1ner service?- soft\.;are con1pany that integrates telephone, en1ail, Web chat, and collaboration channels with knowledge management capabilities in a unified application.

John O. C. UttJc'• t'am.ily. Na11tlldr.et bbind, 51.1mmcr'200l (John. Bmy. and thdr childttn In bold fa«)

&ck row (left 10 right): JOHN, RU~ Sara, ~tax, TOM. Nancy, JACK

Fronl row Oeft co rigtit): BETTY. Ki1thy. Avcsy, iSlac, SARAH. Cora.. Doug. Emil}'. ~n. Erica

TM- families or Jdu\ at1d Bcufs children an.:: JACK t.iulc and N;IJK)' V.'itlcnbcrgffirica and Emity Link: SARAH Little :ind UQUg nc~l\ICor:i :ind l$ii'1C folcl"$ho TOM Lildc and Sari! Btown/~{ax and Stephanie Liu le {Ste:pNnk nor born untiJ 2003)~ RUEL and Kaib}' Little/Dyson and Avety Little.

674 rROFll rs IN 0PFRATION5 RESEARCH

John served as president of ORSA in 1979 and president of TIM~ m 1984- 1985. During his ORSA term of office, he and Fronk Bass, 1hen president of TIMS. persuaded the two societies to found the joint journal Market/11g Scienct. When the two societies merged in 1995 10 form IKFOR..\.IS, he was elected its first president (he chaired the comm illee whose efforts led lo the merger).

H ONORS AND A \'\o'AA.OS

John has b<.>en recogniud for his innovative and seminal research in marketing b)' the Paul D. Converse Award, a lifetime achicvcmcnl award gi\•en by the American Marketing Association (AMA) (1992): the AMA Charles Parlin Aw:ird for contributions to the practi~ of marketing r~arch (1979), and Mrrs Buck Wea,•er Award for oul>lllnding contri· butions to ~ng (2003). I le was ela.ted to the Nol lonalAca&:my of Engineering for outstanding contri­butions to operat ion al systems engit'lccring, including research, education, applica-tions in industry, and leadership (1989). He has receivtd theORSA's George E. Kimball Medal for recognition of distinguished service to the society and profession of OR (1987),

JOHN D.C. LlTIU A WARD

John pr-itSmhnc plaque. 10 I.he winMN o< t.bc 1001 John D. C. Litde /\ward 8l lhe ZOOS Mafb:lin.g Scltncie Confctn1« In Vanoou~r. She>"''" (Id\ 10 right)~ Jahn, P. K. Kanman. and Brian T. R!Mchfotd {co-author~ Lan Luo. ""ti not •bk to .......s).

and the Distinguished Service Me<lal from TIMS. He ~a meml><'r of the International Federation of Operational Research Societies' (IFORS) Operational Resea rch Hall of Fame (Larson 2004), and a fellow of INFORMS and of the INFORMS Society of Marketing Science (ISMS). )oho has receh«d honorary degrees from the Univen.ity of London; University of Liege, Belgium: and Facultcs Universitaircs Catholiques de

CHAPTER 36: JOHN D. C. LITIL~ 675

Mons, Belbtjum. He has been honored by having a most prestigious annual award in markeUng science named for him-the John D. C. Little Award­given annually by ISMS for tlie b.:st marketing paper published in an INFORMS journals (including Marketing Science and Mam1gement Science).

ACKNOWLEDGMENTS

The authors, with appreciation, wish to note the following sources of material: ' !FORS' operational research hall of fame: John D. C. little; I.arson (2004): and an unpublished presentation by John at his 80th birthday celebration. We also thank John Little for adding many historical facts and insights to our su11unary of his life and W(>rk.

REFERE."CE.~

8<ilman RU (1957) Dynamic programming. Princeton Unimsil)' Press, Princeton, NJ <iartner N, Kelson M, Little JDC (198 1) MAXBAND: a program for setting signals on

arteries and triangular oct\\'Orks. Transport Re$ Rec 795:40-46 Guadagni I', Ll1tle JDC ( 1983) A logit modeJ of brand choice calibratt<l on scanner

dam. Market Sci 2(3):203- 238

Larson R (2001) !FORS' operallonal research hall of fame: john D. C. Little. Int Trans Oper Res l 1(3):361-364

little E (1955) T>)'Tlan1ic behavior of dornain "-alls in barium titanafe. Phys Rc:v 98(4):978-984

Little JJJC (1955) Use of storoge water in ,~ hydr<)electric S)'Stem. Oper Res 3(2):187-197

Lillie JDC ( 196la) A proof for the queuing formula: L = ).W. Oper Res 9(3):383-401

Little JDC ( l96 i b) App(OXiJnalc expected delays for several 1naneuvers by a dri\'er in Poi~<on traffic. Oper Res 9(1):39-52

Little JDC {l966a) The $)'J\Chronlzation of traffic. signals b)1 mL'Cedwinlegcr lineay programming. Oper Res 14{4):568-594

l ittle JDC (1966b) A modd of adaptive control of promotional spending. Oper R<:> 11(6): 1075- 1097

Liule JDC (1970) lvlas~agc:rs and models: the concept of a decision calcu1us. Manage Sci t6(8):B466-485

Lillie JDC {1975a) llRANDAID: a mark.cting-mix model. Part l: structure. Oper Res 23(4):628-655

Little JDC (1975b) BRANDA.ID: parl 2: itnplem_cntation. ca1ibration, and c-.i.sc: study. Oper Res 23(4):656-673

676 PRO~ll ES 1:-101'£RATJONS RESEARCH

Litdc JOC (J9n) Optimal 1cnp1i\,. control: • multk .. nat< model for m•rktting applocotioos. !UF. Transact Automar CA>ntr 22(2):187-195

Little JDC ( 1979) Aggregate a<lvcrtisfng models: 1hc state of' lhe arL OP<'r Rco;

27(4):62~7

U11ic JDC (2002) Philip M. Mor., and 1he beginning>. Oper Res S-0(1):116 149

Little JDC (2007) Life as the f'irsl OR doGtoral $tudent - and other prehistoric tales.. In: J.orsoo I (cd) The operations re«orch center ot MJT. 11'TORMS Topics in Opcrat"'ns R<scarch Series, Hano>'<r. MD

Little JDC (2008) Peuonal communication

Little JDC. Cohen S (1982) Tbe MAX!IAND program for arterial •lgnal liming plaru;. Public Road• 46(2):61 ~

Litdc JDC. Gravn S (2008) l.11de's law. In: Chhajcd D, Lowe T (cds) Building intuition: insights fro111 b;isic openuions manag(nleJH modcls an<l principles. Springer, New York, NY. pp 8 1-100

Uttle JDC. Loduh L (1969) A media pli.nning calculu'- Oper Res 17(1),1-JS

Uttle JOC, Murty K, S-.·<enC)' D, Karel C (1963) An algorithm for the traveling salc•man problem. Oper Re.< 11 (6):972-989

Mo'l!•n J. Little JDC (1964) Synchronl..ting traflk signals for m.uimal bondwi<lth. Oper Res 12(6):896-912

1'.1orse P ( 1958) Queu~. inventories. and 1nainlcnance. \Viley, Ne"' York. NY Mor>e 1.1, Kimball G ( 195 i) Methods or op<ratlons resean:h. Wiley, ~•w York. NY

Schmitz J, Arrrutrnng G, Little JDC (1990) CoverS1ory-autommd oe..~ f1J1dillg m mmchng. lnt<rfoccs 20(6):29-38

37 EVELYN MARTIN LANSDOWNE

BEALE

)OHN A. T OMLIN

Eva~ MARTIS l.A'<soows£ Biw.t, always known as Martin to his friends and colleagues, was a giant of the operations research (OR) proression, especially in the U.K, and an outstanding contributor

to all asp«ts of mathematical programming {MP). He not only made major contributions to theory and algorithms, but to the development of pr~ctical mathematical-programming computer systems. l lis pioneering work oo developing algorithm• for real-world problems, and overseeing their implementation in large-scale commercial software systems, made a major impact on the practice of OR at the tlme and left a lasting imprint.

He was a founding member and chaim1an of the Mothematlcal Programming Society. Martin was elected a Fellow of the Royal Society and S<:tved on its Council He wa.s awarded the Sih·er Medal of the Operational Research Society of Great Brllain. He is also remembered as an outstanding contributor to the field of applied statistics, a wonderful coUeague, and an inspiring teachtr.

Martin Beale was born on September 8, 1928, at Stanwell Moor in Middlesex, the elder child of Evelyn Stewnrt Lansdowne Bea.le and Muriel Rebecca (Slade). His father "'~' a S<:nior physicist and research engineer at the research station of the Anglo-Persian Oil Company at Sunbury, but his work took the family to Persia for the year 1932, about 1 year after the

A.A. .~ SJ. Gus (td..).1'1of.les "' 0,.-i:>ns Rts<otrh. lnkmalioml S<rb in 677 Op<ratioi1> R.scard\ & Managem<nt Science 147, DOl lO.t007/978-l ·4419-621l1-2_.l7, C Springer Scicnce-BusJne~~ t\'1edia, Ll.C 201 1

678 l'ROFILES IN OPFHATIONS RF~EARCH

b1nh of Martin's brother Julian. On their return, the family moved 10

Chelsea, keeping a house in Middlesex. Martin then suffered the first of many bouLS of ill-health that interrupted his early rormal education. It Wl1' round thal he had contracted malaria in Persia, so he did not starl al the Montessori School in London until 1934, attending it for 2 year$. His father left the oil company to found a private consullancy firm for Industry with R. Denman and worked brilliantly on a wide range of engineering problems.

Martin showed an early ap titude for mathemali~s at school but, at age 8, also studied Latin with his mother, anticipating his entry into the more convemional t?ducational system. He was enrolled at St. Aubyn's preparatory school (Rottingdean, Sussex) in l 937, but he was at home throughout 1939-1940 due to another occurrence of ill health. This home was now above Treyarnon Bay; the Beales had become captivated by thi< pan of Cornwall and had built Windhovec House there. Manin studied al home with Julian and some other children during that )'tar, and this small school continued throughout the war, although Martin returned 10 St. Aubyn's in 1940. He then aimed for a scholarship to Winchester in 1941, but ill health struck again; measles prevented him rrom traveling for the examinalion. After a funher year al St. Aubyn's, his ma1hematics master, the late E. Webber, who coached him for the .cholarship, said 10 his wife: "I cannot teach any more mathematics 10

Manin Beale, I have taught him all I know" (Dantzig and Tomlin, 1987, 117- 118). Martin was at Winchester from 1942 to 1946, ha\'ing gained the second scholarship in 1942. Although he was the joint winner of the school's Richardson prize for mathematics, he was advised not to try lo go from Winchc.'stcr to Trinity College, Cambridge (as his father did), because the competition might be too st rong. Characteristically, Martin rejected this advice and In due course went to Trinity with a scholarship in 1946.

C HAPTER 37: EVE LYN MARTIN l..A1'SDOWN E BEALE 679

While at Cambridge, Marlin's interest in mathematics seems to have been nearly overshadowed by his absorption in bridge. He (and his brother Julian) played for Cambridge against Oxford, and Martin became fuscinated with a new bidding system about which he was planning to write a book. lnten•iewing Beale, his high])' respected prospective employer, Steven Vajda of the Admiralty Research Laboratory (ARL). asked him if he 'would like to be told about the work he would be expected to do there. However, he did nol; nothing was allowed to dis-tract him from his writing a book on Bridge Bidding" (Dantzig and Tomlin 1987, 118). Despite this, a~er Martin graduated in 1949 and gained his diploma in mathematical statistics in 1950, he joined ARL working under Vajda. The bridge book never materialized.

AT THE ADMIRALTY RBSEARCIJ WORATORY

T he particular projects that Martin worked on for A RL do not seem to be widely known. 'Ibey apparently included work on direction finding as well as other unpublished work. What has become widely kno"~l is that Steven Vajda introduced Martin to the field of MP. He soon outstripped his mentor. As Vajda wrote: 'l am sometimes praised for having introduced Martin to linear programming [l.P). l did and I am glad of it. But there is no meril in having done it. I have introduced LP to others as well. but they did not nurture the seed the same way as Martin has done· (Dantzig and Tomlin 1987, l 18).

Martin's first research paper, "An .• a!ternative method for linear progranuning• (Beale 1954), described an independently discovered dual simplex method for solving LP problems. 'I11is was soon followed by one of his best-known early papers "On mini.miting a •onvex funclion subject to linear inequalities" (Beale 1955). This important paper describes not only \vhat came to be known as the Beale-Tucker representation of a linear program and one of the first quadnitic programming algorithms, but also one of the flrst treatmems of stochastic programming. It is interesting to obsen•e that this latter work was independently carried oul in parallel "~th a very similar approach by George Dantzig ( 1955). which of course Marlin acknowledged. Martin went on to publish many papers on quadratic, nonlinear, aod stochastic programming. further papers on cycling in the dual simplex method, the convex-cost transportation problem, and

680 PROFJ L[S IN 01'f,llATIONS RESEARCH

quadratic programming (Beale 1959) as well as some others on applications and statistical subjects appeared while Martin was at ARL.

On July I, 1953, Martin married Violette Elizabeth (lletty) Anne Le\'is at St Mary's Church, Hampton. They had met in time to celebrate his 22nd birthday together; she was a scientific assistant in the A.RL Mathematics Group (he had spent his 21st birthday playing bridge). Betty soon became part of the Beale family, visiting Windhover se\'eral limes before their marriage and enjoying cycling, walking, and playing bridge with Martin. Their first home was a small terrace house at Strawberrv Hill, Twickenham, within cycling distance of ARL, where Betty continued working umil a few weeks before the birth of their first son, Nicholas, in Febrnary 1955. Their daughter, Rachel, was born in May 1957, to be followed by a second son, Marcus.

The Beale family spent most of 1958 in the U.S., the majority of the tiJnc at Princeton, where Martin is reported t<> have explained to Ralph Gomory that integer programming was "impos..•ib\e• (Gomory 2602, 79). It was one of the bv times that Marlin would be qnitc wrong, and he would spend much tin1e working in that field later in his career. On this trip, he also traveled to California and visited the RAND Corporation. George Dantz,ig noted: 1 don't recaU meeting him in person until 1958 when he, in his unasswning way, dropped into my oftke at RAND Corporation in Santa Monica, California. Still in his twenties, Beale had already 1Hitten three important papers on linear programming. I was struck by his youthJi.tl enthusiasm, a characteristic that stayed with him always. Martin, I believe, made a special detour to the West Coast on bis way from England lo Princeton to drop in, but he never said so. I suspect he was curious to see what Full<erson, Johnson, Shapley, Bellman, Wolfe and I were up to• (Dantzig and Tomlin 1987, 118).

The Beales returned to England, and Martin remained with ARL until 1961. During this time, he continued to display some of the eccenlricilies which were an integral part of his cliaracter. Ken Bowen (1986, 8-9) ,_,·or-= ·1 remember, and they will never forge4 his performance for a U.S.A.-Canadian group of analysts in Room 39, in the Admiralty. With an array of tabulations and diagrams on a long table, he started by kneeling on a chair and finished on the table, wandering about the data on hands and knees.' However, as Vajda tells us, · He was highly appreciated at ARL. When members had to be assessed, it might have been asked: 'Is (s)he as good as Beale?' Few were' (Dantzig and Tomlin 1987, I 19).

CHAPTER 37: f.VF.~YN 1\.\ARTIN LANSDOWNE BEALE 681

CoKSWtL~G AT C-E-1-R, LTD.

A.S. (Sandy) Douglas and lhe distinguished statistician Maurice (later Sir Maurice) Kendall founded the Corporation for Economic and industrial Research (CEIR), U.K., in 1'960 as a subsidiary of the Washington DC consulting services company C-E-1-R, Inc. Martin joined the young compan)' as employee number 29 in 1961. Outstanding as his work at the Admiralty had been, CEIR provided the framework in which Martin really made his mark as the great pioneer of real-world MP. He consulted on all manner of applications, pursued his research on computational MP, and saw it applied. Through his worik with the LP/90/94 computer-based software team (and, hence, with CEIR in the U.S.), he established many of the procedures and practices used in .MP computer systems to this day. Eli Hellerman (of the U.S. company) recalled: "His insight into how algorithms COLtld be implemented on a computer was phenomenal. He was the dynamo behind the extensions to the LP/90/94 System in the areas of separable programming. mixed integer, Dantzig-Wolfe decomposition, and a bost of other practical algorithms" (Dantzig and Tomlin 1987, ll9).

As Philip Wolfe observed:

... ln his career lvf;,;rtin had a tmique role in the field Along with. baste research, thc:n: is difficult and important \\~ork to be done in app1)'ing rese;lrch coocepls tu Lhe real \\·orld. Por us \lfho "'·ork in univerSities and research centers. the prospect that our rcst:.'lrch '~Ube applied in pral.'.tice ls a gre;:it stimuJus; and a fl!\\· of us participate aJ times in practical developntents. On the 1tppli01tion side there are lndivldual$ or great ability in lndustI)' who deserve much credit for their \.;ork and leadership in the use of mathematical progtatnrning in rcal~\vorld ;:ippli~tions. ln the primary ranks in the fldd it was only l\1artin \.\'hO truly and con1plete]y bridged both: scholarly research and practical applications. It \\'<LS only lic~·bo both directed the Jnathe1nacical progr;,imming work of an lmportant cOn$ulLing and service firm and at the same time contrib\1ted outstandiJ1g basic research (Danti.ig and To1nlin 1987, 119).

In the early to mid-1960s, Martin was the first to make three powerful extensions of LP into pr:actical tools. These were nonlinear pr0b'11llllming (via separable programming), the Dantzig-Wolfe decomposition method, and integer programming (via branch and bound). AU of tbese were implemented under Martin's direction as

682 PROFI LES IN OPlRATIONS RES EARCH

extensions of the CE! R LP/90194 system, then the most powerful of its day, but whose limitatiolls were severe by today's standards. Foremost amoog these were the limit of 1024 constraints (illduding simple upper bounds!).

Philip Hughes ( 1988), in his memoir about Martin, described how the standard LP/90194 system was illadequale for solution of an oil-field model, which was both large-thus requiring decomposition-and involved una,·oidable nonlinearities, whid1 could only be handled by separ•ble programming. II tumcd out to be c!Jfficult to make decomposition work in practice, but with the implementation of several new features, Martin and his colleagues (in 1965) succeeded in solving this problem (Beale et al. I 965a).

Separable programming was to be a major field of development and publication by Martin, and various refinements, such as automatic illterpolatioll, were to be features of the improved LP/90/94. He had quite definite ideas on the way it should be do!le. Eli Hellerman remembered:

... J \'/aS assigned the task of \'frilin,g the User>s Manual fot the CElR E.-<tended LP/90 Sptem. One of the new algorithms on th~ syswru was Separable Prograoun.ing and J tried to find a shnple and instructive model to illustrate its use .... \\'hen Reale revi~·OO the first draft. he inlmcdiatd)' cQmmunicatcd to me that (n1y example} i,v-as not ;.1 proper modeJ and indeed iL ·\.\·a.~

uosatJsfilctory. 1 \\'tote back tu ask him \\rhether there ,.,.as anythi11g incorrect in the model and v.·ould he please send enc a sintpler 111odel if he had one.

He responded. by repealing the <:harg.es he n1ade in the first communication. I again '\'TOie to hitn for eolig.htenml'nl. It looked very 1nuc.J1 like an hnpasse until one day. quite unexpectedt}'. ?\1artin strode into my office (he had just arrived fro1n London). put do,,r:n ltis briefcase and \vithout e-.·en saying "heUo" n1a.ri,;hed up to the blackOOac:d ru~d ~aid, ·No'''• about this Separable thing, here is ho\v it should be done'" (Dantzig and Tomlin 1987. 120- 121).

During this same period, .Martin oversaw the implementation of the firs! commercially successful mixed integer programming (MIP) code (Beale and Small 1965). Integer programming turned out to be possible, but the preferred method in practice proved to be branch and bound, not cutting planes, and this was implemented in the LP/90194 system; the method was a little diJTerent from that described by l<>nd and Doig ( 1960) using a binat/' tree and depth first Oast in, first out, or UFO) search. Tllis code was able to solve substantial MIP problems with a few dozen integer variables- a significant practical advance.

CllAPTER 37: EVELYN MARTIN LANSDOWN E BEALE 6&3

Martin's contributions were by no means limited to algorithm devel(lpment and system implementation. He 1A'aS perhaps even more active in model formulation and consulting on client problems. He developed a systematic method of apprc:>aching new applications of MP and devoled considerable attention to the apparently mundane tasks of matri.' generation and report writing-essential features of applied work LP/ 90/94 used SHARE standard

MARTIN ON PROGRAMMING

1. Undt:stand the environment you are modeJjng.

2. Logically ruld death' naa-it and Order variabJes.

3. Present back to the clit'nt his input data clearly laJd ou1.

4 . ProdU«' some rest1!1$ quickly.

5 . Do not get s.la\·ishly tied IQ a soitW<l.tt P>Ckage,

t6. Alw;)ys keep sight o( I.he nwnbers.

input where the variables and (Hughes 1988, 7)

constraints had ~i,~-chara«er names, which could be used to encode the meaning of these entities. Since problems had grown to the size where hand-preparation of this input was out of the question, matrix generators were required to generate the input to the LP code. Martin was emphatic about the need to ""·ite these matrix gener•tors (in Fortran) in a systematic way with naming conventions, not just for the LP variables ;utd constraints, but for the arrays and indices in the code itself. His paper presented at the 1%7 Princeton Mathematical Programming Symposium (Be-ale 19703) dealt with some of these Lo;sues at length and was unique in those proceedings for doing so.

Also in 1967, Martin's best-known statistical paper "The discarding of variables in multi -variate analysis• (with M. G. Kendall and D. W. Mann) was published. Aboout 20% of Martin's published work was in statistics, and, thus, mostly beyond the scope of this profile, but this and several other papers wer·e in the related field of multiple regression. He maintained a parallel career as a respected statistician throughout his life.

Martin's research and related developments in MP through 1967 (including quadratic programming, separable programming, de­composition, and partitioning) are given in a survey article "Numerical

684 PROFILES IN 0PF.ltATIONS R!SCARCI I

metl1ods" (Beale 1967, 133-206), Chapter VII i11 the book Nonlinear Programming, edited by J. Abadie (1967).

His eccentricities continued, and even flourished, in the CElR envi­ronment. Sandy Douglas (1986, 12.0) recalled: 'He never worried what people might think of him. If it improved his thought processes he would Ue down and raise a leg or climb on tine table or stuff his handkerchief in his mouth. (His colleague) Peter Windley did once comment to me that he 'wished Martin would take his handkerchief out of h.is mouth when dropping one of his pearls of wisdom' - but it was said in amusement rather than annoyance. Indeed no one minded what he did, since he always came up with useful and perceptive remarks, from whatever position and through whatever obstructions they were delivered!"

CoNSULTINC AT ScrcoN, LTD.

In the mid 1960s, British Petroleum acquired CElR (U.K.) with the parent U.S. company acquired by Cc.mtrQ! Pata Corpora!iQn in 1968. Not wishing to have its name associated with any particular hardware vendor, the U.K. company changed it• name to Scientific Control Systems, Ltd., eventually abbreviated to Scicon, Ltd. This had little immediate impact on :'-4artin's work, but did coincide with the phasing out of the IBM 7090/94 computer and the Extended LP/90/94 software system. The ultimate capabilities of LP/90/94 are nice!)' summed up in Martin's tlrst book, Matliematical Programmi11g in Practice (1968).

The new system, begun from scratch when Martin called his progran1mer into his office to \\rrite 1ht first subroutine, 'vas to he named UMPIRE (Universal Mathematical Progranuniug System Incorporating Refinements and Extensions) and WOldd include many new ideas not in LP/90/94 (and omit some that were). It was written bya team of four or five people which included at various times the present author, Gautam Mitra, and crucially, John Forrest, who had irecently returned from a year studying in Berkeley under Dantzig (on a NATO scholarship arranged b)' Martin). It was during this exciting period that Martin made the remark that he ·woLtld rather work with today's a.lgorithms on )'CSterday's computers than on today's computers witl1 yesterday's algorithms• (Tomlin 1989, 159), an indication of the importance he placed on algorithmic jnnovation and in1provernent.

CHAPTER 37: EVELYN MARTIN LANSDOWNE BEALE 685

A notable feature of UlvfPIRE was the inclusion nol only of simple upper bounds, but generalired upper bounds or GUB (Dantzig and Van Slyke I %7). Martin was very enthusiastic about CUB, since it provided a way of extending the solvable size of many models, and main memory was still very limited, even on the new L'NIVAC 1108, for which UJl;IPIRE was designed. GUB also received considerable anention in some of the many survey papers he was a.1ked to write ( &-.tle l970b}. Many of these papers were presented at conferences and S)~Jl posia, where Martin was always to be seen in his uniform of suit, tie, and black shiny shoes and socks. Even in warm sunny locations, such as the south of France, he was always to be seen in this uniform, though it is reported th.at he was once seen on a French nude beach wearing only the socks and shiny black shoes. One can only imagine.

GI.JR infl uenced the UMPIRE system in other ways. It made the concept of sets of ''ariablcs attractive, which in tum led to special ordered sets (Beale and Tomlin 1970) which enabled non-convex programming without resort 10 integer variables (Fc>rrest and Tomlin 2007). This was to be a rich source of ne'" developn1ents in non-convex and nonlinear programming throughout the rest of Beale's career.

MARTIN ON MODELING ~It is useful to distinguish bctwttn cstablishcd and new mathematical prosram.ming

models. An .cstabli~ed model is run from tin11eto time ~itll updated data a~ part of some operarionat dtclsiQn·maJting coutine. The purpose ls th.en to suggest a sptd.fk course of acuon 10 ll)•IJl<ll!lte•nent, inti thesuggcstiou w1ll w.uaUybc aocepted. A ntt'l• ruodel may ilso be ustd ln thls way but iS m<>re often cmplO)·td lo gain greater understanding of the situation. H may be run under a ''ariety of assumptions that lt"ad to different oonclusK1ns. and the model itself ·wiU not Ml88CSI which sct of assun1ptions is most appropriate.

·ourint; i..\e mod<~ dc\'dopmc:'nl and d.ata-galhtring phase we must therefo~ be prcpiu:~ to make nl&n)' optimization calculations which can be shown to management to .stt if the}' arc sensible. If '~·hat the model recon1nlends \$ n0t con~idered $t'll.sjb!e, -we havt: tCI tind 0\11 why ii is not a~pt11btf.\ Nel•her the anal}'S\ ot the Jnin3gershould aocep1 the reco~nd~IJons f'roin tit(' modd unl~ tht)' can be ttplaln~ qu.illt'8lh'd)' as the oatural oonstquencts of tht' phrskal and economic assumptions. \Vt' can paraphrase th~ b)" saying lhat the rcsuh.s should only be KCC)3'tcd if tltty OJre obvious. Tht' reader may think that the nlOdel is then o( JJQ real use! Tb1$.,. lJO\\'e\"el'1 ts not so. because n1311y tblngs are olrtr!Qus once siomeone h\J.S: poi.nted them ou.t ..... hen they \\'t~ not at all obvlow. befoteb•nd" (Beal< 1988, 12).

UMP IRE was also the f!J'st IV.IP system to use the Gaussian, rather than Gauss-Jordan fonn of the product form inverse. The first step in this process was Martin's observation that a block factorization could be used to avoid fill-in of a substantial part of the (sparse) basis, followed b)' the realization

686 l'ROFILES IN OPERATIONS RESEARCH

that this could be even further improved by using Gaussian triangular fac.torization. This wot~d eventually lead to the first practical method of updating triangular factors, with considerable improvements in speed.

Quadratic programming was not implemented in UMPIRE, and its separable progra1runing facilities were less elaborate than those ofLP/90/94, but this was off.<et by the implementation of a new conjugate gradient method for approximation programming to handle large-scale, general nonlinear programs (Beale 1974). An important outcome of this work was a ne'"' \\'<l}' of vie\\1ing nonlinearities in a model. \.Vhereas previous treatments had considered each constraint as consisting of linear temis plus a function of nonlinear variables, Martin considered the whole problem as if it were a linear progrnm where certain of the matri< coefficients, and the right-hand-sides, were not constant> but themselves functions of the nonlinear variables. 'l11is approach often drastically reduced the number of variables which had to be considered as nonlinear and was to prove useful in later, more gene.ral, nonlinear programming systems.

During the same time period, the first matr ix generator generator (MGG) was developed at Scicon. Mar tin had been strongly in favor of using a general purpose language, such as Fortran, for matrix generarion, but MGG, developed primarily by our colleague Peter Alsbury, overcame his objections, and be V.'3S to use it in man)' modeling projects. There were at least two good reasons for this. First, MGG generated an intermediate Fortran program (the MG, or matrix generator), which the developer was free to specialize and modify, if desired. Second, the mathematical, equation-like, model description, later adopted (without acknowledgment) by such systems as G&>IS, AM Pl, and others, greatly speeded up and simplified the modeling process. Once convinced of the value of this approach, Martin jettisoned his previous stance and seems to have never written a Fortran matrix generator again. This was typical of Martin Deale. He had very firm views on the way things shoo.Id be done, but if a colleague could come up v.1th, and justify, a new and better idea, he would readily abandon his own and, what is more, publicly give credit where it was due.

In its tum, UMPIRE and the UNIVAC 1108 wotUd also become obsolete, and a new Mathematical Progr.unming System (MPS), to be named SCICONJC, was again written under Martin's direction, with John Forrest the primary developer. A later version, intended to be machine independent, was known as SCICONTC VJ\'! and was substantially rewritten and extended by R.C (Bob) Daniel.

CHAPTER 37: EVELYN IV\ARTIN LANSDOWNE BEALE 687

SCICONIC did not include GUB, but did carry on with the further development of special ordered sets, first, through Martin's new technique of pseudo-shadow-prices to guide the tree search (Beale and Forrest 1976), interpolation to handle continuous non -convexities, and later linked ordered sets to handle non-separable non-convex non­linearities. Th is continued to be a major theme of his work and is perhaps best represented by one of his last survey papers •integer programming• (Beale 1985a).

Martin continued his development of SCICONlC and its applications with a new generation of young colleagues, who, like earlier ones, benefited from Martin's propensity for teaching. This benefit also extended to his students at Imperial College, London, where he regularly taught on Mondays from 1967 on. He was sometimes jokingly known as the Monday Professor.

O THER P ROFESSIONAL hn'ERESTS

In addition to his demands at Scicon and time spent with his famil)', it is remarkable that Martin found time for a multitude of other interests. His parallel career as a statistician has alread)' been noted, and he was acti\'e in the Royal Statistical Society and the Institute of Statisticians. as well as Treasurer of the Statistical Dinner Club for a good many years.

Martin lle<lle was also a key figure in the foundation and direction of the Mathematical Programming Society. He had been one of the organizers of the 1964 London International Symposium on Mathematical Programming, the fi rst such meeting held oul<ide the U.S. Subsequently, finding a small surplus of fwtds in their treasury, the organizers designated it the International Programming Fund and chose a small international commillee to hold it. 'Dlis was the first step in the identification of MP a.< a professional specialty and eventual!)' led to the formation of the Mathematical Programming Society in 1972.

Martin was the second chairman of the newly formed society, serving from L 974 to 1976. Prior to that, he was asked to join the board of senior editors of the Sociel)'s new journal, Mathematical Programming. He served on the C'.ouncil of the Society from 1982 to 1985 and otherwise on several of its committees.

688 PROl ILES IN O!'FRATIONS RISCAl\CH

Ho.-<oRS "-"'o AWARDS

There is no doubt that the honor of which Martin was most proud was hh election as a Fellow of Lhe Royal Society in 1979. As an ardent conserva1ive. royalisL, and pillar of the e;tablishment, as well as a distinguished scientist, he can only have been delighted.

ln a 1975 letter supporting Martin's nomination to the Royal Society, George Dantzlg wrote:

l rate ll<ale among lh< top '"'"or lltr« people in !he world in lh< field or Opuotio.u Rocarch. He is also weU known among smistidans. He bas done outstanding lhtomial WQr\< on llgonthms for solV111g linear and nonlmear progromming systems. On !he prac1ic31 sldt, he ha. played (and continues to play) a kq1 role in the d~vclopn1c;nl of $Oflware packages.. These \lrC M>phi11rlcnted nunhematica) anJ C:()mputarion:il tools Lhat have n1adc it possible 10 model and optilnolJy solve lnlpormnt c.ornplex Jarge~scalt

plannlni:; problems in national plannh1g und industty.

ln my opinion Martin Beale has one of the tinest 1ninds ln England (and the world) today (l>.Ultzigand Tomlin t987. t25).

His citation read in part: • ... dutinguishtd for his application• of mathematical and statistical technique> to industrial problems, and for his coniributions to the theory of mathematical programming.'

Ma rtin Beale's honors did not stop Lhcre. In 1980, the Operational Research Society of Great Britain awnrded him the Silver Medal, its highest honor. In 1984, he was elected 10 the Council of the Royal Society.

TowAJU> THE E.>m

Martin ~amc seriously ill in lhe 1980s, but was able to attend the Boston Mathematical Programming Symposium in 1985. Bob lla1tcrsley recalled: • ... (in that) year, as always, his interests ranged across the speclrum or linear, mixed integer and non -linear progranuning; from more accurate methods for inversion and updating the Inverse. LO

cut generation and new approache~ to estimation for special ordered seLs' (Danlzig and Tomlin 1987, 121-123). He returne<I to a lifelong

CHAPTER 37: ~VELYN MARTIN LANSDOWNE ~EALE 689

interest-stochastic programming-and his last paper (lleale et al. 1986) dealt in a novel way with the diffkull problem of multi -time-period stochastic programming.

After treatment in 1984, Beale insisted he was on the road to recovery. He declared himself "too busy to die,• and as la1e as November 1985, he wrote that he was "on the mend and very confident that all will be well" (Beale J98Sb). Alas, this was not to be the case.

1\ltartin \Vas active \-V'ith his students and colleagues until tl1e t Ith hour. His devoted secretary, Bev Peherdy, and several of his proreges-Robert Ashford, Bob Daniel, Bob Hattersley, and Robert Watson-were at his bedside listening while Martin talked about his ideas until close to lht very end, "''hich came at his home in Cornwall on December 23, 1985 (Daniel 1985). He was 57 years old. His wife Betty, in the year that followed, received hundreds of letters from friends around the world.

lkny '™-' ;\W11o. \\'lfldhovt1 HOl•H!,

Com•••all. 1983.

A magnificent Martin Beale Memorial, Symposium was held at the Royal Society's premises in Carlton House Terrace, London, in the summer of 1987, with procc,'<lings edited by Michael Powell (1988). Martin's final book, lntmduction to Optimization (Reale 1988), was posthumously edited by Lynne Mackley.

ACl\1'110\VLf::D(;f\>11~NTS

In preparing this chapter, T have relied on 1nt1ch of the sa1ne 1naterial that Martin's friends and coUeagues provided for the memorial article that G. B. Dantzig and I V\rrote tOr publi.::ation in lvfttthen1atjcal Prograrn1ning in 1987, where the)' are acknowledged in detail. Some of the material has been further paraphrased or condensed. I am also extremely grateful to M. J. D. Powell for permission to draw freely on his biographical memoir of

690 l'RO.U.f.S IN Ol'F.ltATIONS RtSFARCH

l\farlin Beale (Powell 1987). That memoir is also invaluable for its complete bibliography of Martio Beale's published works. Finally I wish lo adu1owledge my own indebtedness to Martin, the finest mentor irnaginable.

RF.FERF.NCFS

.A.badie J (<.:<l) {196i} Nonlinear programming. North·Hol.land, Amsterdam Beale E~1L ( 1954) An alternative mc1hod tOr linc3r programming. Proc C.,.amb Philos

Soc SO(Part 4):513- 523

Beale EML (1955) On 1nini1nizing a convex function subjecl Lo linear ioequ<llities. J R Stat Soc ( II) 17(2):173- 184

Buie EML (1959) On quadratic programming. Nav Res Logistics Q 6(3):227- 243

Beale EML (1967) Numerical methods. Jn: Abadie I (ed) Nonlinear programming. North-I Tolland, Am$1Crdam, pp 133- 206

Reale ErvtL (1968) l\.1athemalical programrning in practice. Pitn1an'.s, London, and

\Vil<')'· Ney.• York, NY Beale E~·tl ( J970a} l\-1alrix generalors and oulpul anal>·zc:rs. In: KuhJl H\V (ed)

Proceedings of the princeton symposium on malhen1atic.al progran1ming. Princeton University Press. Princeton, NI, pp 2S-36

Beale Ef\11. {llJ70b} Ach~anccd algorith1n ic: fcatorcs for genera) mathcmatiO'll progran1ming systcm.s. In: Abadie J (cd) Integer and nonlinear programming. Norlh liulla1~d. :\n)i.lt rdaru, pp 119-1!37

Beale Etvfl (1974} A con.iugate gradient n1ethod of appr<>:<imaLion progr.:i.1nn1ing. Jo: Cottle R, Krarup J (eds) Optin1ization methods for resoul'ce allo.c.ation. English Universities Press, London. pp 26 1- 277

Beale- t:f\1L (1985a) Jntcger progra1n1ning. In: Sch.ittkowski K (cd) Computational n1athematical programming. 1' ATO A:SI Series F: Computer and System Sciences. IS, Spri,,ger. Berlin, pp l - 24

Beale E~·IL ( I 98Sb) Priv.lle co1n1nunication) November 11 Beale E~·IL (1988} introduction co optilnization. \Vile>·· Chichester Beale EML. t>anti.ig G, \Vatson Rl> (1986) A ii1·st·Ol'der approa<h to a class of

1nulti·tin1c·period stochastic programs. f\1ath Progran1 Study 27: 103-117 Be•de EJ\.1L. Forrest I (1976} Global Qptimization \Ising special ordered SCI$. 1'.i ath

Program I 0( I ):52- 69 Reale EMI., 1-lughes P) Small R ( t 965a} F..x-pcricnc:c in using a decomposition program.

Comput J 8: 13- 18 Beale E~·tL, S1nall R (1965b) f\•tixed integer progra1nn1iog by a branch and

bound technique. In: Kalenich WA (ed) Proceedu1gs of Llie lfll' congrc~< l965, MacMillan/Spartan Press, LondoniWashington, DC, pp 450-45l

CHAPTER 37: EVELYN MARTIN LANSDOWNE B[ALE 69 1

Beale EML, Tomhn I (19i0) Speci31 faohties m •per.ti mathematical prog1111Dming system for non""'°"''CI problems UStng onlcrtd K't5 of variables.. In: La\\-TI:ncc J (ed) ProccOOings of the fifth intematio11al conference on opentionaJ tt:st~rch.

Tavi'1od<, London, pp 447-454

ll<itffll K ( 1986) Professor E. M. L llcalc - pcnonal ttlbut•. 0.R. Ne<,,.lcttcr, Fcbniory 8-9 Daniel R ( 1985) Obituary of E. M. L. Beak. The Times, Dea1nher 28 Dantdg G (1955) l.1neor p rogramming lUld<r uncertainty. Manage Sd 1(3-4):197-206

Dantzig G, Tomlln J (1987) E .M. L Beale, PRS: friend and colleague. Math Program 38(2):117-131

Dantzig G, Van Slykt R (1967) Generalized upp<r bounding tecbniques. ) Comput Sy>t Sci 1:213-226

Douglas AS ( 1986) Obituary: Professor faclyn Mortin LansdOl•'n< Bak. FRS. FIMA. !.M.A. Bullelin 22: 120-122

Forr<>t J, Tomlin I (2007) Bruich and bound .. intcgcr. and non-integer programming. Ann Op<r Res 149(1):81-87

Gomory R. (2002) Early integer programming. Op<r Res 50(1 ):78-81

Hughes P (1988) Marrin Beale: a pcrwnal memory. Math Program 42(1):5-9

Land A. Doig A (1960) AJl aulomatic n1ethod for solving diKrete program1ning problems. Econom('(riai 1.8(3):49i-520

Powell M (1987) Evelyn Martin Lansdowne Bcok Biogr Mem Fellows R Soc 33(Dcc):22-15

Powdl M (cd) (1988) Ma1hcmatical mod<ls and the1r solutions: contribution• to the Martin Ilea)< Memorial S)'ml""'um. Math Program 42(1):1-202

T omhn J ( 1989) lh• inilu.:nccs of algonthmic and hardware de<-elopm<r11> on

comput.atlonal mathematicaJ prognmming. E. ~·1. L Beale MemotiaJ LectUtt at the 13th lnlcrnauona) S)'mpos1wn on ti.iathfm~tic.al Programming. 'l'okyo. Jn; lri M. 1'anabe K (eds} Ji..1atheu1ati<."'.i.I programming: recent developments a.nd applications. Kluwer. Dordre<ht, pp 159- 175