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InterfacesVol, 37, No, 2, March-April 2007, pp, 163-175ISSN 0092-21021 EISSN 1526-551X1071370210163

DOI 10,1287/inte,1060,0225©2007 INFORMS

Ranking US Army Generals of the 20th Century:A Group Decision-Making Application of

the Analytic Hierarchy Process

Todd RetchlessDepartment of Mathematical Sciences, United States Military Academy, West Point, New York 10996,

todd,retchless@usma,edu

Bruce GoldenR, H, Smith School of Business, University of Maryland, College Park, Maryland 20742,

bgolden@rhsmith,umd ,edu

Edward WasilKogod School of Business, American University, Washington, DC 20016,

ewasil@american,edu

The pantheon of 20th century US Army generals contains many great wartime commanders. Military historianshave written about their leadership qualities but have not ranked the best generals. We asked 10 experts in USmilitary history to evaluate seven generals—Omar Bradley, Dwight Eisenhower, Douglas MacArthur, GeorgeMarshall, George Patton, John Pershing, and Matthew Ridgway—using the analytic hierarchy process in a groupsetting. We developed a ratings hierarchy, and each participant scored each general. We combined individualpairwise comparisons using the geometric-mean method and a new method based on linear programming andobtained a clear, three-tier ranking of generals with George Marshall judged the best US Army general of the20th century, closely followed by Dwight Eisenhower,

Key words: decision analysis: multiple criteria; military: personnel.History: This paper was refereed.

In the last 50 years or so, historians have writtenabout the traits of the great 20th century US military

leaders but have not formally ranked the best armygenerals. We asked 10 experts in US military historyto evaluate and rank the greatest wartime comman-ders in recent US history using the analytic hierarchyprocess (AHP) in a group decision-making setting.We developed a ratings hierarchy for their use, andall 10 experts scored all the generals. We combinedindividual pairwise comparisons using a traditionalgeometric-mean method and a new method based onlinear programming. We obtained the final scores andranking for the generals using both methods.

Participants and AlternativesWe invited 10 professional and amateur military his-torians to participate in our study and make up

our decision-making group. They included a USArmy history institute director, university professors,national defense and security specialists, and an oper-ations research analyst, Retchless (2005) described theparticipants' backgrounds in detail. We structured thehierarchy and asked the participants individually toprovide the pairwise comparisons needed to establishthe priorities for factors, subfactors, and alternatives.

In developing the set of alternatives, we startedwith a set of 21 generals. Most served in World War II,including such notables as Dwight Eisenhower andGeorge Marshall and lesser-known commanders, suchas Walter Krueger, Several served in Vietnam, includ-ing William Westmoreland, Several served in the GulfWar, including Norman Schwarzkopf, We consultedour 10 participants and pared the initial set of gen-erals to seven—Omar Bradley, Dwight Eisenhower,Douglas MacArthur, George Marshall, George Patton,

163

164Retchless, Golden, and Wasil: Ranking US Army Generals

Interfaces 37(2), pp. 163-175, ©2007 INFORMS

John Pershing, and Matthew Ridgway—for this study(Appendix).

The US Army currently has four ranks of general:brigadier general (one star), major general (two stars),lieutenant general (three stars), and full general (fourstars). General of the army (five stars) is reserved forwartime. The rank of general of the armies of theUnited States was assigned to John Pershing in 1919to honor his wartime service. No other officer heldthat title until 1976, when George Washington wasposthumously appointed general of the armies of theUnited States to signify his rank as first among all USArmy officers.

Developing the HierarchyWe developed a ratings hierarchy in Expert Choice(2005) to score and rank the seven generals (Figure 1).We used two key criteria—skills and actions.

The Skills CriterionUsing the current United States Army Field Manual22-100 (1999) on leadership as our guide, we brokedown skills into four subcriteria: conceptual, interper-sonal, tactical, and technical.

People rely on conceptual skills to handle ideas: toestablish intent, to filter information, to understand

® Goal: Rank US Army generals of the 20th century

- ^ Skills

Conceptual

Interpersonal

TacticalTechnical

'—(?) Actions

Contribution to confiict

Responsibiiity

Success

'—^ Time span

• Superior

% Very good

• Good

• Poor

Figure 1: The ratings hierarchy for ranking US Army generals has four lev-els. The goal is hroken down info fwo key criferia—skills and actions. Thecircle with a dot indicates that fhe goal, criferia, and subcriteria are bro-ken down further. Skills and actions are broken down into four subcriteria.Under the eight subcriferia are fhe four rafings shown below time span.

how organizations work, to develop frames of refer-ence, and to deal with ambiguity and uncertainty.

They rely on interpersonal skills to communicateand work with others: to conduct dialogue, to nego-tiate with others, to achieve consensus, and to buildteams.

People acquire tactical skills to attain proficiencyand experience in their professions (fighting wars inthis study). They use these skills to synchronize theactivities of subordinates, respecting their indepen-dent decisions.

People need technical skills to operate at the highestlevels of their professions. In the military commandstructure, generals need technical skills to assembletheir equipment, personnel, schedules, budgets, andfacilities to accomplish missions, to understand theeffects of their actions, and to translate political goalsinto military objectives (United States Army FieldManual 22-100 1999).

Actions CriterionWe broke down the actions criterion into four subcri-teria: contribution to conflict, responsibility, success,and time span.

Contribution to conflict includes a general's impacton the wartime conflicts he conducted and his specificcontributions to their outcomes. In this subcriterion,we included the importance of theaters and the devel-opment of tactics, techniques, and procedures.

Responsibility includes the scope of a general'swartime activities, the geographical area of responsi-bility, the size of forces, and the importance of deci-sions made throughout the conflict.

Success includes a general's success in executinghis responsibilities from tactical victories to strategic-level planning. All the generals considered were verysuccessful during wartime, some as battlefield com-manders and some as coalition builders.

Time span includes the number of wars a generalserved in and total wartime service.

RatingsWe developed a set of ratings for the eight subcriteria:superior, very good, good, and poor. We used theseratings to evaluate each general's performance withrespect to the eight subcriteria.

Retchless, Golden, and Wasil: Ranking US Army CeneralsInterfaces 37(2), pp. 163-175, ©2007 INFORMS 165

A superior rating indicates that a general's perfor-mance is the best of all US Army generals in the 20thcentury, A very good rating indicates that a general'sperformance is comparable to that of a small numberof generals, A good rating indicates that a general'sperformance is as good as most of the generals in the20th century, A poor rating indicates that a general'sperformance was below the average of US Army gen-erals of the 20th century,

Pairwise-Comparison MatricesThe 10 participants completed pairwise-comparisonmatrices at the first level of the hierarchy (skills andactions criteria) and at the second level of the hierar-chy (the four subcriteria of skills and the four subcri-teria of actions) (Appendix),

First-Level CriteriaAll first-level pairwise-comparison matrices for theparticipants were perfectly consistent. Three partici-pants judged skills to be more important than actions,four participants judged actions to be more importantthan skills, and three participants judged skills andactions equally important (Appendix),

We combined the pairwise comparisons of theparticipants: Let a denote the comparison of ele-ment / to element / for participant k (k = 1,2,...,10)in pairwise-comparison matrix A. We combined theindividual judgments of the 10 participants usingthe geometric mean to produce the entry ajj = [a]j xfl2. X ,,. X a]ff'^°. Aczel and Saaty (1983) showed thatthe geometric mean preserves the reciprocal prop-erty in the combined-pairwise-comparison matrix.The geometric mean is the most common approachused by groups to set priorities (Condon et al, 2003),

Using the geometric-mean approach, we obtainedthe combined entry for the comparison of Skills toActions in the first-level pairwise-comparison matrix(Table 1):

flj2 = [7 X 1/9 X 1/5 X 1 X 1 X 1/3 X 5 X 6 X 1 X 1/7] ^ °

= 0,8604,

This matrix is perfectly consistent,

Second-Level SubcriteriaFor the four subcriteria of skills, conceptual (CO),interpersonal (IN), tactical (TA), and technical (TE),

Skills Actions Priority

SkillsActions

0,86041

0.46250,5375

Table 1: The first-level group-pairwise-comparison matrix and prioritiesproduced by combining tbe judgments of the 10 participants.

we obtained the second-level pairwise-comparisonmatrix for each participant, the priorities, and the con-sistency ratio (CR) (Appendix), All 10 participantswere reasonably consistent in their judgments (theconsistency ratio of each matrix is less than the widelyused upper limit of 0,10),

Four participants gave tactical skills the highest pri-ority (three with values over 0,63), They commentedthat all generals deal with tactics either directly on thebattlefield or indirectly in the theater headquarters.In addition, they thought that generals should knowwhen not to interfere with their subordinates' tacticaldecisions, A sound understanding of tactics enabled ageneral to win wars while caring for those under hiscommand.

Three participants gave conceptual skills the high-est priority. They thought that generals needed to pro-vide a clear vision in wartime and in peacetime. Thebest generals could handle the uncertainty and riskoften hidden in the fog of war. In addition, the bestgenerals could call on their mental abilities to over-come the kinds of adversity they faced during war.

Three participants gave interpersonal skills thehighest priority and thought that the ability to workwith other armed services and other nations distin-guished the best generals of the 20th century. Thefour participants who judged interpersonal skills theleast important subcriteria remarked that in the his-tory of generals, many had serious personality flawsyet managed to be very successful on the battlefield.In addition, these participants thought that only cer-tain postings call for great interpersonal ability.

The group-pairwise-comparison matrix for skillsthat we produced using the geometric-mean approach(Table 2) has a consistency ratio of 0,007, which is lessthan the upper limit of 0,10,

For the four subcriteria of actions, contribution toconflict (CC), responsibility (RE), success (SU), andtime span (TS), we obtained the second-level pairwise-comparison matrix for each participant, the priorities.



(CR = 0.007)

COINTATE

CO

1

IN

1.28211

TA

1.23770.64941

TE

1.55751.07481.16651

Priority

0.30860.21210.27120.2080

SVGGP

S

1

VG

21

G

321

P

4321

Priority

0.46730.27720.16010.0954

Adjustedpriority

1.00000.59320.34260.2042

Table 2: The group-palrwise-comparison matrix and priorities producedby combining the judgments of the participants on the skills criterion.

and the consistency ratio (Appendix). All 10 partici-pants were reasonably consistent in their judgments(the consistency ratio of each matrix is less than thewidely used upper limit of 0.10).

Six participants gave success the highest priority(all six values were greater than 0.60). They com-mented that a general's ultimate responsibility was towin our nation's wars.

Two participants gave contribution to conflict thehighest priority. They remarked that true greatness ismeasured through overall contribution, and it can beachieved in one instant with a key decision regardlessof the level of success a general achieved in the restof his career.

Two participants gave responsibility the highestpriority (one had it tied with success). The best gen-erals are given large commands and sizable areas ofoperation. These participants felt that generals mustbe decisive leaders and make critical decisions with-out being affected by the enormous moral and emo-tional pressures of their positions.

The group-pairwise-comparison matrix for actionsthat we produced using the geometric-mean approach(Table 3) has a consistency ratio of 0.007, which is lessthan the upper limit of 0.10.

Third-Level RatingsUnder each of the eight subcriteria, we have fourratings—superior (S), very good (VC), good (G),

(CR = 0.007) CC RE SU TS Priority

CCRESUTS

0.96031

0.44490.45221

4.11413.29585.96141

0.23380.22550.47300.0678

Table 3: The group-pairwise-comparison matrix and priorities producedby combining the judgments of the participants on the actions criterion.

Tabie 4: Tbe pairwise-comparison matrix that we deveioped for tbe fourratings. The adjusted priorities are used to score seven generals on alleigbt subcriteria.

and poor (P). We developed the pairwise-comparisonmatrix for these four ratings (Table 4) and used thesame matrix for all of the subcriteria.

We calculated the priority of each rating and thenadjusted the priorities by dividing them by the high-est priority (Expert Choice does this automatically).An ideal general who received a superior rating on alleight subcriteria would have a total weighted scoreof one.

Participant and Group Ratings and Overall ResultsWe obtained the ratings from all 10 participants forall seven generals with respect to the eight subcrite-ria. We combined the ratings and produced an overallgroup priority for each general.

Participant and Group RatingsEach participant rated each general on each subcrite-rion using the four ratings (Appendix).

We created a group rating by averaging the ratingsof the 10 participants (Appendix). For example, the10 participants rated General Bradley on conceptualskills (Appendix) as follows:

10

G G VG G G G VG G G VGBradley

Based on the adjusted priorities (Table 4) (VG = 0.5932and G = 0.3426), Bradley's group rating is

(0.3426 + 0.3426 -I- 0.5932 + 0.3426 + 0.3426 -I- 0.3426

-I- 0.5932 + 0.3426 + 0.3426 + 0.5932) • 10" = 0.4178.

Overall ResultsWe used hierarchical composition to determine theoverall group priority for each general. Using the

Retchless, Golden, and Wasil: Ranking US Army GeneralsInterfaces 37(2), pp. 163-175, ©2007 INFORMS 167

Goal: Rank US Army generals of the 20th centurySkills (L: 0.4625)—H Conceptual (L: 0.3086)—a Interpersonal (L: 0.2121)- H Tactical (L: 0.2712)- O Technical (L: 0.2080)Actions (L: 0.5375)

—B Contribution to conflict (L: 0.2338)—S Responsibility (L: 0.2255)- a Success (L: 0.4730)

Time span (L: 0.0678)- • Superior (L: 0.4673; A: 1.000)- a Very good (L: 0.2772; A: 0.5932)

Good (L; 0.1601; A: 0.3426)Poor (L: 0.0954; A: 0.2042)

Figure 2: After the criteria and subcriteria, we give tfie local priorities (L)generated by Expert Cboice using tfie group-pairwise-comparison matri-ces. We sbow tbe adjusted priorities (A) for the tour ratings below timespan and use tbem for aii eight subcriteria.

criteria and subcriteria priorities (Figure 2) and thegroup ratings (Appendix), we calculated GeneralBradley's priority as follows:

(0.4625) [(0.3086) (0.4178) + (0.2121) (0.4930)

+ (0.2712) (0.4585) + (0.2080) (0.5086)]

+ (0.5375)[(0.2338)(0.5242) + (0.2255) (0.5994)

+ (0.4730) (0.5838) + (0.0678) (0.4930)] = 0.5193.

We obtained group priorities for all seven generals(Table 5). All priorities are between 0 and 1, and thepriorities of the alternatives in a ratings hierarchy donot sum to one as they do in a standard applicationof the AHP (Expert Choice 2005).

We sorted the priorities, and the generals fall intothree tiers. The upper tier contains Marshall and

General Group priority

MarshallEisenhowerRidgwayiVIacArthurPershingPattonBradley

0.86360.76790.66370.65700.64700.57610.5193

Eisenhower, with scores of 0.8636 and 0.7679, the mid-dle tier contains Ridgway, MacArthur, and Pershing,with scores of 0.6637, 0.6570, and 0.6470, and thelower tier contains Patton and Bradley, with scores of0.5761 and 0.5193.

Estimating Group Priorities Using LinearProgrammingWe used the traditional geometric-mean approach tocombine the pairwise comparisons of the 10 partici-pants and produce a single group entry in a matrix.We then used Expert Choice (2005) to generate the pri-orities for each matrix using the eigenvector method(Tables 1-3). Recently Chandran et al. (2005) devel-oped a linear-programming model for estimating thepriorities when a pairwise-comparison matrix con-tains interval judgments. We can illustrate their modelwith the matrix in which the two criteria, skills andaction, are compared. This matrix takes the form

where [1^2' "12] is the interval judgment for the com-parison of skills to actions and [I21, M21] is the intervaljudgment for the comparison of actions to skills. Wecalculated the intervals using the comparisons of all10 participants in the following way:

= min{7,1/9,1/5,1,1,1/3,5, 6,1,1/7) = 1/9,

= max(7,1/9,1/5,1,1,1/3,5,6,1,1/7} = 7,

= min{l/7,9,5,1,1, 3,1/5,1/6,1, 7} ^ 1/7,

Tabie 5: We combined the criteria and subcriteria priorities and the rat-ings to produce the overaii group priorities for aii seven generals.

= max(l/7,9,5,1,1,3,1/5,1/6,1, 7} = 9.

We produced the first-level group comparison matrixwith interval judgments (Table 6), the second-levelgroup comparison matrices with interval judgmentsfor skills (Table 7), and for actions (Table 8).

We applied the interval-linear-programming ap-proach (Chandran et al. 2005) (Appendix) to generatethe priorities (Tables 6-8).



Skills Actions Priority CC RE SU TS Priority

SkillsActions [1/7,9]

[1/9,7]1

0.46860.5314

Table 6: We produced the first-level group-pairwise-comparison matrixwith intervai judgments hy using the comparisons of ail 10 participants.

We used hierarchical composition with the grouppriorities for interval judgments and the adjusted pri-orities for the ratings to generate the group priorityfor each general. For example. General Bradley's pri-ority is

(0.4686) 1(0.3368) (0.4178) + (0.2416) (0.4930)

+ (0.2416) (0.4585) + (0.1800)(0.5086)]

+ (0.5314) [(0.2932) (0.5242) + (0.2932) (0.5994)

+ (0.3468)(0.5838) -I- (0.0668)(0.4930)] = 0.5167.

We obtained the group priority for each generalgenerated from the linear-programming (LP) mod-els using interval judgments with all 10 participants(Table 9) denoted by LP 10. We also generated thefirst-level group-comparison matrix of skills versusactions and the second-level skills comparison matrixand actions comparison matrix by deleting the out-lier entries of some participants in an attempt toreduce the variability of the judgments. To producethe results, LP 8 (Table 9), we deleted the highest andlowest entries in the first-level and second-level matri-ces (this is similar to the trimmed mean in statisticsand subjective scoring in such sporting events as div-ing in the Olympic Games where the high and lowscores are deleted and the remaining scores are tal-lied), and then solved our LP models to obtain thegroup priorities. In the third-level ratings, we deletedthe highest and lowest ratings (for example, in the

CO TA TE Priority

COiNTATE

1[1/9,5][1/9,8][1/7,2]

[1/5,9]1

[1/9,9][1/6,7]

[1/8,9][1/9,9]

1[1/9,5]

[1/2,7][1/7,6][1/5,9]

1

0.33680.24160.24160.1800

Tahle 7: We produced the group-pairwise-comparison matrix and priori-ties with interval judgments by using the comparisons of the participantson the skills criterion.

CCRESUTS

1[1/5,5][1/5,7][1/7,1]

[1/5,5]1

[1/5,7][1/9,3]

[1/7[1/7

1[1/9,

,5],5]

1/3]

[1,7][1/3,9][3,9]

1

0.29320.29320.34680.0668

Table 8: We produced tbe group-pairwise-comparison matrix and priori-ties with intervai judgments by using the comparisons of tbe participantson tbe actions criterion.

conceptual ratings (Appendix), we deleted a G anda VG for General Bradley), and then used hierarchi-cal composition to generate the group priority. Sim-ilarly, we deleted the two highest and two lowestentries to produce the results, LP 6 (Table 9). Retchless(2005) describes the matrices and LP models for LP 8and LP 6.

All four methods (GM, LP 10, LP 8, and LP 6) givepriorities and three tiers of generals that are very sim-ilar. All four methods produce exactly the same order-ing of generals in the upper and lower tiers. All threelinear-programming models produce exactly the sameordering of generals in the middle tier. The fact thatdifferent methods yield essentially the same rankingand priorities gives us a high level of confidence inthe results.

Based on the results of all four methods, the 10participants judged General of the Army GeorgeC. Marshall the best US Army general of the 20th cen-tury, closely followed by General of the Army DwightD. Eisenhower. The remaining five generals were farbehind in the rankings.

Finally, we examined the sensitivity of the rankingsto changes in the weights of the criteria at the firstlevel of the hierarchy (skills and actions). We variedthe weight of skills from 0.05 to 0.95 (we varied thecorresponding w^eight on actions from 0.95 to 0.05)and tracked changes in the rankings. Marshall andEisenhower stayed at one and two in the rankingsregardless of the weights. Decreasing the weight onskills from 0.4625 (generated by the group (Table 1))to about 0.41 caused MacArthur and Ridgway toexchange positions in the rankings. Increasing theweight on skills from 0.4625 to about 0.80 caused Pat-ton and Pershing to exchange positions. Patton moveddown one spot in the rankings when the weight onskills was roughly 0.80 or greater. Pershing moved up

Retchless, Golden, and Wasil: Ranking US Army GeneralsInterfaces 37(2), pp, 163-175, ©2007 INFORMS

Table 9: We obtained the group priorities for seven generals using four methods: the geometric-mean approach(GM) and three variants ot the interval linear-programming approach (LP 10, LP 8, and LP 6),

169

General

MarshallEisenhower

RidgwayMacArthurPershing

PattonBradley

GM

0,86360,76790,66370,65700.6470

0,57610,5193

General

MarshallEisenhowerMacArthurPershingRidgwayPattonBradley

LP10

0,86490,78200,66460,66200,65490,54950,5167

General

MarshallEisenhower

MacArthurPershingRidgwayPattonBradley

LP8

0,88750,8072

0,66710,65730,63960,54940,4927

General

MarshallEisenhowerMacArthurPershingRidgwayPattonBradley

LP6

0,88910,80660,65270,63850,60270,56100,4853

in the rankings when it was roughly 0,40 and thenagain when it was 0,80, Ridgway moved down twopositions in the rankings when the weight on skillsincreased from 0.35 to 0,45,

ConclusionsThe 10 experts in US military history evaluated andranked the seven greatest US Army generals of the20th century. They used the AHP in a group settingand generated results using two different methods.The final results from the different methods showedessentially the same rankings with George C, Marshalland Dwight D, Eiserihower as the best US Army gen-erals of the last 100 years.

Appendix

Biosketches of the Alternatives: Seven US ArmyGenerals of the 20th CenturyOmar N, Bradley was born in 1893 in Clark, Missouriand graduated from West Point in 1915, During the1920s and 1930s, he was an instructor and student inthe Army educational system. In February 1942, hewas promoted to major general. He assumed com-mand of the 82d Infantry Division and began prepar-ing untrained soldiers for combat. He performed sowell in this task that, after only four months, he wasasked to train the 28th Infantry, In February 1943,Bradley served as Eisenhower's personal representa-tive in the field in North Africa, In April 1943, heassumed command of II Corps in North Africa, IICorps spearheaded the Seventh Army assault on Sicilyand captured Messina in August 1943, In the monthsprior to D-Day, Bradley supervised the training of sol-diers. He led the First Army in D-Day assaults on Utah

and Omaha beaches. In late July 1944, he plarmed andled a successful breakout of the Normandy beachhead.Based on this success, Eisenhower activated the 12thArmy Group (21 divisions and 900,000 soldiers) withBradley in command. When the 12th Army Groupreached the Elbe River in April 1945, it had taken315,000 Germans prisoner. By V-E Day, Bradley wasin charge of 48 divisions and 1,3 million soldiers. InAugust 1949, he became the first chairman of the JointChiefs of Staff (United States Army Center of MilitaryHistory 1992),

Dwight D, Eisenhower was born in 1890 in Denison,Texas and graduated from West Point in 1915, DuringWorld War I, he commanded the tank corps at Gettys-burg, Pennsylvania, From 1933 until the beginning ofWorld War II, he served as the chief military aide toDouglas MacArthur, In early 1942, he became chief ofthe War Plans Division, In November 1942, he led theallied landings in North Africa and then directed oper-ations in North Africa, Sicily, and Italy, In late 1943,he became supreme commander of the allied expedi-tionary force and began planning for the invasion ofFrance, By the end of 1944, he was coordinating themarch of two million soldiers through France towardsGermany, In late 1944, he was promoted to general ofthe army. On May 7, 1945, he accepted the uncondi-tional surrender of Germany, He was the 34th pres-ident of the United States from 1953 to 1961 (UnitedStates Army Center of Military History 1990),

Douglas MacArthur was born in 1880 in Little Rock,Arkansas and graduated from West Point as the topcadet in 1903, In 1917, he served as chief of staff for the42d Infantry Division in France, He was promoted tobrigadier general in 1918, At the end of World War I,he commanded the 84th Brigade and had received



12 US and 19 allied medals and decorations. In 1925,he was promoted to major general and then to gen-eral while serving as chief of staff of the US Armyfrom 1930 to 1935. He resigned from military servicein 1937 and was brought out of retirement in 1941to command the US Army forces in the Far East anddefend the Philippines. In early 1942, with the fallof the Philippines almost certain, he was ordered toAustralia. In mid 1943, he began his island-hoppingoffensive that liberated the Philippines in early 1945.In September 1945, General of the Army DouglasMacArthur accepted the surrender of Japan. He super-vised the reconstruction of Japan as its supreme alliedcommander. In 1950, he was designated commander.United Nations Command, Far East and directed UNforces in South Korea. In April 1951, he was relievedof his command (Manchester 1978).

George C. Marshall was born in 1880 in Uniontown,Pennsylvania and graduated from the Virginia Mil-itary Institute in 1901. In World War I, he servedas chief of staff for operations of the First Divisionand returned to the US as aide de camp to JohnPershing for five years. In 1939, he was promotedto general and served as chief of staff of the USArmy. In late 1941, he participated in the Arcadiaconference, serving as the primary US representativeto the British contingent. In 1942, he coordinated thedefense of Guadalcanal and prepared for an offensivein North Africa. From Washington, he was responsi-ble for managing the global operations of an army ofeight million soldiers. In late 1944, he was promotedto general of the army. He later served as secretary ofstate and secretary of defense (Pogue 1965).

George S. Patton Jr. was born in 1885 near SanGabriel, California and graduated from West Pointin 1909, joining the cavalry. In 1912, he finished fifthin the modern pentathlon at the Olympic Games inStockholm. In 1913, he became the US Army's firstmaster of the sword. In early 1916, he served as an aideto John Pershing in the Punitive Expedition in Mexico.In November 1917, he became the first soldier of thenew US Army Tank Corps. In November 1942, Pattoncommanded the Western Task Force in the invasionof Casablanca. He commanded II Corps in 1943, lead-ing them to victories in Gafsa and El Guettar. He ledthe Seventh Army in Sicily, capturing Palermo and

Messina in July 1943. After slapping two soldiers, Pat-ton was brought to England in early 1944 to secretlycommand the Third Army. In August 1944, he led theThird Army in the Normandy breakout and, at theend of the year during the Battle of the Bulge, he redi-rected three divisions to stop the German advance intothe Ardennes. He was promoted to general in the finalweeks of World War II (D'Este 1995).

John J. Pershing was born in 1860 in Laclede,Missouri and graduated from West Point in 1886. Heserved with the 10th Cavalry in the Spanish AmericanWar and saw action in the Battle of San Juan Hill. In1906, President Theodore Roosevelt promoted him tobrigadier general over 862 ranking officers. In 1916,Pershing led a force of over 7,000 into Mexico inresponse to Pancho Villa's murderous rampage. In1917, shortly after the US declared war on Germany,Pershing was selected to command the AmericanExpeditionary Force (AEF)—about 25,000 soldiers atthe time—that was to fight in France alongside Britishand French forces. In one year, he created, equipped,and trained the largest ever US army. By late 1918, theAEF had over two million soldiers. In 1919, Pershingwas awarded the rank of general of the armies tohonor his wartime service (Smith 1998).

Matthew B. Ridgway was born in 1895 in FortMonroe, Virginia and graduated from West Point in1917. His first assignment was along the Mexican bor-der. In 1918, he returned to West Point and spent sixyears as an instructor. In the remainder of the 1920sand in the 1930s, he served in Latin America, thePhilippines, and the United States. In 1939, he joinedthe War Department in Washington. In early 1942, hewas promoted to brigadier general and worked forOmar Bradley as the deputy commander of the 82dInfantry Division. He later assumed command of thedivision. Ridgway and the 82d saw action in Salerno,Italy in September 1943 and participated in an air-borne drop on D-Day. He then assumed commandof the XVIII Airborne Corps (82d and 101st AirborneDivisions). In early fall 1944, the XVIII Airborne Corpsparticipated in many airborne drops, fought for 60days in Holland, and were a strategic reserve duringthe Battle of the Bulge. In 1950, Ridgway became com-mander of the Eighth Army in Korea, retook Seoul,and stabilized the front around the 38th parallel. In1951, he replaced MacArthur as the American and

Retchless, Golden, and Wasil: Ranking US Army GeneralsInterfaces 37(2), pp, 163-175, ©2007 INFORMS 171

supreme allied commander in the Far East, He wasarmy chief of staff for President Eisenhower (Arling-ton National Cemetery Web Site 2006),

Pairwise-Comparison MatricesThe two first-level criteria:

SkillsActions

SkillsActions

SkillsActions

SkillsActions

SkillsActions

SkillsActions

SkillsActions

Participant 1

1 7— 1

Participant 2

1 1/9— 1

Participant 3

1 1/5— 1

Participant 4

1 1— 1

Participant 5

1 1— 1

Participant 6

1 1/3— 1

Participant 7

1 5— 1

Priority

0,87500.1250

Priority

0.10000.9000

Priority

0,16670.8333

Priority

0,50000,5000

Priority

0.50000.5000

Priority

0,25000.7500

Priority

0.83330,1667

SkillsActions

SkillsActions

SkillsActions

Participant 8

1 6— 1

Participant 9

1 1— 1

Participant 10

1 1/7

Priority

0,85710.1429

Priority

0.50000.5000

Priority

0,12500.8750

The four subcriteria of skills:

Participant 1 (CR = 0,10)

Priority

CO 1IN —TA —TE —

Participant 2 (CR = 0.06)

Priority

91

71/61

11/71/3

1

0.48590.03830.12740,3484

COINTATE

— 1


51/4

1

31/61/31

0.56560,04630.12290.2652

Priority

COINTATE

1/41

—

1/211

1221

0,13570,38580.31900.1595


Priority

COINTATE

41

1/21/51

1/21/521

0.20170.06390,43070,3037



COINTATE

COINTATE

COINTATE

COINTATE

COINTATE


1/21

1/81/51

1371


1/31

25

1/21




Priority

0.08080.17230.67020.0767

Priority

0.23520.59280.05650.1155

Priority

1/51—

1/71/61

1691

0.05860.21910.67050.0519

Priority

1/51—

681

261/31

0.19970.64280.04740.1101

Priority

5

1—1

1/51/91

21/551

0.19090.04240.63090.1358

The four subcriteria of actions:


Priority

CCRESUTS

CCRESUTS

CCRESUTS

CCRESUTS

CCRESUTS

1 1/41—

1/71/51

3391

0.09240.20190.65330.0524


Priority

51

1/41/71

7391

0.26240.08150.61500.0411


Priority

41

1/61/61

11/341

0.16040.06180.61980.1580

Participant 4 (CR - 0.06)

Priority

21

431

6441

0.49320.29710.14830.0614


Priority

1/51—

151

3941

0.14460.64600.15740.0520

COINTATE


Priority

51

961

721/51

0.65500.18890.03940.1187

CCRESUTS

Participant 6 (CR - 0.05)

Priority

31

51/21

7231

0.18690.13890.19360.0699



CCRESUTS

1—

_

1/31

1/7

1/51

3

4

9

1

Priority

0.09650.19480.65990.0487

BradleyEisenhower


CCRESUTS

1——

21

—

1/4

1/51

7591

Priority

0.22060.13540.60430.0397

The interpersonal subcriterion of skills:

Participant

10

VG G VG G G VG VG G VG VGS S S S S S S V G S S

MacArthur G G VG VG P VG G G G GMarshall S S VG S VG VG G S S S

Patton P V G P G G V G G P P P

Pershing S VG VG VG VG VG G VG G S

Ridgway VG VG G VG VG

The tactical subcriterion of skills:

Participant

1 10


CCRESUTS

1——

1/2

1—

1/21

1

55

51

Priority

0.21790.36040.36040.0613


CCRESUTS

1——

1/31

—

1/7

1/4

1

57

91

Priority

0.10930.23020.62250.0380

Ratings of the ParticipantsThe conceptual subcriterion of skills:

Participant

8 10

Bradley G G VG G GEisenhower S G VG VG VG SMacArthur S S G VG P S VG GMarshall S VG VG S S S VG SPatton VG VG G VG VG VG VG G

G VG G G VGS VG S S

S SS SG GS VGPershing VG G VG VG VG G S

Ridgway VG VG VG G S VG VG VG VG S

Bradley VG VG GEisenhower G P V G G G G P G G GMacArthur VG VG S VG G G G VG S SMarshall G VG G VG G VG VG G VG VGPatton S S S G S S S S S V GPershing VG P VG G G VG G G G VG

Ridgway VG S VG VG

The technical subcriterion of skills:

Participant

1 10

Bradley G G VG G G S G VG VG VGEisenhower VG S S VG VG S VG S S GMacArthur S S G VG G VG G VG S VGMarshall VG S S S S VG G VG S SPatton VG VG G VG G S S G S VGPershing VG VG VG G VG G G VG S VGRidgway VG S G G S S VG VG VG S

The contribution-to-conflict subcriterion of actions:

Participant

1

Bradley GEisenhower SMacArthur VGMarshall S

10

G V G G G G V G G S SS S VG VG S VG VG S SS S VG VG S G VG P VGS V G S S S S S S S

PattonPershingRidgway

VG G VG G VG VG GS VG

VG VGS VG VG G

G VG VG G VG VG

174Retchless, Golden, and Wasil: Ranking US Army Generais


The responsibility subcriterion of actions:

Participant

BradleyEisenhowerMacArthurMarshallPattonPershingRidgway

1

VGSS

sVGSG

2

GSS

sG

VGS

3

VGS

ssG

sG

4

VGS

ssG

sVG

The success subcriterion of

BradleyEisenhowerMacArthurMarshallPattonPershing

1

VGSGS

VGVG

2

VGS

VGS

sG

3

VGSGS

VGS

4

GVGVGS

VGVG

5

VGS

ssG

sVG

6

GS

ssG

sVG

actions:

Participant

5

VGVGPS

sVG

6

GS

ss

VGVG

7

VGSG

VGVGS

S

7

VGGGS

VGS

8

GVGVGSG

VGG

8

VGVGVGS

VGVG

9

SSSSSSS

9

VGS

sss

VG

10

S

sVG

sp

ss

10

ssssG

VGRidgway

The time-span subcriterion of actions:

Participant

10

Bradley VG G VG G G VG VG G VG VGEisenhower VG G VG G G VG VG VG VG VGMacArthur S S S S S S S S S SMarshall VG VG VG VG S S S VG VG S

Patton VG G VG G VG G VG G VG GPershing VG G G S S G S G VG VGRidgway VG VG VG G VG G VG G VG VG

Group RatingsGroup ratings for the skills subcriterion:

Conceptual Interpersonal Tactical Technical


0.41780.77150.70760.87800.49300.59940.6495

0.49300.95930.40390.81220.32350.62440.5086

0.45850.34000.64010.49300.89360.42900.8780

0.50860.77150.64010.81220.64010.55870.7058

Group ratings for the actions subcriterion:

Contributionto conflict Responsibility Success Time span


0.52420.83730.65130.95930.42900.74650.5587

0.59940.95930.85290.95930.44460.91860.6807

0.58380.81220.60121.00000.69020.64950.6746

0.49300.51801.00000.75590.46790.61500.5180

Linear-Programming ApproachThe two-stage linear-programming approach for gen-erating a priority vector was developed by Chandranet al. (2005). In the first stage, we formulated a lin-ear program that provides a consistency bound fora pairwise-comparison matrix. In the second stage,we used the consistency bound in a linear programwhose solution is a priority vector.

Let A = {ajj) for all /, j = 1,1,... ,n, denote a squarepairwise-comparison matrix, where «;. is a singlenumber that gives the importance of element i rel-ative to element /. Each entry in matrix A is posi-tive (fl,y > 0) and reciprocal (a^ = l/oy, for all i, / = 1,1,...,n). We wanted to compute a vector of weights(Wj, zii2/ • • • / '^n) associated with A. Let wJWj = Oj S; ,

i, j = 1,2,... ,n, define an error e;y in the estimateof the relative preference a . The decision variablesare given by x, = hi(w,), y^j = ln(e;y), and z^j = |i/; |.Using these variables, we obtained the objective func-tion and constraints of the first-stage linear program:

Minimize E (1)

subject to Xj — Xj — yij = In a^,

Zjj > ytj, i, i = l,2,...,n; i< j , (3)

z , ; > ! / ; / , i,j = l , 2 , . . . , n ; i < j , ( 4 )

Xi-0, (5)

Xi-Xj>0, i,j = l,2,...,n; fl;y>l, (6)

Xi -Xj>0, i,j = l , 2 , . . . , n; o,- > Uji,

for all k; a, > Oj^ for some q, (7)


Zii>0, i,i = l,2,...,n, (8)

X,, yij u n r e s t r i c t e d , i, j = 1,2,... ,n.{9)

The solution set of the first-stage linear programcontains all of the priority vectors that minimize theproduct of all errors Sjj. There may be multiple opti-mal solutions to the first-stage model. In the secondstage, the solution to the linear program selects fromthis set of alternative optima the priority vector thatminimizes the maximum of errors e^. The second-stage linear program is given by

Minimize

n—l n

subject to Y. E 2,7 = z*.

(10)

(11),=1 /=i

/, ; = 1,2 n;i^i, (12)

Zij>yij, i,i = l,2,...,n;i<j, (13)

Zij>yji, i,j = 1,2 n;i<j, (14)

2max>2,y , i, j = 1,2, ..., 11; i < j , (15)

x,=0, (16)

Xi-Xj>Q, i,j = l,2,...,n; fl,.y>l, (17)

for all k; a, > fly^ for some (/, (18)

Zij>0, i,j = l,2,...,n, (19)

X,, yij unrestricted, i,j = l,2,...,n, (20)

Zmax > 0. (21)

Constraint (11) ensures that only those solution vec-tors that are optimal in the first-stage linear programare feasible in the second-stage linear program (z* isthe optimal objective function value of the first-stagemodel). Constraints (15) find z^^^, the maximum valueof the errors Z;. The objective function (10) minimizesZn,3x' Constraint (21) is the nonnegativity restriction for

z^3x (this constraint is redundant). The remaining con-straints are the same as the corresponding constraintsin the first-stage model.

The two-stage approach can easily be extendedto handle interval judgments for each a (Table 6)(Chandran et al. 2005).

AcknowledgmentsWe thank the 10 experts—Conrad Crane, Andrew Dziengel-ski, Robert Goldich, Kenneth Hamburger, Douglas Johnson,James Mennell, Stephen Pound, Edgar Raines, JamesReseau, and David Reynolds—for participating in thisstudy. We could not have produced this ranking of 20thcentury US Army generals without their individual insightsand collective judgments. We thank the referee for com-ments that improved the paper's readability and for aspreadsheet model that helped us to conduct a sensitivityanalysis of the weights.

ReferencesAczel, ]., T. Saaty. 1983. Procedures for synthesizing ratio judge-

ments. /. Math. Psych. 27(1) 93-102.Arlington National Cemetery Web Site. 2006. Matthew Bunker

Ridgway. Retrieved March 13, http://www.arlingtoncemetery.net/ ridgway.htm.

Chandran, B., B. Golden, E. Wasil. 2005. Linear programming mod-els for estimating weights in the analytic hierarchy process.Comput. Oper. Res. 32(9) 2235-2254.

Condon, E., B. Golden, E. Wasil. 2003. Visualizing group decisionsin the analytic hierarchy process. Comput. Oper. Res. 30(10)1435-1445.

D'Este, C. 1995. Patton: A Genius for War. HarperCollins, New York.Expert Choice. 2005. www.expertchoice.com. Arlington, VA.Manchester, W. 1978. American Caesar: Douglas MacArthur 1880-

1964. Random House, New York.Pogue, E 1965. George C. Marshaii: Ordeal and Hope 1939-1942.

Penguin Books, New York.Retchless, T. 2005. Ranking US Army generals of the twentieth

century using the group analytic hierarchy process. Master'sthesis. Applied Mathematics and Scientific Computation, Uni-versity of Maryland, College Park, MD.

Smith, G. 1998. Until the Last Trumpet Sounds: The Life of General ofthe Armies John J. Pershing. John Wiley & Sons, New York.

United States Army Center of Military History. 1990. Dwight DavidEisenhower: The Centennial. Publication 71-40, Washington, D.C.

United States Army Center of Military History. 1992. Omar NelsonBradley: The Centennial. Publication 71-41, Washington, D.C.

United States Army Field Manual 22-100.1999. Army Leadership. USGovernment Printing Office, Washington, D.C.

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