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Mathematical Contest in Modeling (MCM/ICM) Summary Sheet
(Attach a copy of this page to your solution paper.)
Research on Choosing the Best College Coaches Based on Data Envelopment Analysis
Summary
In order to get the rank of coaches in differ ent sports and look for the ―best all time college coach‖ male or female for the previous century, in this paper, we build a comprehensive evaluation model for choosing the best college coaches based on data envelopment analysis. In the established model, we choose the length of coaching career, the number of participation in the NCAA Games, and the number of coaching session as the input indexes, and choose the victory ratio of games, the number of victory session and the number of equivalent champion as the output indexes. In addition, each coach is regarded as a decision making unit (DMU).
First of all, with the example of basketball coaches, the relatively excellent basketball coaches are evaluated by the established model. By using LINGO software, the top 5 coaches are obtained as follows: Joe B. Hall, John Wooden, John Calipari, Adolph Rupp and Hank Iba.
Secondly, the year 1938 is chosen as a time set apart to divide the time line into two parts. And then, basketball coaches are still taken as an example to evaluate the top 5 coaches used the constructed model in those two parts, respectively. The evaluated results are shown as: Doc Meanwell, Francis Schmidt, Ralph Jones, E.J. Mather, Harry Fisher before 1938, and Joe B. Hall, John Wooden, John Calipari, Adolph Rupp and Hank Iba after 1938. These results are accordant with those best coaches that were universally acknowledged by public. It suggests that the model is valid and effective. As a consequence, it can be applied in general across both genders and all possible sports.
Thirdly, just the same as basketball coaches, football and field hockey coaches are also studied by using the model. After the calculation, the top 5 co aches of football’s results are as follows: Phillip Fulmer, Tom Osborne, Dan Devine, Bobby Bowden and Pat Dye, and field hockey’s are Fred Shero, Mike Babcock, Claude Julien, Joel Quenneville and Ken Hitchcock.
Finally, although the top 5 coaches in each of 3 different sports have been chosen, the above-mentioned model failed to sort these coaches. Therefore, the super- efficiency DEA model is introduced to solve the problem. This model not only can evaluate the better coaches but also can rank them. As a result, we can choose the ―best all time college coach‖ from all the coaches easily.
Type a summary of your results on this page. Do not include
the name of your school, advisor, or team members on this page.
Research on Choosing the Best College Coaches Based on Data
Envelopment Analysis
Summary
I n order to get the rank of coaches in different sports and look for the ―best all time college coach‖ male or female for the previous century, in this paper, we build a comprehensive evaluation model for choosing the best college coaches based on data envelopment analysis. In the established model, we choose the length of coaching career, the number of participation in the NCAA Games, and the number of coaching session as the input indexes, and choose the victory ratio of games, the number of victory session and the number of equivalent champion as the output indexes. In addition, each coach is regarded as a decision making unit (DMU).
First of all, with the example of basketball coaches, the relatively excellent basketball coaches are evaluated by the established model. By using LINGO software, the top 5 coaches are obtained as follows: Joe B. Hall, John Wooden, John Calipari, Adolph Rupp and Hank Iba.
Secondly, the year 1938 is chosen as a time set apart to divide the time line into two parts. And then, basketball coaches are still taken as an example to evaluate the top 5 coaches used the constructed model in those two parts, respectively. The evaluated results are shown as: Doc Meanwell, Francis Schmidt, Ralph Jones, E.J. Mather, Harry Fisher before 1938, and Joe B. Hall, John Wooden, John Calipari, Adolph Rupp and Hank Iba after 1938. These results are accordant with those best coaches that were universally acknowledged by public. It suggests that the model is valid and effective. As a consequence, it can be applied in general across both genders and all possible sports.
Thirdly, just the same as basketball coaches, football and field hockey coaches are also studied by using the model. After the calculation, the top 5 coaches of football’s results are as follows: Phillip Fulmer, Tom Osborne, Dan Devine, Bobby Bowden and Pat Dye, and field hockey’s are Fred Shero, Mike Babcock, Claude Julien, Joel Quenneville and Ken Hitchcock.
Finally, although the top 5 coaches in each of 3 different sports have been chosen, the above-mentioned model failed to sort these coaches. Therefore, the super- efficiency DEA model is introduced to solve the problem. This model not only can evaluate the better coaches but also can rank them. As a result, we can choose the ―best all time college coach‖ from all the coaches easily.
Key words: college coach；data envelopment analysis; decision making unit; comprehensive evaluation
Contents
1. Introduction (4)
2. The Description of Problem (4)
3. Models (5)
3.1Symbols and Definitions (5)
3.2 GeneralAssumptions (6)
3.3 Analysis of the Problem (6)
3.4 The Foundation of Model (6)
3.5 Solution and Result (8)
3.6 sensitivity analysis (17)
3.7 Analysis of the Result (19)
3.8 Strength and Weakness (19)
4.Improved Model............................................................................................................................ .. (20)
4.1super- efficiency DEA model (20)
4.2 Solution and Result (21)
4.3Strength and Weakness (25)
5. Conclusions (25)
5.1 Conclusions of the problem...............................................................................,.25 5.2 Methods used in our models (26)
5.3 Applications of our models (26)
6.The article for Sports Illustrated (26)
7.References (28)
I. Introduction
At present, the scientific evaluation index systems related to college coach abilities are limited, and the evaluation of coach abilities are mostly determined by the sports teams’game results, and it lacks of systematic, scientific and accurate evaluation with large subjectivity and one-sidedness, thus it can not objectively reflect the actual training level of coaches. In recent years, there appear many new performance evaluation methods, which mostly consider the integrity of the evaluation system. Thus they overcome a lot of weaknesses that purely based on the evaluation of game results. However, it is followed by the complexity of evaluation process and index system, as well as the great increase of the implementation cost. Data envelopment analysis is a non-parametric technique for evaluating the relative efficiency of a set of homogeneous decision-making units (DMUs) with multiple inputs and multiple outputs by using a ratio of the weighted sum of outputs to the weighted sum of inputs. Therefore, it not only simplifies the number of indexes, but also avoids the interference of subjective consciousness, thus makes the evaluation system more just and scientific.
Based on the investigation and research of the US college basketball coach for the previous century, this paper aims at establishing a scientific and objective evaluation index system to assess their coaching abilities comprehensively. It provides reference for the relating sports management department to evaluate coaches and continuously optimize their coaching abilities. For this purpose, the DEA is successfully introduced into this article to establish a comprehensive evaluation model for choosing the best college coaches. It makes the assessment of the coaches in different time line horizon, different gender and different sports to testify the validity and the effectiveness of this approach.
II. The Description of the Problem In order to find out the ―best all time college coach‖ for the previous century, a comprehensive evaluation model is needed to set up. Therefore, a set of scientific and objective evaluation index system should be established, which should meet the following principles or requirements:
The principle of sufficiency and comprehensiveness
The index system should be sufficiently representative and comprehensively
cover the main contents of the coaches’ coaching abilities.
The principle of independence
Each of the index should be clear and comparatively independent.
The principle of operability
The data of index system comes from the existing statistics data, thus copying the unrealistic index system is not allowed.
The principle of comparability
The comparative index should be used as far as possible to be conveniently
compared for each coach.
After the establishment of evaluation index system, it requires the detailed model to make assessment and analysis for each coach. Currently, the comprehensive assessment is mostly widely used, but most of them need to be gave a weight. It is more subjective and not very scientific and objective. To avoid fixing the weight, the DEA method is adopted, which can figure out coaches’ rank eventually from the coach’s actual data.
For the different time line horizon, the coaches’ rank is inevitably influenced by the team’s l evel and the sports, thus it requires discussion in different time line horizon to get the further results.
Finally, the DEA model is applied to all coaches (either male or female) and all possible sports to get the rank, and then the model’s whole assessm ent basis and process should be explained to the readers in understandable words.
III. Models
3.1 Terms Definitions and Symbols
Symbol
Explanation DMU k the k th DMU
0DMU the target DMU, which is one of the n
evaluated DMUs; ik x the i th input variable consumed 0i x
the i th input variable consumed jk y the j th output variable produced 0j y
the j th output variable produced 1I The length of coaching career 2I
The number of taking part in NCAA
tournament
3I
coaching session 1O
victory ratio of game
3.2 General Assumptions
The same level game difficulty in different regions and cities is equal for all teams.
The value of the champion in different regions and cities is equal (without regard to team’s number in the region, the power and strength of the teams and other factors).
The same game’s value is equal in different years (without regard to the team number in the year and other factors).
The college’s level has no influence to the coach’s coaching performance.
3.3 Analysis of the Problem
For the current problem, first of all, a comprehensive evaluation model is
needed to set up. Therefore, a set of scientific and objective evaluation index system should be established. The evaluation system of the coaches is comparatively mature, but it mainly based on the people’s subjective consciousness, thus the evaluation system we build requires more data to explain the problem, and it tries to assess each coach in a objective and just way without the interference of subjective factors.
Secondly, the evaluation system we used is different due to the different games in different time periods. So the influence of different time periods to the evaluation results should be taken into account when we deal with the problem. Furthermore, it should be discussed in different cases.
3.4 The Foundation of Model
Data Envelopment Analysis (DEA), initially proposed by Charnes, Cooper and Rhodes [3], is a non-parametric technique for evaluating the relative efficiency of a set of homogeneous decision-making units (DMUs) with multiple inputs and multiple outputs by using a ratio of the weighted sum of outputs to the weighted sum of inputs.
2O
the number of victory session
3O
The number of equivalent champion 1Q
the number of regular games champion 2Q
the number of league games champion 3Q
the number of NCAA league games
champion
One of the basic DEA models used to evaluate DMUs efficiency is the input-oriented CCR model, which was introduced by Charnes, Cooper and Rhodes [1]. Suppose that there are n comparatively homogenous DMUs (Here, we look upon each coach as a DMU), each of which consumes the same type of m inputs and produces the same type of s outputs. All inputs and outputs are assumed to be nonnegative, but at least one input and one output are positive.
DMU k : the k th DMU, 1,2,
,=k n ;
0DMU : the target DMU, which is one of the n evaluated DMUs; ik x : the i th input variable consumed by DMU k , 1,2,,=i m ; 0i x : the i th input variable consumed by 0DMU , 1,2,
,=i m ; jk y : the j th output variable produced by DMU k , 1,2,,=j s ; 0j y : the j th output variable produced by 0DMU , 1,2,,=j s ;
i u : the i th input weight, 1,2,
,=i m ;
In DEA model, the efficiency of 0DMU , which is one of the n DMUs, is obtained by using a ratio of the weighted sum of outputs to the weighted sum of inputs under the condition that the ratio of every entity is not larger than 1. The DEA model is formulated by using fractional programming as follows:
()()0
11
11
12121,1,2,...,..,,,0,,,0max s
r
rj r m
j i
ij i s
r rj
r m i ij i T
m T
s j n s t v v v v u u u u y
u h
v x
y u v x =====
???≤=????=≥??=≥??
∑∑∑∑ （2）
The above model is a fractional programming model, which is equivalent to the
following linear programming model:
111
010,1,2,...,..1,0,1,2,..;1,2,...,max s
j r
rj r s
m
i ij r rj r i m i ij i i r j n s t i m r s
y
h
y w x w x w μ
μμ=====?-≤=???=???≥==??
∑∑∑∑ （3）
Turned to another form is:
01
1
min ..0,1,2,,n
j j j n j j j j x x s t j n
y y θ
λθθλλ==?≤????≥???≥=???∑∑无约束
3.5 Solution and Result
3.5.1 Establishing the input and output index system
In the DEA model, it requires defining a set of input index and a set of output index,
and all the indexes should be the common data for each coach. Regarding the team as an unit, then the contribution that the coach made to the team can be regarded as input, while the achievement that the team made can be regarded as reward. In the following, we take the basketball coaches of NACC as an example to establish the input and output index system. These input indexes could be chosen as follows: 1I :The length of coaching career
The more game seasons a coach takes part in, the more abundant experience he has. This ki nd of coach’s achievement is easily affirmed by others. As the Figure 1 shows, the famous coach mostly experienced the long-time coaching career.
Furthermore, the time the coach has contributed to the team is fundamental if they want to have a good result in the game. Thus the length of coaching career can be regarded as an index to evaluate the coach’s contribution to the team.
Figure 1 The relationship between the length of coaching career and the number of
champions
I: The number of taking part in NCAA tournament
2
Whether the coach takes the team to a higher level game has a direct influence on the team’s performance, and also it can reflect the coach’s coaching abilities, level and other factors.
I: coaching session
3
For the reason of layers of elimination, the coaching session is not necessarily determined by the length of coaching career. It can be shown in the comparison between Figure 2 and Figure 3. Thus the number of coaching session can also be regarded as an index.
Figure 2
These output indexes could be chosen as follows:
O: victory ratio of game
1
The index reflects the coach’s ability of command and control, and it a ttaches great importance to the evaluation of coach’s coaching abilities.
O: the number of victory session
2
The case that the number of victory session reflected is different from that of victory ratio, only if get the enough number of victory session in a large number of coaching session, the acquired high victory ratio can reflect the coach’s high coaching level. If the victory occurs in a limited games, this kind of high victory ratio can not reflect the rules. It can be shown in the comparison between Figure 3 and Figure 4.
Figure 3
Figure 4
3O :The number of equivalent champion
The honor that US college basketball teams acquired can be divided into three types: 1Q : the number of regular games champion; 2Q : the number of league games champion; 3Q : the number of NCAA league games champion. The three
championship honor has different levels, and their importance is increasing in turn according to the reference. The weight 0.2、0.3、0.5 can be given respectively, and the number of equivalent champion can be figured out and used as an output index, as it shown in Table 1.
5.0Q 3.0Q 2.0Q O 3213?+?+?=
Table 1
Coach names Number of regular games champion (weight 0.2) Number of league games champion (weight 0.3) Number of
NCAA league
games
champion
Number of
equivalent
champion
According to Internet, the data of input and output are given by Table 2.
Table 2
(weight 0.5)
Phog Allen 24 0 1 5.3 Fred Taylor 7 0 1 1.9 Hank Iba 15 0 2 4 Joe B. Hall 8 1 1 2.4 Billy Donovan 7 3 2 3.3 Steve Fisher 3 4 1 2.6 John Calipari 14 11 1 6.6 Tom Izzo 7 3 1 2.8 Nolan Richardso 9 6 1 3.9 John Wooden 16 0 10 8.2 Rick Pitino 9 11 2 6.1 Jerry Tarkanian 18 8 1 6.5 Adolph Rupp 28 13 4 11.5 John Thompson 7 6 1 3.7 Jim Calhoun 16 12 3 8.3 Denny Crum 15 11 2 7.3 Roy Williams 15 6 2 5.8 Dean Smith 17 13 2 8.3 Bob Knight 11 0 3 3.7 Lute Olson 13 4 1 4.3 Mike Krzyzewski 12 13 4 8.3 Jim Boeheim 11 5 1 4.2 Doc Meanwell 10 0 0 2 Ralph Jones 4 0 0 0.8 Francis Schmidt
6
1.2
Coach names
Input index
Output index
1I
2I
3I
1O 2O
3O
NCAA tourament The
length of coaching career
Coaching session Win-Lose %
Wins
Number of equivalent champion
Phog Allen 4
48
978
0.735 719 5.3 Fred Taylor 5 18 455 0.653 297 1.9 Hank Iba
8
40
1085
0.693
752
4
Since the opening of NACC tournament in 1938, thus the year 1938 is chosen as a time set apart. The finishing time point of coaching before 1938 is a period of time, while after 1938 is another period of time.
For the time period before 1938, take the length of coaching career 1I , coaching session 3I as input indexes, and then take W-L %1O , victory session 2O , the number of regular games champion 1Q as output indexes. The results is shown in Table 3 after the data statistics of each index.
For the time period after 1938, because they all take part in NACC, the input index and output index are just the same as that of all time period. The data statistics is just as shown in Table 3.
Table 3
Coach names
Input index
Output index
1I
3I
1O
2O
1Q
The length
of coaching
career
Coaching
session
W-L % Wins
Number of regular games champion
Joe B. Hall 10 16 463 0.721 334 2.4 Billy Donovan 13 20 658 0.714 470 3.3 Steve Fisher 13 24 739 0.658 486 2.6 John Calipari 14 22 756 0.774 585 6.6 Tom Izzo 16 19 639 0.717 458 2.8 Nolan Richardson 16 22 716 0.711 509 3.9 John Wooden 16 29 826 0.804 664 8.2 Rick Pitino 18 28 920 0.74 681 6.1 Jerry Tarkanian 18 30 963 0.79 761 6.5 Adolph Rupp 20 41 1066 0.822 876 11.5 John Thompson 20 27 835 0.714 596 3.7 Jim Calhoun 23 40 1259 0.697 877 8.3 Denny Crum 23 30 970 0.696 675 7.3 Roy Williams 23 26 902 0.793 715 5.8 Dean Smith 27 36 1133 0.776 879 8.3 Bob Knight 28 42 1273 0.706 899 3.7 Lute Olson 28 34 1061 0.731 776 4.3 Mike Krzyzewski 29 39 1277 0.764 975 8.3 Jim Boeheim
30
38
1256
0.75
942
4.2
Louis Cooke 27 380 0.654 248 5 Zora Clevenger 15 223 0.677 151 2 Harry Fisher 14 249 0.759 189 3 Ralph Jones 17 245 0.792 194 4 Doc Meanwell 22 381 0.735 280 10 Hugh McDermott 17 291 0.636 185 2 E.J. Mather 14 203 0.675 137 3 Craig Ruby 16 278 0.651 181 4 Francis Schmidt 17 330 0.782 258 6 Doc Stewart 15 291 0.663 193 2 James St. Clair
16
263
0.582
153
2
3.5.2 Solution and Result
In this section, take Phog Allen as an example and make calculation as follows:
Taking Phog Allen as 0DMU , then the input vector is 0x , the output vector is 0y , while the respective input and output weight vector are:
From the Figure 2 it can be inferred that
T x )978,48,4(0= T y )3.5,719,735.0(0=
After the calculation by LINGO then the efficiency value h 1 of DMU 1 is
0.9999992.
For other coaches, their efficiency value is figured out by the above calculation process as shown in Table 4.
Table 4
Coach names
Input index
Output index
Efficiency value 1I
2I
3I
1O 2O
3O
NCAA Tourna ment The
length of coachin g career
Coachin g session W-L % Wins Number of
equivalent champion
Joe B. Hall 10 16 463 0.721 334 2.4 1
John Wooden 16 29 826 0.804 664 8.2 1
John Calipari 14 22 756 0.774 585 6.6 1
Adolph Rupp 20 41 1066 0.822 876 11.5 1
Hank Iba 8 40 1085 0.693 752 4 1
Mike Krzyzewski 29 39 1277 0.764 975 8.3 1
Roy Williams 23 26 902 0.793 715 5.8 1
Jerry Tarkanian 18 30 963 0.79 761 6.5 0.9999997 Fred Taylor 5 18 455 0.653 297 1.9 0.9999996 Phog Allen 4 48 978 0.735 719 5.3 0.9999992 Tom Izzo 16 19 639 0.717 458 2.8 0.9785362 Dean Smith 27 36 1133 0.776 879 8.3 0.9678561 Jim Boeheim 30 38 1256 0.75 942 4.2 0.941031 Billy Donovan 13 20 658 0.714 470 3.3 0.9405422 Rick Pitino 18 28 920 0.74 681 6.1 0.9401934 Nolan Richardson 16 22 716 0.711 509 3.9 0.920282 Lute Olson 28 34 1061 0.731 776 4.3 0.9114966 John Thompson 20 27 835 0.714 596 3.7 0.8967647 Jim Calhoun 23 40 1259 0.697 877 8.3 0.8842854 Denny Crum 23 30 970 0.696 675 7.3 0.8823837 Bob Knight 28 42 1273 0.706 899 3.7 0.8769902 Steve Fisher 13 24 739 0.658 486 2.6 0.8543039
For those coaches in the time period after 1938, the efficiency values, which is shown in Table 5, are figured out from the similar calculation process as Phog Allen.
Table 5
Coach names
Input index Output index
Efficiency
value 1
I
3
I
1
O
2
O
1
Q
The
length
of
coachin
g career
Coachin
g session
W-L % Wins
Number
of regular
champion
Doc Meanwell 22 381 0.735 280 10 1
Francis Schmidt 17 330 0.782 258 6 1
Ralph Jones 17 245 0.792 194 4 1
E.J. Mather 14 203 0.675 137 3 0.9999999
Harry Fisher 14 249 0.759 189 3 0.999999 Zora Clevenger 15 223 0.677 151 2 0.9328517 Doc Stewart 15 291 0.663 193 2 0.8910155 Craig Ruby 16 278 0.651 181 4 0.859112 Louis Cooke 27 380 0.654 248 5 0.8241993 Hugh McDermott 17 291 0.636 185 2 0.8091489 James St. Clair 16 263 0.582 153 2 0.7468237
Choose basketball, football and field hockey and make calculations
The calculation result statistics of basketball is shown in Table 4.
The calculation result statistics of football is shown in Table 6.
Table 6
Coach Names
Input index Output index
Efficiency
value Total of
the Bowl
The
length of
coaching
career
Coachi
ng
session
W-L % Wins
Number
of
champion
Phillip Fulmer 15 17 204 0.743 151 8 1 Tom Osborne 25 25 307 0.836 255 12 1 Dan Devine 10 22 238 0.742 172 7 1 Bobby Bowden 33 40 485 0.74 357 22 1 Pat Dye 10 19 220 0.707 153 7 1 Bobby Dodd 13 22 237 0.713 165 9 1
Bo Schembechler 17 27 307 0.775 234 5 1 Woody Hayes 11 28 276 0.761 205 5 1.000001 Joe Paterno 37 46 548 0.749 409 24 1 Nick Saban 14 18 228 0.748 170 8 0.9999993 Darrell Royal 16 23 249 0.749 184 8 0.9653375 John Vaught 18 25 263 0.745 190 10 0.9648578 Steve Spurrier 19 24 300 0.733 219 9 0.9639218 Bear Bryant 29 38 425 0.78 323 15 0.9623039 LaVell Edwards 22 29 361 0.716 257 7 0.9493463 Terry Donahue 13 20 233 0.665 151 8 0.9485608 John Cooper 14 24 282 0.691 192 5 0.94494 Mack Brown 21 29 356 0.67 238 13 0.9399592 Bill Snyder 15 22 269 0.664 178 7 0.9028372 Ken Hatfield 10 27 312 0.545 168 4 0.9014634 Fisher DeBerry 12 23 279 0.608 169 6 0.9008829 Don James 15 22 257 0.687 175 10 0.8961777
Bill Mallory 10 27 301 0.561 167 4 0.8960976 Ralph Jordan 12 25 265 0.674 175 5 0.8906943 Frank Beamer 21 27 335 0.672 224 9 0.8827047 Don Nehlen 13 30 338 0.609 202 4 0.8804766 Vince Dooley 20 25 288 0.715 201 8 0.8744984 Jerry Claiborne 11 28 309 0.592 179 3 0.8731701 Lou Holtz 22 33 388 0.651 249 12 0.8682463 Bill Dooley 10 26 293 0.558 161 3 0.8639017 Jackie Sherrill 14 26 304 0.595 179 8 0.8435327 Bill Yeoman 11 25 276 0.594 160 6 0.8328854 George Welsh 15 28 325 0.588 189 5 0.820513 Johnny Majors 16 29 332 0.572 185 9 0.807564 Hayden Fry 17 37 420 0.56 230 7 0.792591
The calculation result statistics of field hockey is shown in Table 7.
Table 7
Coach names
Input index Output index
Efficiency
value Total of
the Bowl
The
length of
coaching
career
Coachi
ng
session
W-L % Wins
Number
of
champio
n
Fred Shero 110 10 734 0.612 390 2 1 Mike Babcock 131 11 842 0.63 470 1 1 Claude Julien 97 11 749 0.61 411 1 1 Joel Quenneville 163 17 1270 0.617 695 2 1 Ken Hitchcock 136 17 1213 0.602 642 1 1 Marc Crawford 83 15 1151 0.556 549 1 0.9999998 Scotty Bowman 353 30 2141 0.657 1244 9 0.9999996 Hap Day 80 10 546 0.549 259 5 0.9999995 Toe Blake 119 13 914 0.634 500 8 0.9999994 Eddie Gerard 21 11 421 0.486 174 1 0.999999 Art Ross 65 18 758 0.545 368 1 0.9854793 Peter Laviolette 82 12 759 0.57 389 1 0.9832692 Bob Hartley 84 11 754 0.56 369 1 0.9725678 Jacques Lemaire 117 17 1262 0.563 617 1 0.9706553 Glen Sather 127 13 932 0.602 497 4 0.9671556 John Tortorella 89 14 912 0.541 437 1 0.9415468 John Muckler 67 10 648 0.493 276 1 0.9379403 Lester Patrick 65 13 604 0.554 281 2 0.9246999 Mike Keenan 173 20 1386 0.551 672 1 0.8921282 Al Arbour 209 23 1607 0.564 782 4 0.8868355 Frank Boucher 27 11 527 0.422 181 1 0.8860263
Pat Burns 149 14 1019 0.573 501 1 0.8803399 Punch Imlach 92 14 889 0.537 402 4 0.8795251
Darryl Sutter 139 14 1015 0.559 491 1 0.8754745
Dick Irvin 190 27 1449 0.557 692 4 0.8688287
Jack Adams 105 20 964 0.512 413 3 0.8202896 Jacques Demers 98 14 1007 0.471 409 1 0.7982191 3.6 sensitivity analysis
When determining the number of equivalent champion, the weight coefficient is artificially determined. During this process, different people has different confirming method.Consequently, we should consider that when the weight coefficient changes in a certain range, what would happen for the evaluation result?
For the next step, we will take the basketball coaches as example to illustrate the above-mentioned case.The weight coefficient changes is given by Table 12. The changes of evaluation results is shown in Table 13.
Table 12
Coach names Number of
regular
games
champion
(weight
0.2)
Number of
league
games
champion
(weight 0.4)
Number of
NCAA league
games
champion(weight
0.4)
Number of
equivalent
champion
Phog Allen 24 0 1 5.2 Fred Taylor 7 0 1 1.8 Hank Iba 15 0 2 3.8 Joe B. Hall 8 1 1 2.4 Billy Donovan 7 3 2 3.4 Steve Fisher 3 4 1 2.9 John Calipari 14 11 1 7.6 Tom Izzo 7 3 1 3 Nolan
Richardso
9 6 1 4.4 John Wooden 16 0 10 7.2 Rick Pitino 9 11 2 7 Jerry
Tarkanian
18 8 1 7.2 Adolph Rupp 28 13 4 12.4 John
Thompson
7 6 1 4.2 Jim Calhoun 16 12 3 9.2 Denny Crum 15 11 2 8.2 Roy Williams 15 6 2 6.2
Dean Smith 17 13 2 9.4 Bob Knight 11 0 3 3.4 Lute Olson 13 4 1 4.6 Mike
Krzyzewski
12 13 4 9.2 Jim Boeheim 11 5 1 4.6
Table 13
Coach names
I nput index O utput index
Efficiency
value 1
I
2
I
3
I
1
O
2
O
3
O
NCAA
Tourna
ment
The
length of
coaching
Career
Coachi
ng
session
W-L %Wins
Number of
equivalent
champion
John Wooden 16 29 826 0.804 664 7.2 1.395729 John Calipari 14 22 756 0.774 585 7.6 1.318495 Joe B. Hall 10 16 463 0.721 334 2.4 1.220644 Adolph Rupp 20 41 1066 0.822 876 12.4 1.157105
Hank Iba 8 40 1085 0.693 752 3.8 1.078677 Roy Williams 23 26 902 0.793 715 6.2 1.034188 Fred Taylor 5 18 455 0.653 297 1.8 1.013679 Jerry Tarkanian 18 30 963 0.79 761 7.2 1.007097 Phog Allen 4 48 978 0.735 719 5.2 0.999999 Jim Boeheim 30 38 1256 0.75 942 4.6 0.984568
Tom Izzo 16 19 639 0.717 458 3 0.978536 Dean Smith 27 36 1133 0.776 879 9.4 0.96963
Mike Krzyzewski 29 39 1277 0.764 975 9.2 0.960445 Rick Pitino 18 28 920 0.74 681 7 0.940614 Billy Donovan 13 20 658 0.714 470 3.4 0.940542 Nolan Richardson 16 22 716 0.711 509 4.4 0.920282 Lute Olson 28 34 1061 0.731 776 4.6 0.911496 John Thompson 20 27 835 0.714 596 4.2 0.896765 Jim Calhoun 23 40 1259 0.697 877 9.2 0.884227 Denny Crum 23 30 970 0.696 675 8.2 0.882805 Bob Knight 28 42 1273 0.706 899 3.4 0.87699 Steve Fisher 13 24 739 0.658 486 2.9 0.854304
From the Table 13, it can been seen that the top 5 coaches are: John Wooden, John Calipari, Joe B. Hall, Adolph Rupp, Hank Iba. The result is in accordance with
the result that occurred before the weight changes. The fact suggested that the established model has a good sensitivity.
3.7 Analysis of the Result
From the data analysis of Table 4 it can be known:
Taking the basketball for example, the ―best all time college coach‖ appraised by the model is Joe B. Hall.
From the comparison of the best popular coach on the Internet, we find that the calculating result is essentially the same with the online result. It suggests that the model can be applied to the assessment of coach with certain objectivity and scientificity.
From the data analysis of Table 5 it can be known:
The calculating result is essentially the same with the universally acknowledged best coach.
Thus, the model is not only applicable for the existing coaches but also for the previous coaches, and different time periods have little influence on model result. It is accepted that change the input and output indexes according to the actual data in different time periods.
From the Table 4 it can be known that the top five basketball coaches are: Joe B. Hall、John Wooden、John Calipari、Adolph Rupp、Hank Iba
From the Table 6 it can be known that the top five football coaches are:
Phillip Fulmer、Tom Osborne、Dan Devine、Bobby Bowden、Pat Dye
From the Table 7 it can be known that the top five field hockey coaches are:
Fred Shero、Mike Babcock、Claude Julien、Joel Quenneville、Ken Hitchcock
3.8 Strength and Weakness
●Strength:
The model avoided the confirmation of weight value of each index in priority.
It is not necessarily to confirm the explicit expression between input and output.
●Weakness:
All indexes should be datamation, and some non-quantization data is not
applicable.
After the first assessment, it also need the further assessment if the result is
1 and can not be sorted.
IV . Improved Model
4.1 super- efficiency DEA model
In order to make up the weakness that the coaches can not be sorted in the last model, then the super efficient DEA model is introduced. The further calculation to the coach who get the 1 in the first evaluation is needed to achieve the rank result. The ordering method of super efficient DEA model remove the restraint of DMU j0 (if available) on CCR model, thus to make the effective DMU j0 get the efficiency value higher or equal to 1, and it is not the invariability of efficiency value of the effective unit. The model is shown as follows:
,01
00
10
min s.t.
0,1,2,,,.
n
i i
i i n
i i
i i i x
x y
y i n R λθ
θ
λθλλθ=≠=≠≤≥≥=∈∑∑
The main differences between the model and the last one is that the restraint condition of assessed DMU is different: The restraint condition of the last model is the linear combination of all 0
j DMU , that is to make a comparison between DMU and
the linear combination of all 0
j DMU , but the restraint condition of the model doesn’t
include the 0
j DMU . In other words, when evaluate 0
j DMU by using the model, the
input and output is replaced by the linear combination of all other 0
j DMU ’s input and
output, but the DMU itself is not included. Because the effective decision making unit is on the frontier of the production, if it is removed and the frontier is changed, then the efficiency value is also changed, but the invalid decision making making units lies in the lower part of the frontier, it will not change the frontier’s place when it is removed with the invariant efficiency value. Thus, in the super efficient DEA model, for those invalid decision making unit, the efficiency value is in accordance
承诺书 我们仔细阅读了中国大学生数学建模竞赛的竞赛规则. 我们完全明白，在竞赛开始后参赛队员不能以任何方式（包括、电子、网上咨询等）与队外的任何人（包括指导教师）研究、讨论与赛题有关的问题。 我们知道，抄袭别人的成果是违反竞赛规则的, 如果引用别人的成果或其他公开的 资料（包括网上查到的资料），必须按照规定的参考文献的表述方式在正文引用处和参 考文献中明确列出。 我们重承诺，严格遵守竞赛规则，以保证竞赛的公正、公平性。如有违反竞赛规则 的行为，我们将受到严肃处理。 我们授权全国大学生数学建模竞赛组委会，可将我们的论文以任何形式进行公开展 示（包括进行网上公示，在书籍、期刊和其他媒体进行正式或非正式发表等）。 我们参赛选择的题号是（从A/B/C/D中选择一项填写）： 我们的参赛报名号为（如果赛区设置报名号的话）： 所属学校（请填写完整的全名）： 参赛队员 (打印并签名) ：1. 2. 3. 指导教师或指导教师组负责人 (打印并签名)： 日期：年月日赛区评阅编号（由赛区组委会评阅前进行编号）：
编号专用页 赛区评阅编号（由赛区组委会评阅前进行编号）： 全国统一编号（由赛区组委会送交全国前编号）：全国评阅编号（由全国组委会评阅前进行编号）：
题目（黑体不加粗三号居中） 摘要（黑体不加粗四号居中） （摘要正文小4号，写法如下） （第1段）首先简要叙述所给问题的意义和要求，并分别分析每个小问题的特点（以下以三个问题为例）。根据这些特点对问题 1 用······的方法解决；对问题 2 用······的方法解决；对问题3 用······的方法解决。 （第2段）对于问题1，用······数学中的······首先建立了······ 模型I。在对······模型改进的基础上建立了······模型II。对模型进行了合理的理论证明和推导，所给出的理论证明结果大约为······，然后借助于······数学算法和······软件，对附件中所提供的数据进行了筛选，去除异常数据,对残缺数据进行适当补充,并从中随机抽取了3 组数据（每组8 个采样）对理论结果进行了数据模拟，结果显示，理论结果与数据模拟结果吻合。（方法、软件、结果都必须清晰描述，可以独立成段，不建议使用表格） （第3段）对于问题2用······ （第4段）对于问题3用······ 如果题目单问题，则至少要给出2种模型，分别给出模型的名称、思想、软 件、结果、亮点详细说明。并且一定要在摘要对两个或两个以上模型进行比较， 优势较大的放后面，这两个（模型）一定要有具体结果。 （第5段）如果在……条件下，模型可以进行适当修改，这种条件的改变可能来自你的一种猜想或建议。要注意合理性。此推广模型可以不深入研究，也可以没有具体结果。 关键词：本文使用到的模型名称、方法名称、特别是亮点一定要在关键字里出现，5~7个较合适。 注：字数700-1000 之间；摘要中必须将具体方法、结果写出来；摘要写满几乎 一页，不要超过一页。摘要是重中之重，必须严格执行！。 页码：1（底居中）
2014年数学建模美赛题目原文及翻译 作者：Ternence Zhang 转载注明出处：https://www.doczj.com/doc/4b3840188.html,/zhangtengyuan23 MCM原题PDF： https://www.doczj.com/doc/4b3840188.html,/detail/zhangty0223/6901271 PROBLEM A: The Keep-Right-Except-To-Pass Rule In countries where driving automobiles on the right is the rule (that is, USA, China and most other countries except for Great Britain, Australia, and some former British colonies), multi-lane freeways often employ a rule that requires drivers to drive in the right-most lane unless they are passing another vehicle, in which case they move one lane to the left, pass, and return to their former travel lane. Build and analyze a mathematical model to analyze the performance of this rule in light and heavy traffic. You may wish to examine tradeoffs between traffic flow and safety, the role of under- or over-posted speed limits (that is, speed limits that are too low or too high), and/or other factors that may not be
PROBLEM A: The Keep-Right-Except-To-Pass Rule In countries where driving automobiles on the right is the rule (that is, USA, China and most other countries except for Great Britain, Australia, and some former British colonies), multi-lane freeways often employ a rule that requires drivers to drive in the right-most lane unless they are passing another vehicle, in which case they move one lane to the left, pass, and return to their former travel lane. Build and analyze a mathematical model to analyze the performance of this rule in light and heavy traffic. You may wish to examine tradeoffs between traffic flow and safety, the role of under- or over-posted speed limits (that is, speed limits that are too low or too high), and/or other factors that may not be explicitly called out in this problem statement. Is this rule effective in promoting better traffic flow? If not, suggest and analyze alternatives (to include possibly no rule of this kind at all) that might promote greater traffic flow, safety, and/or other factors that you deem important. In countries where driving automobiles on the left is the norm, argue whether or not your solution can be carried over with a simple change of orientation, or would additional requirements
数学建模美赛公式 由假设得到公式 1．W e assume laminar flow and use Bernoulli’s equation:（由假设得到的公式） 公式 W here 符号解释 A ccording to the assumptions, at every junction we have （由于假设） 公式 由原因得到公式 2．Because our field is flat, we have公 式, so the height of our source relative to our sprinklers does not affect the ex it speed v2 （由原因得到的公式）； 公式 S ince the fluid is incompressible(由于液体是不可压缩的), we have 公式 W here 公式 用原来的公式推出公式 3．P lugging v1 into the equation for v2 ,we obtain （将公式1代入公式2中得到） 公式 11．P utting these together(把公式放在一 起), because of the law of conservation of energy, yields： 公式 12．T herefore, from (2),(3),(5), we have the ith junction（由前几个公式得） 公式 P utting (1)-(5) together, we can obtain pup at every junction . in fact, at th e last junction, we have 公式 P utting these into (1) ,we get（把这些公式代入1中） 公式 W hich means that the C ommonly, h is about F rom these equations, （从这个公式中我们知道）we know that ……… 引出约束条件 4．Using pressure and discharge data from Rain Bird 结果, W e find the attenuation factor （得到衰减因子，常数，系数）to be 公式 计算结果 6．T o find the new pressure ,we use the ( 0 0),which states that the volume of water flowing in equals the volume of water flowing out : （为了找到新值，我们用什么方程）
A题 The world medical association has announced that their new medication could stop Ebola and cure patients whose disease is not advanced. Build a realistic, sensible, and useful model that considers not only the spread of the disease, the quantity of the medicine needed, possible feasible delivery systems, locations of delivery, speed of manufacturing of the vaccine or drug, but also any other critical factors your team considers necessary as part of the model to optimize the eradication of Ebola, or at least its current strain. In addition to your modeling approach for the contest, prepare a 1-2 page non-technical letter for the world medical association to use in their announcement. 世界医学协会日前宣布，其新的药物可以阻止埃博拉病毒和治愈患者的疾病，谁的病没有进入晚期。因此，建立一个现实的、合理的，并且有用的模型是认为制造的疫苗或药物的不仅是这种疾病的传播、所述药物的所需要的数量、可能的可行交付系统、交付地点、制造的疫苗或药物的速度，但也可以是任何你的团队认为有必要为模型做贡献的其他关键因素，以便优化消灭埃博拉病毒或者至少抑制其目前的压力。除了为大赛的建模方法，你的队伍还需要准备为世界医学协会发表公告的一份1-2页非技术性的信。
PROBLEM A: Eradicating（根除）Ebola The world medical association has announced that their new medication could stop Ebola and cure patients whose disease is not advanced（晚期的）. Build a realistic, sensible, and useful model that considers not only the spread of the disease, the quantity of the medicine needed, possible feasible （可行的）delivery systems, locations of delivery, speed of manufacturing of the vaccine or drug, but also any other critical factors your team considers necessary as part of the model to optimize the eradication of Ebola, or at least its current strain（压力）. In addition to your modeling approach for the contest, prepare a 1-2 page non-technical letter for the world medical association to use in their announcement. PROBLEM B: Searching for a lost plane Recall the lost Malaysian flight MH370. Build a generic（一般的）mathematical model that could assist "searchers" in planning a useful search for a lost plane feared to（恐怕） have crashed in open water such as the Atlantic, Pacific, Indian, Southern, or Arctic Ocean while flying from Point A to Point B. Assume that there are no signals from the downed （坠落的） plane. Your model should recognize that there are many different types of planes for which we might be searching and that there are many different types of search planes, often using different electronics or sensors. Additionally, prepare a 1-2 page non-technical paper for the airlines to use in their press conferences concerning their plan for future searches.
马剑整理 历年美国大学生数学建模赛题 目录 MCM85问题-A 动物群体的管理 (3) MCM85问题-B 战购物资储备的管理 (3) MCM86问题-A 水道测量数据 (4) MCM86问题-B 应急设施的位置 (4) MCM87问题-A 盐的存贮 (5) MCM87问题-B 停车场 (5) MCM88问题-A 确定毒品走私船的位置 (5) MCM88问题-B 两辆铁路平板车的装货问题 (6) MCM89问题-A 蠓的分类 (6) MCM89问题-B 飞机排队 (6) MCM90-A 药物在脑内的分布 (6) MCM90问题-B 扫雪问题 (7) MCM91问题-B 通讯网络的极小生成树 (7) MCM 91问题-A 估计水塔的水流量 (7) MCM92问题-A 空中交通控制雷达的功率问题 (7) MCM 92问题-B 应急电力修复系统的修复计划 (7) MCM93问题-A 加速餐厅剩菜堆肥的生成 (8) MCM93问题-B 倒煤台的操作方案 (8) MCM94问题-A 住宅的保温 (9) MCM 94问题-B 计算机网络的最短传输时间 (9) MCM-95问题-A 单一螺旋线 (10) MCM95题-B A1uacha Balaclava学院 (10) MCM96问题-A 噪音场中潜艇的探测 (11) MCM96问题-B 竞赛评判问题 (11) MCM97问题-A Velociraptor(疾走龙属)问题 (11) MCM97问题-B为取得富有成果的讨论怎样搭配与会成员 (12) MCM98问题-A 磁共振成像扫描仪 (12) MCM98问题-B 成绩给分的通胀 (13) MCM99问题-A 大碰撞 (13) MCM99问题-B “非法”聚会 (14) MCM2000问题-A空间交通管制 (14) MCM2000问题-B: 无线电信道分配 (14) MCM2001问题- A: 选择自行车车轮 (15) MCM2001问题-B 逃避飓风怒吼（一场恶风...） .. (15) MCM2001问题-C我们的水系-不确定的前景 (16) MCM2002问题-A风和喷水池 (16) MCM2002问题-B航空公司超员订票 (16) MCM2002问题-C (16) MCM2003问题-A: 特技演员 (18)
连环作案嫌疑人“地理轮廓”估计的统计模型 摘要：在不同地点发生的系列谋杀案对社会的危害极大，如何确定其犯罪嫌疑人的住所是破案的关键。对犯罪嫌疑人住所的估计，给出了3种方法，即圆周假设、质心法和最小距离法，通过对比验证表明，最小距离法较优；一般犯罪分子都会选择”不近不远”的作案地点，基本上服从二维正态分布。同时考虑犯罪分子的心理特征，作案方式等进一步对模型进行优化，得出更合理的模型，提高对连环作案的案件的效率。 关键字：连环作案、圆周假设、质心法、最小距离、概率分布一．问题叙述： 1.1问题重述 1981年Peter Sutcliffe(萨克利夫)被判刑因为他参与了十三起谋杀和对其他人的恶毒攻击。缩小搜索Sutcliffe的方法之一是发现一个攻击位置的“质心”.最终犯罪嫌疑人恰好生活在该方法预测的同一个小镇。从那时起，已经发展出一系列更加复杂的技术用来预测基于犯罪地点的具有地理效应（地理轮廓）的系列犯罪行为。 你的团队被一个当地警察局要求发展出一种方法用来帮助他们的系列犯罪调查。 （1）你们的方法应该至少需要利用两种不同的情景以生成地理效应（地理轮廓），进而根据不同情况下的分析结果对执法人员提供有效的预测。 （2）基于以往犯罪的时间和位置，预测信息应该提供一些估计或指导下次可能的犯罪地点。如果在预测中用到了其它的信息，必须提供特别的细节说明告诉我们这些信息是如何被整合的。 （3）你们的方法中也应该包括在给定条件下（包括适当警告信息）下预测的可靠性估计。 1.2“地理画像” 地理轮廓是是一项刑事调查方法,分析确定最有可能的罪犯居住面积确定的罪行的连接一连串的位置。通过采用定性和定量的方法，它有助于理解空间的违法行为和针对较小的区域的社会调查。通常用于在连环谋杀或强奸（但还纵火，轰炸，抢劫及其他犯罪）的情况下，技术可帮助警方侦探优先考虑大规模的重大犯罪调查，往往需要成百上千个嫌疑人和提示中的信息。基本原则是犯罪相关的地点提供关于受害人的资料和罪犯的与地理环境的相互作用。它甚至可以显示罪犯对周边地理情况的熟悉程度和罪犯对安全距离的界定，可以反映了他的非刑事空间生活方式方面即其居住地的规划。 二．模型假设： 由于犯罪活动的巨大变动以及几乎所有连环杀人案的凶手通常患有心理疾病，所以采用相对简单的计算机模型去预测连环杀人案一般都面临几个障碍。以下是应用我们模型的对犯罪行为所采取的假设： 犯罪是单独作案的。我们假设模型中的案件都是由单独个体作案的，我们的模型不对有组织的犯罪，团伙犯罪和暴动进行分析。
问题A 空间交通管制 为加强安全并减少空中交通指挥员的工作量，联邦航空局(FAA)考虑对空中交通管制系统添加软件，以便自动探测飞行器飞行路线可能的冲突，并提醒指挥员。为完成此项工作，FAA的分析员提出了下列问题。 要求A: 对于给定的两架空中飞行的飞机，空中交通指挥员应在什么时候把该目标视为太靠近，并予以干预。 要求B: 空间扇形是指某个空中交通指挥员所控制的三维空间部分。给定任意一个空间扇形，我们怎样从空中交通工作量的方位来估量它是否复杂当几个飞行器同时通过该扇形时,在下面情形所确定的复杂性会达到什么程度：（1）在任一时刻（2）在任意给定的时间范围内（3）在一天的特别时间内在此期间可能出现的冲突总数是怎样影响着复杂性来的 提出所添加的软件工具对于自动预告冲突并提醒指挥员，这是否会减少或增加此种复杂性 在作出你的报告方案的同时，写出概述（不多于二页）使FAA分析员能提交给FAA当局Jane Garvey ，并对你的结论进行答辩。
问题B 无线电信道分配 我们寻找无线电信道配置模型.在一个大的平面区域上设置一个传送站的均衡網絡,以避免干扰.一个基本的方法是将此区域分成正六边形的格子(蜂窝状),如图 1.传送站安置在每个正六边形的中心点. 容许频率波谱的一个区间作为各传送站的频率.将这一区间规则地分割成一些空间信道,用整数1,2,3,…来表示.每一个传送站将被配置一正整数信道.同一信道可以在许多局部地区使用,前提是相邻近的传送站不相互干扰. 根据某些限制设定的信道需要一定的频率波谱,我们的目标是极小化频率波谱的这个区间宽度.這可以用跨度这一概念.跨度是某一个局部区域上使用的最大信道在一切滿足限制的配置中的最小值.在一个获得一定跨度的配置中不要求小于跨度的每一信道都被使用. 令s为一个正六边形的一侧的长度.我们集中考虑存在两种干扰水平的一种情况. 要求A: 频率配置有几个限制,第一,相互靠近的两个传送站不能配给同一信道.第二,由于波谱的传播,相互距离在2s內的传送站必须不配给相同或相邻的信道,它们至少差2.在這些限制下,关于跨度能说些什么. 要求B: 假定前述图1中的格子在各方向延伸到任意远,回答要求A. 要求C: 在下述假定下,重复要求A和B.更一般地假定相互靠近的传送站的信道至少差一个给定的整数k,同时那些隔开一点的保持至少差1.关于跨度和关于设计配置的有效策略作为k的一个函数能说点什么. 要求D: 考虑问题的一般化,比如各种干扰水平,或不规则的传送站布局.其他什么因素在考虑中是重要的. 要求E: 写一篇短文(不超过两页)给地方报纸,阐述你的发现. 问题：大象题 大象群落的兴衰归根到底，如果象群对于栖息地造成不尽人意的影响，就要考虑对它们的驱除，即使是运用淘汰法则。国家地理杂志（地球年鉴）1999年12月 在位于南非的一个巨大的国家公园里，栖息着近乎11000只象。管理策略要求一个健康的环境
2018MCM Problem A: 多跳短波无线电传播 背景：在高频率（HF，定义为3 - 30兆赫），无线电波可以长途旅行（从地球表面的 一个点到地球表面的另一个遥远的地方）通过电离层和地球以外的多次反射。下面的最高可用频率（MUF），高频无线电波从地面源反映了电离层返回地球，在那里他们可以 再次回到电离层反射，在那里他们可以再次回到地球的反映，等等，旅行还与每个连 续跳。在其他因素中，反射表面的特性决定了反射波的强度，以及信号在保持有用信 号完整性的情况下最终会传播多远。而且，随着季节的变化，白天的时间和太阳的条 件也不同。上面的MUF频率不是反射和折射，但通过电离层进入太空。在这个问题上，重点特别是海面上的反射。经验发现，在汹涌的海洋中，反射比平静的海面上的反射 减弱。海洋湍流将影响海水的电磁梯度，改变海洋的局部介电常数和磁导率，改变反 射面的高度和角度。一个汹涌的海洋，其中浪高、形状和频率变化很快，波的传播方向也可能改变。 问题： 第一部分：建立海洋信号反射的数学模型。一个100瓦的高频恒定载波信号，低于MUF，从陆地上的点源，确定第一反射强度和湍流海洋用了平静的海洋的第一反射强度的比较。（注意，这意味着这个信号在电离层上有一次反射）如果额外的反射（2到n）在平静 的海洋上发生，那么信号在强度低于可用的信噪比（SNR）阈值10分贝之前，可以达到的最大跳数是多少？ 第二部分：你如何从第一部分的调查结果与HF反射在山区或崎岖的地形与光滑的地形 比较？ 第三部分：穿越海洋的船将使用短波进行通信，并接收天气和交通报告。你的模型如何改变以适应船上的接收器在湍流的海洋上行驶？使用相同的多跳路径，船舶能保持多长时间通信？ 第四部分：准备一份简短的（1到2页）你的结果概要，适合作为IEEE通讯杂志中的简短说明发表。 您的提交应包括： ?一页摘要表， ?两页简介， ?你的解决方案不超过20页，最多有23页的摘要和概要。 注：参考清单和任何附录不计入23页的限制，并应在您完成的解决方案之后出现。
数学建模中必须注意的七点 《Word 在论文写作中的技巧》、《计算机算法设计与分析》一、看论文 说到看论文啊，我真是觉得，优秀的论文就像《九阴真经》一样，看了之后会让你功力大增的。大家一定要多看，特别是想在数学建模竞赛中取得好成绩的朋友。看过论文之后，明白的不仅仅是论文要怎么写，也在同时学到了作者的思考方式。我建议，有决心的朋友不如背几篇优秀论文。 很多优秀的论文，其高明之处并不是用了多少数学知识，而是思维比较全面，切合实际，能解决问题或是有所创新。有时候，在论文中可能碰见一些没有学过的知识，怎么办？现学现用呗，在优秀论文中用过的数学知识就是最有可能在数学建模竞赛中用到的，你当然有必要去翻一翻啦。 二、做数学建模题的小经验 顺便说一点儿做数学建模题的小经验。 1. 随时记下自己的假设。有时候在自己很合理的假设下开始了下一步的工作，我们就应该顺手把这个假设给记下来，否则到了最后会搞忘记的。而且这也会让我们的解答更加严谨。 2. 随时记录自己的想法，并且不留余地的完全的表达自己的思想。在比赛后，老师讲评优秀论文时，有很多同学常常抱
怨，这个想法我也想到了的啊，就是没有表达出来，或是没有表达清楚。但常常就是这一点别人没有表达清楚的东西，促成了一篇优秀论文。 3. 要有自己的特色。这么多数学建模竞赛论文，凭什么让老师们投自己一票？当然得有自己的特色了。通俗点儿，就是要有自己的闪光点即使面对的是无法超越的崖，也要勇敢的跳过去。不试，你怎么知道呢？没有必要去学那么多的东西，数学建模竞赛，竞赛而已。 三、时间分配 竞赛中时间分配也很重要，分配不好可能完不成论文，所以开始时要大致做一下安排。不必分的太细，比如第一天做第一小题，第二天做第二小题，这样反而会有压力，一切顺其自然。开始阶段不忙写作，可以将一些小组讨论的要点记录下来，不要太工整，随便写一下，到第三天再开始写论文也不迟的。也不要象偶去年到第三天晚上才开始，还好自己那时体力好，全部写完了。另外要说的就是体力要跟上，三天一般睡眠只有不到10 个小时，所以没有体力是不行的，建议是赛前熬夜编程几次，既训练了自己的建模能力，也达到了训练体力的目的，赛前锻炼身体我觉得没什么用处，多熬夜就行了，但比赛前一天可不许熬呀，呵呵 四、摘要写法 摘要首先不要写废话，也不要照抄题目的一些话，直奔主题，
美赛数学建模专用- 第三章MATLAB程序设计基础 chapter 3: Foundation of MATLAB program design 一、数据及数据文件(Data and Data file) 1. 数据类型：(Data mode)用于编程和计算的数据类型（表3—1） 数组： 字符数组(Character array)、 数值数组(Numeric array)— 包括整形(int8,uint8,int16,uint16,int32,uint32)单精度 (signal), 双精度(duble)（MATLAB最常用的变量类型）, 稀疏（sparce）数组。、 Int---Integrate. Uint---Unsigned Integer data 单元数组(Cell array)、 结构数组(Structure array) Java类（Java class） 函数句柄(Function handle) 在工作空间浏览器中不同的数据类型有着不同的图标标识，（见图3—2）_ 2. 数据文件(Data file) MATLAB支持的各种数据文件(Readable file formats of MATLAB)及其调用方法和返回值见（表3—2） （1）二进制数据文件:(Binary date file)以.mat为扩展名。是标准的MATLAB数据文件，以二进制编码形式存储。.mat文件可以由MATLAB提供的save和load命令直接存取。 （2）ASCⅡ码数据文件：（ASCⅡcode data file）扩展名为.txt, .dat
等，可以是在MATLAB环境下存储的，也可能是其他软件的计算结果，可以被MATLAB调用，也可以用文本编辑器打开进行观察与修改。可以用save和load命令进行读入和存取。 (3).图象文件:(Graphics file)扩展名为.bmp, .jpg .tif等，用于图形图象处理，可以用imread和imwrite命令进行读入和存取。 (4).声音文件:(Sound file) 扩展名为.wav ,用waveread和wavwrite 命令进行读入和存取。 Readable file formats. Data formats Command Returns MAT- MATLAB workspace load Variables in file. CSV- Comma separated numbers csvread Double array. DAT- Formatted text importdata Double array. DLM- Delimited text dlmread Double array. TAB- Tab separated text dlmread Double array. Spreadsheet formats XLS - Excel worksheet xlsread Double array and cell array. WK1- Lotus 123 worksheet wk1read Double array and cell array. Scientific data formats CDF - Common Data Format cdfread Cell array of CDF records FITS- Flexible Image Transport System fitsread Primary or extension table data HDF - Hierarchical Data Format hdfread HDF or HDF-EOS data set Movie formats A VI - Movie aviread MATLA B movie. Image formats TIFF - TIFF image imread Truecolor, grayscale or indexed image(s). PNG - PNG image imread Truecolor, grayscale or indexed image. HDF - HDF image imread Truecolor or indexed image(s). BMP - BMP image imread Truecolor or indexed image. JPEG - JPEG image imread Truecolor or grayscale image. GIF - GIF image imread Indexed image. PCX - PCX image imread Indexed image. XWD - XWD image imread Indexed image. CUR - Cursor image imread Indexed image. ICO - Icon image imread Indexed image. RAS - Sun raster image imread Truecolor or indexed.
PROBLEM A: The Leaves of a Tree "How much do the leaves on a tree weigh?" How might one estimate the actual weight of the leaves (or for that matter any other parts of the tree)? How might one classify leaves? Build a mathematical model to describe and classify leaves. Consider and answer the following: ? Why do leaves have the various shapes that they have? ? Do the shapes “minimize” overlapping individual shadows that are cast, so as to maximize exposure? Does the distribution of leaves within the “volu me”of the tree and its branches effect the shape? ? Speaking of profiles, is leaf shape (general characteristics) related to tree profile/branching structure? ? How would you estimate the leaf mass of a tree? Is there a correlation between the leaf mass and the size characteristics of the tree (height, mass, volume defined by the profile)? In addition to your one page summary sheet prepare a one page letter to an editor of a scientific journal outlining your key findings. 问题A：一棵树的叶子“一棵树上的叶子有多重？”如何估计叶子的实际重量（或树的其他部分）的实际重量？如何对叶子进行分类？建立一个数学模型来描述和分类叶子。考虑并回答以下问题： ?为什么叶片有现在的各种形状？ 树叶的形状会“最小化”他们之间的阴影重叠，来让他们接受阳光照射达到最大码？？叶子在树和分支上“体积”的分布影响叶子的形状吗？ 说到轮廓，叶子的形状（一般特征）与树的轮廓和枝干结构有关联吗？ ?你将如何估计树的叶重？叶质量和树（由轮廓定义的高度，质量，体积）的大小特征之间有无联系？ 除了总结，你还需要准备一篇给科技期刊编辑的信来说明你的主要发现。
PROBLEM A: Eradicating Ebola The world medical association has announced that their new medication could stop Eb ola and cure patients whose disease is not advanced. Build a realistic, sensible, and us eful model that considers not only the spread of the disease, the quantity of the medici ne needed, possible feasible delivery systems, locations of delivery, speed of manufac turing of the vaccine or drug, but also any other critical factors your team considers ne cessary as part of the model to optimize the eradication of Ebola, or at least its current strain. In addition to your modeling approach for the contest, prepare a 1-2 page non-technical letter for the world medical association to use in their announcement. 世界医学协会日前宣布，其新的药物可以阻止埃博拉病毒和治愈患者的疾病（这种疾病没有恶化）。请建立一个现实的、合理的，并且有用的模型。该模型不仅应该考虑如下因素：病毒的传播，所需的药量，可行的输送系统，输送地点，疫苗或药品的制造速度；也应该考虑其他的你们认为建模时必要的因素。这些因素用以优化埃博拉病毒的根除，或者至少优化[①. 埃博拉病毒的目前的分类，strain: 病毒株，这里strain是血统的意思；②埃博拉病毒目前的控制，strain，有抑制之意。] 除了你的建模及其方法，要为世界医学协会出具1-2页的非技术性文档。 PROBLEM B: Searching for a lost plane Recall the lost Malaysian flight MH370. Build a generic mathematical model that cou ld assist "searchers" in planning a useful search for a lost plane feared to have crashed in open water such as the Atlantic, Pacific, Indian, Southern, or Arctic Ocean while fl ying from Point A to Point B. Assume that there are no signals from the downed plane . Your model should recognize that there are many different types of planes for which we might be searching and that there are many different types of search planes, often using different electronics or sensors. Additionally, prepare a 1-2 page non-technical paper for the airlines to use in their press conferences concerning their plan for future searches. 回想一下失联了的马来西亚航班MH370。建立一个通用的数学模型，可以为恐已坠毁的失联飞机规划一个有用的模型以辅助“搜索者”在开阔水域搜索，例如大西洋，太平洋，印度洋，南或北冰洋，这里假设从A点飞行到B点。假定没有从被击落的飞机信号。模型应认识到，当我们搜索的时候可能有许多不同的飞机型号，并且由于经常使用不同的电子器件或传感器，会有不同类型的搜索飞机方法。另外，准备一个1-2页的非技术论文，为航空公司在其新闻发布会提出自己未来的搜寻计划。 ICM PROBLEMS PROBLEM C: Managing Human Capital in Organizations
2015 Contest Problems MCM PROBLEMS PROBLEM A: Eradicating Ebola The world medical association has announced that their new medication could stop Ebola and cure patients whose disease is not advanced. Build a realistic, sensible, and useful model that considers not only the spread of the disease, the quantity of the medicine needed, possible feasible delivery systems, locations of delivery, speed of manufacturing of the vaccine or drug, but also any other critical factors your team considers necessary as part of the model to optimize the eradication of Ebola, or at least its current strain. In addition to your modeling approach for the contest, prepare a 1-2 page non-technical letter for the world medical association to use in their announcement. PROBLEM B: Searching for a lost plane Recall the lost Malaysian flight MH370. Build a generic mathematical model that could assist "searchers" in planning a useful search for a lost plane feared to have crashed in open water such as the Atlantic, Pacific, Indian, Southern, or Arctic Ocean while flying from Point A to Point B. Assume that there are no signals from the downed plane. Your model should recognize that there are many different types of planes for which we might be searching and that there are many different types of search planes, often using different electronics or sensors. Additionally, prepare a 1-2 page non-technical paper for the airlines to use in their press conferences concerning their plan for future searches. ICM PROBLEMS PROBLEM C: Managing Human Capital in Organizations