GAMS Example

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题目：

Exercise # 3 (GAMS (2009))

Question 1 Given the transportation problem with the following parameters:

Distance in 1000s of miles New York Chicago Topeka

Seattle 2.5 1.7 1.8

San Diego 2.3 1.9 1.4

Demand at markets

Plant capacities

New York 400

Seattle 350

Chicago 300

San Diego 600

Topeka 275

Takethe freight to be 90 dollars per thousand miles. Unless otherwisestated, in each consecutive question use the setting from the previousone.

Considerthe setting from (c) again. Change the objective function fromcost minimization to profit maximization. To do this, maximize thedifference between revenue and cost. The revenue in each market can becomputed by multiplying the total quantity delivered to that markettimes the price. In addition to the transportation cost there is aproduction cost which is equal to a constant times the quantityproduced and the constants are different for each plant as given below.

Seattle 0.2

San Diego 0.4

The prices are given by:

New York Chicago Topeka

0.9 0.7 0.8

The values in both tables are given in thousands of dollars per case. Implement the changes in GAMS.

题解：

* initial Sets

set i markets / NewYork, Chicago, Topeka / ;

set j Plant capacities / Seattle, SanDiego / ;

* initial parameters

parameter a(i) Demand at markets

/ NewYork 375

Chicago 300

Topeka 275 / ;

parameter b(j) Plant capacities

/ Seattle 350

SanDiego 600 / ;

parameter ar(i) Market Preis in thousands of dollars per case

/ NewYork 0.9

Chicago 0.7

Topeka 0.8 / ;

parameter bc(j) Plant cost in thousands of dollars per case

/ Seattle 0.2

SanDiego 0.4 / ;

* initial table

table d(i,j) Distance in 1000s of miles

Seattle SanDiego

NewYork 2.5 2.3

Chicago 1.7 1.9

Topeka 1.8 1.4 ;

*initial scalar

scalar f the freight to be 90 dollars per thousand miles /90/ ;

parameter c(i,j) transport cost in thousands of dollars per case ;

c(i,j) = f * d(i,j) / 1000 ;

* initial variables

positive variable x(i,j) quantities of freight ;

variable z total transport cost ;

variable z1 total production cost ;

variable rtotal revenue ;

variable rmzdifferent between z and r ;

*initial eqs

equations

cost total transport cost (1)

cost1 total production cost (1)

revenue total revenue (1)

diff revenue - cost (1)

demand(i) demand functions (3)

supply(j) supply functions (2) ;

* transportation cost * quantity

cost.. z =e= sum((i,j),c(i,j)*x(i,j)) ;

* st.

demand(i).. sum(j,x(i,j)) =g= a(i) ;

* st.

supply(j).. sum(i,x(i,j)) =l= b(j) ;

* production cost * quantity

cost1.. z1 =e= sum((i,j),bc(j)*x(i,j)) ;

* market price * quantity

revenue.. r =e= sum((i,j),x(i,j)*ar(i)) ;

* revenue

diff.. rmz =e= r - z - z1;

* modeling and solve

model transport /all/ ;

solve transport using lp maximizing rmz ;

display x.l,z.l,z1.l,r.l,rmz.l;

编译器：

GAMS Rev 233 LEX-LEI 23.3.1 x86_64/Linux 11/19/09 02:44:49 Page 1

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C o m p i l a t i o n

1 * initial Sets

2 set i markets / NewYork, Chicago, Topeka / ;

3 set j Plant capacities / Seattle, SanDiego / ;

5 * initial parameters

6 parameter a(i) Demand at markets

7 / NewYork 375

8 Chicago 300

9 Topeka 275 / ;

11 parameter b(j) Plant capacities

12 / Seattle 350

13 SanDiego 600 / ;

15 parameter ar(i) Market Preis in thousands of dollars per case

16 / NewYork 0.9

17 Chicago 0.7

18 Topeka 0.8 / ;

20 parameter bc(j) Plant cost in thousands of dollars per case

21 / Seattle 0.2

22 SanDiego 0.4 / ;

24 * initial table

25 table d(i,j) Distance in 1000s of miles

26 Seattle SanDiego

27 NewYork 2.5 2.3

28 Chicago 1.7 1.9

29 Topeka 1.8 1.4 ;

31 *initial scalar

32 scalar f the freight to be 90 dollars per thousand miles /90/ ;

34 parameter c(i,j) transport cost in thousands of dollars per case ;

35 c(i,j) = f * d(i,j) / 1000 ;

37 * initial variables

38 positive variable x(i,j) quantities of freight ;

39 variable z total transport cost ;

40 variable z1 total production cost ;

41 variable r total revenue ;

42 variable rmz different between z and r ;

44 *initial eqs

45 equations

46 cost total transport cost (1)

47 cost1 total production cost (1)

48 revenue total revenue (1)

49 diff revenue - cost (1)

50 demand(i) demand functions (3)

51 supply(j) supply functions (2) ;

53 * transportation cost * quantity

54 cost.. z =e= sum((i,j),c(i,j)*x(i,j)) ;

56 * st.

57 demand(i).. sum(j,x(i,j)) =g= a(i) ;

59 * st.

60 supply(j).. sum(i,x(i,j)) =l= b(j) ;

62 * production cost * quantity

63 cost1.. z1 =e= sum((i,j),bc(j)*x(i,j)) ;

65 * market price * quantity

66 revenue.. r =e= sum((i,j),x(i,j)*ar(i)) ;

68 * revenue

69 diff.. rmz =e= r - z - z1;

71 * modeling and solve

72 model transport /all/ ;

73 solve transport using lp maximizing rmz ;

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C o m p i l a t i o n

75 display x.l,z.l,z1.l,r.l,rmz.l;

COMPILATION TIME = 0.002 SECONDS 3 Mb LEX233-233 Oct 30, 2009

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Equation Listing SOLVE transport Using LP From line 73

---- cost =E= total transport cost (1)

cost.. - 0.225*x(NewYork,Seattle) - 0.207*x(NewYork,SanDiego) - 0.153*x(Chicago,Seattle) - 0.171*x(Chicago,SanDiego)

- 0.162*x(Topeka,Seattle) - 0.126*x(Topeka,SanDiego) + z =E= 0 ; (LHS = 0)

---- cost1 =E= total production cost (1)

cost1.. - 0.2*x(NewYork,Seattle) - 0.4*x(NewYork,SanDiego) - 0.2*x(Chicago,Seattle) - 0.4*x(Chicago,SanDiego)

- 0.2*x(Topeka,Seattle) - 0.4*x(Topeka,SanDiego) + z1 =E= 0 ; (LHS = 0)

---- revenue =E= total revenue (1)

revenue.. - 0.9*x(NewYork,Seattle) - 0.9*x(NewYork,SanDiego) - 0.7*x(Chicago,Seattle) - 0.7*x(Chicago,SanDiego)

- 0.8*x(Topeka,Seattle) - 0.8*x(Topeka,SanDiego) + r =E= 0 ; (LHS = 0)

---- diff =E= revenue - cost (1)

diff.. z + z1 - r + rmz =E= 0 ; (LHS = 0)

---- demand =G= demand functions (3)

demand(NewYork).. x(NewYork,Seattle) + x(NewYork,SanDiego) =G= 375 ; (LHS = 0, INFES = 375 ****)

demand(Chicago).. x(Chicago,Seattle) + x(Chicago,SanDiego) =G= 300 ; (LHS = 0, INFES = 300 ****)

demand(Topeka).. x(Topeka,Seattle) + x(Topeka,SanDiego) =G= 275 ; (LHS = 0, INFES = 275 ****)

---- supply =L= supply functions (2)

supply(Seattle).. x(NewYork,Seattle) + x(Chicago,Seattle) + x(Topeka,Seattle) =L= 350 ; (LHS = 0)

supply(SanDiego).. x(NewYork,SanDiego) + x(Chicago,SanDiego) + x(Topeka,SanDiego) =L= 600 ; (LHS = 0)

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Column Listing SOLVE transport Using LP From line 73

---- x quantities of freight

x(NewYork,Seattle)

(.LO, .L, .UP, .M = 0, 0, +INF, 0)

-0.225 cost

-0.2 cost1

-0.9 revenue

1 demand(NewYork)

1 supply(Seattle)

x(NewYork,SanDiego)

(.LO, .L, .UP, .M = 0, 0, +INF, 0)

-0.207 cost

-0.4 cost1

-0.9 revenue

1 demand(NewYork)

1 supply(SanDiego)

x(Chicago,Seattle)

(.LO, .L, .UP, .M = 0, 0, +INF, 0)

-0.153 cost

-0.2 cost1

-0.7 revenue

1 demand(Chicago)

1 supply(Seattle)

REMAINING 3 ENTRIES SKIPPED

---- z total transport cost

(.LO, .L, .UP, .M = -INF, 0, +INF, 0)

1 cost

1 diff

---- z1 total production cost

(.LO, .L, .UP, .M = -INF, 0, +INF, 0)

1 cost1

1 diff

---- r total revenue

(.LO, .L, .UP, .M = -INF, 0, +INF, 0)

1 revenue

-1 diff

---- rmz different between z and r

rmz

(.LO, .L, .UP, .M = -INF, 0, +INF, 0)

1 diff

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Model Statistics SOLVE transport Using LP From line 73

MODEL STATISTICS

BLOCKS OF EQUATIONS 6 SINGLE EQUATIONS 9

BLOCKS OF VARIABLES 5 SINGLE VARIABLES 10

NON ZERO ELEMENTS 37

GENERATION TIME = 0.003 SECONDS 4 Mb LEX233-233 Oct 30, 2009

EXECUTION TIME = 0.003 SECONDS 4 Mb LEX233-233 Oct 30, 2009

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Solution Report SOLVE transport Using LP From line 73

S O L V E S U M M A R Y

MODEL transport OBJECTIVE rmz

TYPE LP DIRECTION MAXIMIZE

SOLVER CPLEX FROM LINE 73

**** SOLVER STATUS 1 Normal Completion

**** MODEL STATUS 1 Optimal

**** OBJECTIVE VALUE 298.4250

RESOURCE USAGE, LIMIT 0.000 1000.000

ITERATION COUNT, LIMIT 2 2000000000

ILOG CPLEX Nov 1, 2009 23.3.1 LEX 13908.14234 LEI x86_64/Linux

Cplex 12.1.0, GAMS Link 34

LP status(1): optimal

Optimal solution found.

Objective : 298.425000

LOWER LEVEL UPPER MARGINAL

---- EQU cost . . . -1.0000

---- EQU cost1 . . . -1.0000

---- EQU revenue . . . 1.0000

---- EQU diff . . . 1.0000

cost total transport cost (1)

cost1 total production cost (1)

revenue total revenue (1)

diff revenue - cost (1)

---- EQU demand demand functions (3)

LOWER LEVEL UPPER MARGINAL

NewYork 375.0000 375.0000 +INF .

Chicago 300.0000 300.0000 +INF -0.1280

Topeka 275.0000 275.0000 +INF -0.0190

---- EQU supply supply functions (2)

LOWER LEVEL UPPER MARGINAL

Seattle -INF 350.0000 350.0000 0.4750

SanDiego -INF 600.0000 600.0000 0.2930

---- VAR x quantities of freight

LOWER LEVEL UPPER MARGINAL

NewYork.Seattle . 50.0000 +INF .

NewYork.SanDiego . 325.0000 +INF .

Chicago.Seattle . 300.0000 +INF .

Chicago.SanDiego . . +INF -0.0360

Topeka .Seattle . . +INF -0.0180

Topeka .SanDiego . 275.0000 +INF .

LOWER LEVEL UPPER MARGINAL

---- VAR z -INF 159.0750 +INF .

---- VAR z1 -INF 310.0000 +INF .

---- VAR r -INF 767.5000 +INF .

---- VAR rmz -INF 298.4250 +INF .

z total transport cost

z1 total production cost

r total revenue

rmz different between z and r

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Solution Report SOLVE transport Using LP From line 73

**** REPORT SUMMARY : 0 NONOPT

0 INFEASIBLE

0 UNBOUNDED

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E x e c u t i o n

---- 75 VARIABLE x.L quantities of freight

Seattle SanDiego

NewYork 50.000 325.000

Chicago 300.000

Topeka 275.000

---- 75 VARIABLE z.L = 159.075 total transport cost

VARIABLE z1.L = 310.000 total production cost

VARIABLE r.L = 767.500 total revenue

VARIABLE rmz.L = 298.425 different between z and r

EXECUTION TIME = 0.001 SECONDS 3 Mb LEX233-233 Oct 30, 2009

USER: GAMS Development Corporation, Washington, DC G871201/0000CA-ANY

Free Demo, 202-342-0180, sales@gams.com, www.gams.com DC0000

**** FILE SUMMARY

Input /home/raymond/Desktop/TODO/gams/HW2.gms

Output /home/raymond/Desktop/TODO/gams/HW2.lst