INFEASIBLE EQUATIONS

GAMS
1

hi,everyone
after my model solved with gams error Equation infeasible due to rhs value occured. please help me to correct it.
my code is following:

1 sets
2 j activity / a1a7 /
3 k resource type / k1k3 /
4 t time period / 120 /
5 m mode /m1m2 / ;
6 alias(i,j) ;
7 alias(u,t);
8 variables
9 x(j,m,t) activity j in mode m in time t
10 sr(k) recruitment date of resource type k
11 fr(k) release date of resource type k
12 z1 total present value
13 z2 total cost of resource ;
14 binary variables x ;
15 integer variables sr, fr ;
16 parameters
17 c(k) unit cost of resource types per unit time
18 / k1 14
19 k2 23
20 k3 17 /
21 d(j,m) duration of activity j in mode m
22 / a2. m1 = 4
23 a2. m2 = 7
24 a3. m1 = 3
25 a3. m2 = 7
26 a4. m1 = 2
27 a4. m2 = 4
28 a5. m1 = 6
29 a5. m2 = 8
30 a6. m1 = 3
31 a6. m2 = 5 /
32 cf(j,m) cashflow of activity j in mode m
33 / a2. m1 = 100
34 a2. m2 = 200
35 a3. m1 = 300
36 a3. m2 = 400
37 a4. m1 = 500
38 a4. m2 = 600
39 a5. m1 = 700
40 a5. m2 = 800
41 a6. m1 = 900
42 a6. m2 = 1000 /
43 r(j,k,m) resource requirement of activity j in mode m for resource type k
44 / a2. k1. m1 = 9
45 a2. k1. m2 = 6
46 a3. k1. m1 = 12
47 a3. k1. m2 = 6
48 a3. k3. m1 = 11
49 a3. k3. m2 = 6
50 a4. k1. m1 = 3
51 a4. k1. m2 = 1
52 a4. k2. m1 = 4
53 a4. k2. m2 = 1
54 a4. k3. m1 = 3
55 a4. k3. m2 = 2
56 a5. k2. m1 = 3
57 a5. k2. m2 = 2
58 a5. k3. m1 = 4
59 a5. k3. m2 = 3
60 a6. k1. m1 = 9
61 a6. k1. m2 = 6
62 a6. k2. m1 = 4
63 a6. k2. m2 = 2 /
64 a(k) constant availability of renewable resource type k
65 / k1 30
66 k2 40
67 k3 50 /
68 ES(j) earliest start time of activity j
69 /a2 1
70 a3 1
71 a4 5
72 a5 5
73 a6 4
74 a7 20/
75 LS(j)
76 /a2 7
77 a3 7
78 a4 17
79 a5 13
80 a6 16
81 a7 20/ ;
82 scalar w deadline of the project /20/ ;
83 scalar v discount rate /0.05/ ;
84 equations
85 value define objective function 1
86 cost define objective function 2
87 precedence(i,j) precedence constraint
88 execution(j) start time in one execution mode
89 resources(k,t) renewable resources limitations
90 recruitment(j,k) recruitment dates for resources
91 release(j,k) release dates for resources
92 deadline(j,m) project deadline is not violated ;
93 value… z1 =e= sum((j,m,t)(ord(t)>= ES(j)and ord(t)= ES(j)and ord(t)= ES(i)and ord(t)= ES(j)and ord(t)=(ord(t)-d(j,m)+1)),r(j,k,m)*x(j,m,u) )=l= a(K) ; 98 recruitment(j,k).. sr(k)=l= sum((t,m)(ord(t)>= ES(j)and ord(t)= ES(j)and ord(t)= ES(j)and ord(t)<= LS(j)),ord(t)*x(j,m,t))=
l= w ;
101 model MRCPSP /all/ ;
102 solve MRCPSP using mip maximizing z1 ;
103 solve MRCPSP using mip minimizing z2 ;
104 display x.l,sr.l,fr.l,z1.l,z2.l ;

---- value =E= define objective function 1

value… - 95.1229424500714x(a2,m1,1) - 90.4837418035959x(a2,m1,2)

  • 86.0707976425058x(a2,m1,3) - 81.8730753077982x(a2,m1,4)

  • 77.8800783071405x(a2,m1,5) - 74.0818220681718x(a2,m1,6)

  • 70.4688089718713x(a2,m1,7) - 190.245884900143x(a2,m2,1)

  • 180.967483607192x(a2,m2,2) - 172.141595285012x(a2,m2,3)

  • 163.746150615596x(a2,m2,4) - 155.760156614281x(a2,m2,5)

  • 148.163644136344x(a2,m2,6) - 140.937617943743x(a2,m2,7)

  • 285.368827350214x(a3,m1,1) - 271.451225410788x(a3,m1,2)

  • 258.212392927517x(a3,m1,3) - 245.619225923395x(a3,m1,4)

  • 233.640234921421x(a3,m1,5) - 222.245466204515x(a3,m1,6)

  • 211.406426915614x(a3,m1,7) - 380.491769800286x(a3,m2,1)

  • 361.934967214384x(a3,m2,2) - 344.283190570023x(a3,m2,3)

  • 327.492301231193x(a3,m2,4) - 311.520313228562x(a3,m2,5)

  • 296.327288272687x(a3,m2,6) - 281.875235887485x(a3,m2,7)

  • 389.400391535702x(a4,m1,5) - 370.409110340859x(a4,m1,6)

  • 352.344044859357x(a4,m1,7) - 335.16002301782x(a4,m1,8)

  • 318.814075810887x(a4,m1,9) - 303.265329856317x(a4,m1,10)

  • 288.474905190243x(a4,m1,11) - 274.405818047013x(a4,m1,12)

  • 261.022888380508x(a4,m1,13) - 248.292651895705x(a4,m1,14)

  • 236.183276370507x(a4,m1,15) - 224.664482058611x(a4,m1,16)

  • 213.707465974363x(a4,m1,17) - 467.280469842843x(a4,m2,5)

  • 444.490932409031x(a4,m2,6) - 422.812853831228x(a4,m2,7)

  • 402.192027621384x(a4,m2,8) - 382.576890973064x(a4,m2,9)

  • 363.91839582758x(a4,m2,10) - 346.169886228292x(a4,m2,11)

  • 329.286981656416x(a4,m2,12) - 313.22746605661x(a4,m2,13)

  • 297.951182274846x(a4,m2,14) - 283.419931644609x(a4,m2,15)

  • 269.597378470333x(a4,m2,16) - 256.448959169236x(a4,m2,17)

  • 545.160548149983x(a5,m1,5) - 518.572754477202x(a5,m1,6)

  • 493.281662803099x(a5,m1,7) - 469.224032224948x(a5,m1,8)

  • 446.339706135241x(a5,m1,9) - 424.571461798843x(a5,m1,10)

  • 403.864867266341x(a5,m1,11) - 384.168145265818x(a5,m1,12)

  • 365.432043732711x(a5,m1,13) - 623.040626457124x(a5,m2,5)

  • 592.654576545374x(a5,m2,6) - 563.750471774971x(a5,m2,7)

  • 536.256036828511x(a5,m2,8) - 510.102521297419x(a5,m2,9)

  • 485.224527770107x(a5,m2,10) - 461.559848304389x(a5,m2,11)

  • 439.049308875221x(a5,m2,12) - 417.636621408813x(a5,m2,13)

  • 736.857677770184x(a6,m1,4) - 700.920704764264x(a6,m1,5)

  • 666.736398613546x(a6,m1,6) - 634.219280746842x(a6,m1,7)

  • 603.288041432075x(a6,m1,8) - 573.865336459596x(a6,m1,9)

  • 545.87759374137x(a6,m1,10) - 519.254829342438x(a6,m1,11)

  • 493.930472484624x(a6,m1,12) - 469.841199084914x(a6,m1,13)

  • 446.926773412269x(a6,m1,14) - 425.129897466913x(a6,m1,15)

  • 404.396067705499x(a6,m1,16) - 818.730753077982x(a6,m2,4)

  • 778.800783071405x(a6,m2,5) - 740.818220681718x(a6,m2,6)

  • 704.688089718713x(a6,m2,7) - 670.320046035639x(a6,m2,8)

  • 637.628151621773x(a6,m2,9) - 606.530659712633x(a6,m2,10)

  • 576.949810380487x(a6,m2,11) - 548.811636094026x(a6,m2,12)

  • 522.045776761016x(a6,m2,13) - 496.585303791409x(a6,m2,14)

  • 472.366552741015x(a6,m2,15) - 449.328964117222x(a6,m2,16) + z1 =E= 0 ;

(LHS = 0)


---- cost =E= define objective function 2

cost… 420sr(k1) + 920sr(k2) + 850sr(k3) - 420fr(k1) - 920*fr(k2)

  • 850*fr(k3) + z2 =E= 0 ; (LHS = 0)


    ---- precedence =G= precedence constraint

precedence(a1,a2)… x(a2,m1,1) + 2x(a2,m1,2) + 3x(a2,m1,3) + 4*x(a2,m1,4)

  • 5x(a2,m1,5) + 6x(a2,m1,6) + 7x(a2,m1,7) + x(a2,m2,1) + 2x(a2,m2,2)

  • 3x(a2,m2,3) + 4x(a2,m2,4) + 5x(a2,m2,5) + 6x(a2,m2,6) + 7*x(a2,m2,7)
    =G= 0 ; (LHS = 0)

precedence(a1,a3)… x(a3,m1,1) + 2x(a3,m1,2) + 3x(a3,m1,3) + 4*x(a3,m1,4)

  • 5x(a3,m1,5) + 6x(a3,m1,6) + 7x(a3,m1,7) + x(a3,m2,1) + 2x(a3,m2,2)

  • 3x(a3,m2,3) + 4x(a3,m2,4) + 5x(a3,m2,5) + 6x(a3,m2,6) + 7*x(a3,m2,7)
    =G= 0 ; (LHS = 0)

precedence(a1,a4)… 5x(a4,m1,5) + 6x(a4,m1,6) + 7x(a4,m1,7) + 8x(a4,m1,8)

  • 9x(a4,m1,9) + 10x(a4,m1,10) + 11x(a4,m1,11) + 12x(a4,m1,12)

  • 13x(a4,m1,13) + 14x(a4,m1,14) + 15x(a4,m1,15) + 16x(a4,m1,16)

  • 17x(a4,m1,17) + 5x(a4,m2,5) + 6x(a4,m2,6) + 7x(a4,m2,7)

  • 8x(a4,m2,8) + 9x(a4,m2,9) + 10x(a4,m2,10) + 11x(a4,m2,11)

  • 12x(a4,m2,12) + 13x(a4,m2,13) + 14x(a4,m2,14) + 15x(a4,m2,15)

  • 16x(a4,m2,16) + 17x(a4,m2,17) =G= 0 ; (LHS = 0)

REMAINING 44 ENTRIES SKIPPED

**** Exec Error at line 96: Equation infeasible due to rhs value

**** INFEASIBLE EQUATIONS …

---- execution =E= start time in one execution mode

execution(a1)… 0 =E= 1 ; (LHS = 0, INFES = 1 ****)

REMAINING 6 ENTRIES SKIPPED

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2

Hi: I’m guessing the problem is in parameters LS and ES which are not defined for activity a1, causing summation over t and m not to happen for this activity due to the conditional you write in equation “execution(j)”.

Best regards
Claudio
El 02/06/2014 08:27, “Vahid reza Mohammadi” escribió:

hi,everyone
after my model solved with gams error Equation infeasible due to rhs value occured. please help me to correct it.
my code is following:

1 sets
2 j activity / a1a7 /
3 k resource type / k1k3 /
4 t time period / 120 /
5 m mode /m1m2 / ;
6 alias(i,j) ;
7 alias(u,t);
8 variables
9 x(j,m,t) activity j in mode m in time t
10 sr(k) recruitment date of resource type k
11 fr(k) release date of resource type k
12 z1 total present value
13 z2 total cost of resource ;
14 binary variables x ;
15 integer variables sr, fr ;
16 parameters
17 c(k) unit cost of resource types per unit time
18 / k1 14
19 k2 23
20 k3 17 /
21 d(j,m) duration of activity j in mode m
22 / a2. m1 = 4
23 a2. m2 = 7
24 a3. m1 = 3
25 a3. m2 = 7
26 a4. m1 = 2
27 a4. m2 = 4
28 a5. m1 = 6
29 a5. m2 = 8
30 a6. m1 = 3
31 a6. m2 = 5 /
32 cf(j,m) cashflow of activity j in mode m
33 / a2. m1 = 100
34 a2. m2 = 200
35 a3. m1 = 300
36 a3. m2 = 400
37 a4. m1 = 500
38 a4. m2 = 600
39 a5. m1 = 700
40 a5. m2 = 800
41 a6. m1 = 900
42 a6. m2 = 1000 /
43 r(j,k,m) resource requirement of activity j in mode m for resource type k
44 / a2. k1. m1 = 9
45 a2. k1. m2 = 6
46 a3. k1. m1 = 12
47 a3. k1. m2 = 6
48 a3. k3. m1 = 11
49 a3. k3. m2 = 6
50 a4. k1. m1 = 3
51 a4. k1. m2 = 1
52 a4. k2. m1 = 4
53 a4. k2. m2 = 1
54 a4. k3. m1 = 3
55 a4. k3. m2 = 2
56 a5. k2. m1 = 3
57 a5. k2. m2 = 2
58 a5. k3. m1 = 4
59 a5. k3. m2 = 3
60 a6. k1. m1 = 9
61 a6. k1. m2 = 6
62 a6. k2. m1 = 4
63 a6. k2. m2 = 2 /
64 a(k) constant availability of renewable resource type k
65 / k1 30
66 k2 40
67 k3 50 /
68 ES(j) earliest start time of activity j
69 /a2 1
70 a3 1
71 a4 5
72 a5 5
73 a6 4
74 a7 20/
75 LS(j)
76 /a2 7
77 a3 7
78 a4 17
79 a5 13
80 a6 16
81 a7 20/ ;
82 scalar w deadline of the project /20/ ;
83 scalar v discount rate /0.05/ ;
84 equations
85 value define objective function 1
86 cost define objective function 2
87 precedence(i,j) precedence constraint
88 execution(j) start time in one execution mode
89 resources(k,t) renewable resources limitations
90 recruitment(j,k) recruitment dates for resources
91 release(j,k) release dates for resources
92 deadline(j,m) project deadline is not violated ;
93 value… z1 =e= sum((j,m,t)(ord(t)>= ES(j)and ord(t)= ES(j)and ord(t)= ES(i)and ord(t)= ES(j)and ord(t)=(ord(t)-d(j,m)+1)),r(j,k,m)*x(j,m,u) )=l= a(K) ; 98 recruitment(j,k).. sr(k)=l= sum((t,m)(ord(t)>= ES(j)and ord(t)= ES(j)and ord(t)= ES(j)and ord(t)<= LS(j)),ord(t)*x(j,m,t))=
l= w ;
101 model MRCPSP /all/ ;
102 solve MRCPSP using mip maximizing z1 ;
103 solve MRCPSP using mip minimizing z2 ;
104 display x.l,sr.l,fr.l,z1.l,z2.l ;

---- value =E= define objective function 1

value… - 95.1229424500714x(a2,m1,1) - 90.4837418035959x(a2,m1,2)

  • 86.0707976425058x(a2,m1,3) - 81.8730753077982x(a2,m1,4)

  • 77.8800783071405x(a2,m1,5) - 74.0818220681718x(a2,m1,6)

  • 70.4688089718713x(a2,m1,7) - 190.245884900143x(a2,m2,1)

  • 180.967483607192x(a2,m2,2) - 172.141595285012x(a2,m2,3)

  • 163.746150615596x(a2,m2,4) - 155.760156614281x(a2,m2,5)

  • 148.163644136344x(a2,m2,6) - 140.937617943743x(a2,m2,7)

  • 285.368827350214x(a3,m1,1) - 271.451225410788x(a3,m1,2)

  • 258.212392927517x(a3,m1,3) - 245.619225923395x(a3,m1,4)

  • 233.640234921421x(a3,m1,5) - 222.245466204515x(a3,m1,6)

  • 211.406426915614x(a3,m1,7) - 380.491769800286x(a3,m2,1)

  • 361.934967214384x(a3,m2,2) - 344.283190570023x(a3,m2,3)

  • 327.492301231193x(a3,m2,4) - 311.520313228562x(a3,m2,5)

  • 296.327288272687x(a3,m2,6) - 281.875235887485x(a3,m2,7)

  • 389.400391535702x(a4,m1,5) - 370.409110340859x(a4,m1,6)

  • 352.344044859357x(a4,m1,7) - 335.16002301782x(a4,m1,8)

  • 318.814075810887x(a4,m1,9) - 303.265329856317x(a4,m1,10)

  • 288.474905190243x(a4,m1,11) - 274.405818047013x(a4,m1,12)

  • 261.022888380508x(a4,m1,13) - 248.292651895705x(a4,m1,14)

  • 236.183276370507x(a4,m1,15) - 224.664482058611x(a4,m1,16)

  • 213.707465974363x(a4,m1,17) - 467.280469842843x(a4,m2,5)

  • 444.490932409031x(a4,m2,6) - 422.812853831228x(a4,m2,7)

  • 402.192027621384x(a4,m2,8) - 382.576890973064x(a4,m2,9)

  • 363.91839582758x(a4,m2,10) - 346.169886228292x(a4,m2,11)

  • 329.286981656416x(a4,m2,12) - 313.22746605661x(a4,m2,13)

  • 297.951182274846x(a4,m2,14) - 283.419931644609x(a4,m2,15)

  • 269.597378470333x(a4,m2,16) - 256.448959169236x(a4,m2,17)

  • 545.160548149983x(a5,m1,5) - 518.572754477202x(a5,m1,6)

  • 493.281662803099x(a5,m1,7) - 469.224032224948x(a5,m1,8)

  • 446.339706135241x(a5,m1,9) - 424.571461798843x(a5,m1,10)

  • 403.864867266341x(a5,m1,11) - 384.168145265818x(a5,m1,12)

  • 365.432043732711x(a5,m1,13) - 623.040626457124x(a5,m2,5)

  • 592.654576545374x(a5,m2,6) - 563.750471774971x(a5,m2,7)

  • 536.256036828511x(a5,m2,8) - 510.102521297419x(a5,m2,9)

  • 485.224527770107x(a5,m2,10) - 461.559848304389x(a5,m2,11)

  • 439.049308875221x(a5,m2,12) - 417.636621408813x(a5,m2,13)

  • 736.857677770184x(a6,m1,4) - 700.920704764264x(a6,m1,5)

  • 666.736398613546x(a6,m1,6) - 634.219280746842x(a6,m1,7)

  • 603.288041432075x(a6,m1,8) - 573.865336459596x(a6,m1,9)

  • 545.87759374137x(a6,m1,10) - 519.254829342438x(a6,m1,11)

  • 493.930472484624x(a6,m1,12) - 469.841199084914x(a6,m1,13)

  • 446.926773412269x(a6,m1,14) - 425.129897466913x(a6,m1,15)

  • 404.396067705499x(a6,m1,16) - 818.730753077982x(a6,m2,4)

  • 778.800783071405x(a6,m2,5) - 740.818220681718x(a6,m2,6)

  • 704.688089718713x(a6,m2,7) - 670.320046035639x(a6,m2,8)

  • 637.628151621773x(a6,m2,9) - 606.530659712633x(a6,m2,10)

  • 576.949810380487x(a6,m2,11) - 548.811636094026x(a6,m2,12)

  • 522.045776761016x(a6,m2,13) - 496.585303791409x(a6,m2,14)

  • 472.366552741015x(a6,m2,15) - 449.328964117222x(a6,m2,16) + z1 =E= 0 ;

(LHS = 0)


---- cost =E= define objective function 2

cost… 420sr(k1) + 920sr(k2) + 850sr(k3) - 420fr(k1) - 920*fr(k2)

  • 850*fr(k3) + z2 =E= 0 ; (LHS = 0)


    ---- precedence =G= precedence constraint

precedence(a1,a2)… x(a2,m1,1) + 2x(a2,m1,2) + 3x(a2,m1,3) + 4*x(a2,m1,4)

  • 5x(a2,m1,5) + 6x(a2,m1,6) + 7x(a2,m1,7) + x(a2,m2,1) + 2x(a2,m2,2)

  • 3x(a2,m2,3) + 4x(a2,m2,4) + 5x(a2,m2,5) + 6x(a2,m2,6) + 7*x(a2,m2,7)
    =G= 0 ; (LHS = 0)

precedence(a1,a3)… x(a3,m1,1) + 2x(a3,m1,2) + 3x(a3,m1,3) + 4*x(a3,m1,4)

  • 5x(a3,m1,5) + 6x(a3,m1,6) + 7x(a3,m1,7) + x(a3,m2,1) + 2x(a3,m2,2)

  • 3x(a3,m2,3) + 4x(a3,m2,4) + 5x(a3,m2,5) + 6x(a3,m2,6) + 7*x(a3,m2,7)
    =G= 0 ; (LHS = 0)

precedence(a1,a4)… 5x(a4,m1,5) + 6x(a4,m1,6) + 7x(a4,m1,7) + 8x(a4,m1,8)

  • 9x(a4,m1,9) + 10x(a4,m1,10) + 11x(a4,m1,11) + 12x(a4,m1,12)

  • 13x(a4,m1,13) + 14x(a4,m1,14) + 15x(a4,m1,15) + 16x(a4,m1,16)

  • 17x(a4,m1,17) + 5x(a4,m2,5) + 6x(a4,m2,6) + 7x(a4,m2,7)

  • 8x(a4,m2,8) + 9x(a4,m2,9) + 10x(a4,m2,10) + 11x(a4,m2,11)

  • 12x(a4,m2,12) + 13x(a4,m2,13) + 14x(a4,m2,14) + 15x(a4,m2,15)

  • 16x(a4,m2,16) + 17x(a4,m2,17) =G= 0 ; (LHS = 0)

REMAINING 44 ENTRIES SKIPPED

**** Exec Error at line 96: Equation infeasible due to rhs value

**** INFEASIBLE EQUATIONS …

---- execution =E= start time in one execution mode

execution(a1)… 0 =E= 1 ; (LHS = 0, INFES = 1 ****)

REMAINING 6 ENTRIES SKIPPED

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3

hi Dear Claudio
thanks for your attention, in my model activity a1 and a7 are dummy and my ES and LS calculation base on forward and backward pass calculations. In doing this, the duration of activity i is considered based on execution mode with lowest duration. The backward pass calculation is started from a fixed project deadline T. In this paper, earliest finish time of dummy end activity, EFTn , computed based on execution modes with highest duration is considered as project deadline.

On Monday, June 2, 2014 3:55:38 PM UTC+4:30, Vahid reza Mohammadi wrote:

hi,everyone
after my model solved with gams error Equation infeasible due to rhs value occured. please help me to correct it.
my code is following:

1 sets
2 j activity / a1a7 /
3 k resource type / k1k3 /
4 t time period / 120 /
5 m mode /m1m2 / ;
6 alias(i,j) ;
7 alias(u,t);
8 variables
9 x(j,m,t) activity j in mode m in time t
10 sr(k) recruitment date of resource type k
11 fr(k) release date of resource type k
12 z1 total present value
13 z2 total cost of resource ;
14 binary variables x ;
15 integer variables sr, fr ;
16 parameters
17 c(k) unit cost of resource types per unit time
18 / k1 14
19 k2 23
20 k3 17 /
21 d(j,m) duration of activity j in mode m
22 / a2. m1 = 4
23 a2. m2 = 7
24 a3. m1 = 3
25 a3. m2 = 7
26 a4. m1 = 2
27 a4. m2 = 4
28 a5. m1 = 6
29 a5. m2 = 8
30 a6. m1 = 3
31 a6. m2 = 5 /
32 cf(j,m) cashflow of activity j in mode m
33 / a2. m1 = 100
34 a2. m2 = 200
35 a3. m1 = 300
36 a3. m2 = 400
37 a4. m1 = 500
38 a4. m2 = 600
39 a5. m1 = 700
40 a5. m2 = 800
41 a6. m1 = 900
42 a6. m2 = 1000 /
43 r(j,k,m) resource requirement of activity j in mode m for resource type k
44 / a2. k1. m1 = 9
45 a2. k1. m2 = 6
46 a3. k1. m1 = 12
47 a3. k1. m2 = 6
48 a3. k3. m1 = 11
49 a3. k3. m2 = 6
50 a4. k1. m1 = 3
51 a4. k1. m2 = 1
52 a4. k2. m1 = 4
53 a4. k2. m2 = 1
54 a4. k3. m1 = 3
55 a4. k3. m2 = 2
56 a5. k2. m1 = 3
57 a5. k2. m2 = 2
58 a5. k3. m1 = 4
59 a5. k3. m2 = 3
60 a6. k1. m1 = 9
61 a6. k1. m2 = 6
62 a6. k2. m1 = 4
63 a6. k2. m2 = 2 /
64 a(k) constant availability of renewable resource type k
65 / k1 30
66 k2 40
67 k3 50 /
68 ES(j) earliest start time of activity j
69 /a2 1
70 a3 1
71 a4 5
72 a5 5
73 a6 4
74 a7 20/
75 LS(j)
76 /a2 7
77 a3 7
78 a4 17
79 a5 13
80 a6 16
81 a7 20/ ;
82 scalar w deadline of the project /20/ ;
83 scalar v discount rate /0.05/ ;
84 equations
85 value define objective function 1
86 cost define objective function 2
87 precedence(i,j) precedence constraint
88 execution(j) start time in one execution mode
89 resources(k,t) renewable resources limitations
90 recruitment(j,k) recruitment dates for resources
91 release(j,k) release dates for resources
92 deadline(j,m) project deadline is not violated ;
93 value… z1 =e= sum((j,m,t)(ord(t)>= ES(j)and ord(t)= ES(j)and ord(t)= ES(i)and ord(t)= ES(j)and ord(t)=(ord(t)-d(j,m)+1)),r(j,k,m)*x(j,m,u) )=l= a(K) ; 98 recruitment(j,k).. sr(k)=l= sum((t,m)(ord(t)>= ES(j)and ord(t)= ES(j)and ord(t)= ES(j)and ord(t)<= LS(j)),ord(t)*x(j,m,t))=
l= w ;
101 model MRCPSP /all/ ;
102 solve MRCPSP using mip maximizing z1 ;
103 solve MRCPSP using mip minimizing z2 ;
104 display x.l,sr.l,fr.l,z1.l,z2.l ;

---- value =E= define objective function 1

value… - 95.1229424500714x(a2,m1,1) - 90.4837418035959x(a2,m1,2)

  • 86.0707976425058x(a2,m1,3) - 81.8730753077982x(a2,m1,4)

  • 77.8800783071405x(a2,m1,5) - 74.0818220681718x(a2,m1,6)

  • 70.4688089718713x(a2,m1,7) - 190.245884900143x(a2,m2,1)

  • 180.967483607192x(a2,m2,2) - 172.141595285012x(a2,m2,3)

  • 163.746150615596x(a2,m2,4) - 155.760156614281x(a2,m2,5)

  • 148.163644136344x(a2,m2,6) - 140.937617943743x(a2,m2,7)

  • 285.368827350214x(a3,m1,1) - 271.451225410788x(a3,m1,2)

  • 258.212392927517x(a3,m1,3) - 245.619225923395x(a3,m1,4)

  • 233.640234921421x(a3,m1,5) - 222.245466204515x(a3,m1,6)

  • 211.406426915614x(a3,m1,7) - 380.491769800286x(a3,m2,1)

  • 361.934967214384x(a3,m2,2) - 344.283190570023x(a3,m2,3)

  • 327.492301231193x(a3,m2,4) - 311.520313228562x(a3,m2,5)

  • 296.327288272687x(a3,m2,6) - 281.875235887485x(a3,m2,7)

  • 389.400391535702x(a4,m1,5) - 370.409110340859x(a4,m1,6)

  • 352.344044859357x(a4,m1,7) - 335.16002301782x(a4,m1,8)

  • 318.814075810887x(a4,m1,9) - 303.265329856317x(a4,m1,10)

  • 288.474905190243x(a4,m1,11) - 274.405818047013x(a4,m1,12)

  • 261.022888380508x(a4,m1,13) - 248.292651895705x(a4,m1,14)

  • 236.183276370507x(a4,m1,15) - 224.664482058611x(a4,m1,16)

  • 213.707465974363x(a4,m1,17) - 467.280469842843x(a4,m2,5)

  • 444.490932409031x(a4,m2,6) - 422.812853831228x(a4,m2,7)

  • 402.192027621384x(a4,m2,8) - 382.576890973064x(a4,m2,9)

  • 363.91839582758x(a4,m2,10) - 346.169886228292x(a4,m2,11)

  • 329.286981656416x(a4,m2,12) - 313.22746605661x(a4,m2,13)

  • 297.951182274846x(a4,m2,14) - 283.419931644609x(a4,m2,15)

  • 269.597378470333x(a4,m2,16) - 256.448959169236x(a4,m2,17)

  • 545.160548149983x(a5,m1,5) - 518.572754477202x(a5,m1,6)

  • 493.281662803099x(a5,m1,7) - 469.224032224948x(a5,m1,8)

  • 446.339706135241x(a5,m1,9) - 424.571461798843x(a5,m1,10)

  • 403.864867266341x(a5,m1,11) - 384.168145265818x(a5,m1,12)

  • 365.432043732711x(a5,m1,13) - 623.040626457124x(a5,m2,5)

  • 592.654576545374x(a5,m2,6) - 563.750471774971x(a5,m2,7)

  • 536.256036828511x(a5,m2,8) - 510.102521297419x(a5,m2,9)

  • 485.224527770107x(a5,m2,10) - 461.559848304389x(a5,m2,11)

  • 439.049308875221x(a5,m2,12) - 417.636621408813x(a5,m2,13)

  • 736.857677770184x(a6,m1,4) - 700.920704764264x(a6,m1,5)

  • 666.736398613546x(a6,m1,6) - 634.219280746842x(a6,m1,7)

  • 603.288041432075x(a6,m1,8) - 573.865336459596x(a6,m1,9)

  • 545.87759374137x(a6,m1,10) - 519.254829342438x(a6,m1,11)

  • 493.930472484624x(a6,m1,12) - 469.841199084914x(a6,m1,13)

  • 446.926773412269x(a6,m1,14) - 425.129897466913x(a6,m1,15)

  • 404.396067705499x(a6,m1,16) - 818.730753077982x(a6,m2,4)

  • 778.800783071405x(a6,m2,5) - 740.818220681718x(a6,m2,6)

  • 704.688089718713x(a6,m2,7) - 670.320046035639x(a6,m2,8)

  • 637.628151621773x(a6,m2,9) - 606.530659712633x(a6,m2,10)

  • 576.949810380487x(a6,m2,11) - 548.811636094026x(a6,m2,12)

  • 522.045776761016x(a6,m2,13) - 496.585303791409x(a6,m2,14)

  • 472.366552741015x(a6,m2,15) - 449.328964117222x(a6,m2,16) + z1 =E= 0 ;

(LHS = 0)


---- cost =E= define objective function 2

cost… 420sr(k1) + 920sr(k2) + 850sr(k3) - 420fr(k1) - 920*fr(k2)

  • 850*fr(k3) + z2 =E= 0 ; (LHS = 0)


    ---- precedence =G= precedence constraint

precedence(a1,a2)… x(a2,m1,1) + 2x(a2,m1,2) + 3x(a2,m1,3) + 4*x(a2,m1,4)

  • 5x(a2,m1,5) + 6x(a2,m1,6) + 7x(a2,m1,7) + x(a2,m2,1) + 2x(a2,m2,2)

  • 3x(a2,m2,3) + 4x(a2,m2,4) + 5x(a2,m2,5) + 6x(a2,m2,6) + 7*x(a2,m2,7)
    =G= 0 ; (LHS = 0)

precedence(a1,a3)… x(a3,m1,1) + 2x(a3,m1,2) + 3x(a3,m1,3) + 4*x(a3,m1,4)

  • 5x(a3,m1,5) + 6x(a3,m1,6) + 7x(a3,m1,7) + x(a3,m2,1) + 2x(a3,m2,2)

  • 3x(a3,m2,3) + 4x(a3,m2,4) + 5x(a3,m2,5) + 6x(a3,m2,6) + 7*x(a3,m2,7)
    =G= 0 ; (LHS = 0)

precedence(a1,a4)… 5x(a4,m1,5) + 6x(a4,m1,6) + 7x(a4,m1,7) + 8x(a4,m1,8)

  • 9x(a4,m1,9) + 10x(a4,m1,10) + 11x(a4,m1,11) + 12x(a4,m1,12)

  • 13x(a4,m1,13) + 14x(a4,m1,14) + 15x(a4,m1,15) + 16x(a4,m1,16)

  • 17x(a4,m1,17) + 5x(a4,m2,5) + 6x(a4,m2,6) + 7x(a4,m2,7)

  • 8x(a4,m2,8) + 9x(a4,m2,9) + 10x(a4,m2,10) + 11x(a4,m2,11)

  • 12x(a4,m2,12) + 13x(a4,m2,13) + 14x(a4,m2,14) + 15x(a4,m2,15)

  • 16x(a4,m2,16) + 17x(a4,m2,17) =G= 0 ; (LHS = 0)

REMAINING 44 ENTRIES SKIPPED

**** Exec Error at line 96: Equation infeasible due to rhs value

**** INFEASIBLE EQUATIONS …

---- execution =E= start time in one execution mode

execution(a1)… 0 =E= 1 ; (LHS = 0, INFES = 1 ****)

REMAINING 6 ENTRIES SKIPPED

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