thai.gms : Thai Navy Problem
This model is used to allocate ships to transport personnel from
different port to a training center.
Reference:
- Choypeng, P, Puakpong, P, and Rosenthal, R E, Optimal Ship Routing and Personnel Assignment for Naval Recruitment in Thailand. Interfaces 16, 4 (1986), 356-366.
Small Model of Type: MIP
<![CDATA[
$Title Thai Navy Problem (THAI,SEQ=98)
$Ontext
This model is used to allocate ships to transport personnel from
different port to a training center.
Choypeng, P, Puakpong, P, and Rosenthal, R E, Optimal Ship Routing
and Personnel Assignment for Naval Recruitment in Thailand.
Interfaces 16, 4 (1986), 356-366.
$Offtext
Sets i ports / chumphon, surat, nakon, songkhla /
j voyages / v-01* v-15 /
k ship classes / small, medium, large /
sc(i,k) ship capability / chumphon.(small,medium,large)
(surat,nakon).(medium,large)
songkhla.large /
vc(j,k) voyage capability ;
Parameter d(i) number of men at port i needing transport
/ chumphon = 475, surat = 659
nakon = 672, songkhla = 1123 /
shipcap(k) ship capacity in men / small 100
medium 200
large 600 /
n(k) number of ships of class k available
/ small 2, medium 3, large 4 / ;
Table a(j,*) assignment of ports to voyages
dist chumphon surat nakon songkhla
v-01 370 1
v-02 460 1
v-03 600 1
v-04 750 1
v-05 515 1 1
v-06 640 1 1
v-07 810 1 1
v-08 665 1 1
v-09 665 1 1
v-10 800 1 1
v-11 720 1 1 1
v-12 860 1 1 1
v-13 840 1 1 1
v-14 865 1 1 1
v-15 920 1 1 1 1
Scalar w1 ship assignment weight / 1.00 /
w2 ship distance traveled weight / .01 /
w3 personnel distance travel weight / .0001 / ;
vc(j,k) = prod(i$a(j,i), sc(i,k)); Display vc ;
Variables
z(j,k) number of times voyage jk is used
y(j,k,i) number of men transported from port i via voyage jk
obj ;
Integer Variables z; positive variables y ;
Equations
objdef
demand(i) pick up all the men at port i
voycap(j,k) observe variable capacity of voyage jk
shiplim(k) observe limit of class k ;
demand(i).. sum((j,k)$(a(j,i)$vc(j,k)), y(j,k,i)) =g= d(i) ;
voycap(j,k)$vc(j,k).. sum(i$a(j,i), y(j,k,i)) =l= shipcap(k)*z(j,k) ;
shiplim(k).. sum(j$vc(j,k), z(j,k)) =l= n(k) ;
objdef.. obj =e= w1*sum((j,k)$vc(j,k), z(j,k))
+ w2*sum((j,k)$vc(j,k), a(j,"dist")*z(j,k))
+ w3*sum((j,k,i)$(a(j,i)$vc(j,k)), a(j,"dist")*y(j,k,i)) ;
Model thainavy /all/;
z.up(j,k)$vc(j,k) = n(k) ;
Solve thainavy minimizing obj using mip ;
Display y.l, z.l ;
]]></plaintext></body></div>