$title Thai Navy Problem Extended (THAIX,SEQ=105)

$onText
This model is an extension of the original library model THAI.
Multidimensional sets (tuples and maps) are used to allow a more
compact representation. MIP priorities are used to speed up the
solution process. Data definitions are moved from the beginning to
the end of the model definitions. Overall, the 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.

Keywords: mixed integer linear programming, routing, scheduling, naval
          recruitment, scenario analysis
$offText

Set
   p 'ports'        / chumphon, surat, nakon, songkhla /
   v 'voyages'      / v-01*v-15 /
   k 'ship classes' / small, medium, large /;

Variable
   z(v,k)    'number of times voyage vk is used'
   y(v,k,p)  'number of men transported from port p via voyage vk'
   obj       'objective function to be minimized'
   voyages   'the number of voyages'
   shipmiles 'ship miles'
   manmiles  'man miles';

Integer  Variable z;
Positive Variable y;

Equation
   objdef      'objective function definition'
   dvoyages    'definition of the number of voyages'
   dshipmiles  'definition of ship miles'
   dmanmiles   'definition of man miles'
   demand(p)   'pick up all the men at port p'
   voycap(v,k) 'observe variable capacity of voyage vk'
   shiplim(k)  'observe limit of class k';

Set
   vk(v,k)    'voyage capability'
   vkp(v,k,p) 'trips: voyage - ship class - port';

Parameter
   d(p)       'number of men at port p needing transport'
   shipcap(k) 'ship capacity in men'
   n(k)       'number of ships of class k available'
   dist(v)    'voyage distance';

Scalar
   w1 'ship assignment weight'
   w2 'ship distance traveled weight'
   w3 'personnel distance travel weight';

demand(p)..       sum(vkp(vk,p), y(vkp)) =g=  d(p);

voycap(vk(v,k)).. sum(vkp(vk,p), y(vkp)) =l=  shipcap(k)*z(vk);

shiplim(k)..      sum(vk(v,k), z(vk))    =l=  n(k);

dvoyages  ..      voyages   =e= sum(vk, z(vk));

dshipmiles..      shipmiles =e= sum(vk(v,k), dist(v)*z(vk));

dmanmiles ..      manmiles  =e= sum(vkp(v,k,p), dist(v)*y(vkp));

objdef..          obj       =e= w1*voyages + w2*shipmiles + w3*manmiles;

Model thainavy / all /;

$sTitle Data
Set kp(k,p)   'port capability' / small. (chumphon)
                                  medium.(chumphon,surat,nakon)
                                  large. (chumphon,surat,nakon,songkhla) /;

Parameter
   d(p)       'number of men at port p 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 available'                 / small       2
                                                            medium      3
                                                            large       4 /;

Table a(v,*) '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;

vk(v,k)        = prod(p$a(v,p), kp(k,p));
vkp(vk(v,k),p) = yes$a(v,p);
dist(v)        = a(v,'dist');
z.up(vk(v,k))  = n(k);

z.prior(vk(v,'small'))  = 3;
z.prior(vk(v,'medium')) = 2;
z.prior(vk(v,'large'))  = 1;

thainavy.priorOpt = 1;
thainavy.limCol   = 0;
thainavy.limRow   = 0;

w1 = 1; w2 = 0; w3 = 0;
solve thainavy minimizing obj using mip;

w1 = 0; w2 = 1; w3 = 0;
solve thainavy minimizing obj using mip;

w1 = 0; w2 = 0; w3 = 1;
solve thainavy minimizing obj using mip;