thaix.gms : Thai Navy Problem Extended

**Description**

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.

**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

**Category :** GAMS Model library

**Main file :** thaix.gms

$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. $Offtext Sets p ports / chumphon, surat, nakon, songkhla / v voyages / v-01* v-15 / k ship classes / small, medium, large / Variables 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 Variables z; positive variables y ; Equations 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 Sets vk(v,k) voyage capability vkp(v,k,p) trips: voyage - ship class - port Parameters 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 Scalars 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 ;