ccoil.gms : Oil Pipeline Design Problem using concurrent MIP solves

Description

J. Brimberg, P. Hansen, K.-W. Lih, N. Mladenovic, M. Breton 2003.
An Oil Pipeline Design Problem. Operations Research, Vol 51, No. 2 228-239

Keywords: mixed integer linear programming, designment problem


Reference

  • Brimberg, J, Hansen, P, Lih, K, Mladenovic, N, and Breton, M, An Oil Pipeline Design Problem. Operations Research 51 (2) (2003), 228-239.

Large Model of Type : MIP


Category : GAMS Model library


Main file : ccoil.gms

$title Oil Pipeline Design Problem using concurrent MIP solves (CCOIL,SEQ=370)

$onText
J. Brimberg, P. Hansen, K.-W. Lih, N. Mladenovic, M. Breton 2003.
An Oil Pipeline Design Problem. Operations Research, Vol 51, No. 2 228-239

Keywords: mixed integer linear programming, designment problem
$offText

Set
   n          'nodes in the oil pipeline network'
   nw(n)      'subset of nodes'
   k          'type of oil pipe'
   kk(k)      'reduced set of pipe line types'
   regnode(n) 'non-port nodes'
   port(n)    'port'
   arc(n,n)   'arcs in the network';

Parameter
   cap(k)        'capacity of type k oil pipe'
   pipecost(k)   'monetary units for type k capacity'
   p(n)          'production at each node'
   edgedist(n,n) 'one way distance'
   dist(n,n)     'the distance of the arcs';

Scalar
   cap1      'capacity of type 1 oil pipe'
   pipecost1 'monetary units for pipe of type 1';

Alias (n,m);

Variable
   bk(n,n,k) 'build variable for type k pipe on the arc'
   b(n,n)    'build variable for some pipe on the arc'
   f(n,n)    'flow variable on the arc'
   cost      'the cost for installing pipes in the network';

Binary   Variable bk, b;

Positive Variable f;

Equation
   obj        'oil pipeline network construction cost'
   oneout(n)  'at most one out-flow each node'
   oneoutp(n) 'one out-flow for each production node'
   bal(n)     'flow conservation constraints'
   bigM(n,n)  'the flow capacity constraints'
   defb(n,n)  'additional pipe constraint';

obj..   sum(arc(nw,n), dist(arc)*(pipecost1*b(arc)
      + sum(kk, pipecost(kk)*bk(arc,kk))))     =e= cost;

oneout(m)$(not p(m)).. sum((arc(m,n)), b(m,n)) =l= 1;

oneoutp(m)$p(m)..      sum((arc(m,n)), b(m,n)) =e= 1;

bal(regnode(nw)).. p(nw) =e= sum(arc(nw,m), f(nw,m)) - sum(arc(m,nw), f(m,nw));

bigM(arc(nw,n))..  cap1*b(arc) + sum(kk, cap(kk)*bk(arc,kk)) =g= f(arc);

defb(arc(nw,n))..  sum(kk, bk(arc,kk)) =l= b(arc);

Model ccoil / all /;

Set
   k 'type of oil pipe' / 1*6 /
   n 'nodes in the oil pipeline network'
     /  1 'H87',                2 'ECHIRA',              3 'SIMBA-CONOCO-C'
        4 'AGIP-TASSI',         5 'SIMBA-CONOCO-B',      6 'J87'
        7 'CONN07',             8 'MBASSI-CONOCO',       9 'WELL09'
       10 'NAMBA-TENNECO',     11 'ELF-B',              12 'NDOGO-C-ELF'
       13 'PANGA-AGIP',        14 'BIGORNEAU',          15 'CONN15'
       16 'AGIP-PANGA-B',      17 'CONN17',             18 'MASSANGA-TENNECO-A'
       19 'WELL19',            20 'MASSANGA-TENNECO-B', 21 'TCHIBALA-ELF'
       22 'HOURICULA',         23 'LUCINA-SHELL',       24 'CONN24'
       25 'CONN25',            26 'TCHIBOBO-TRITON-A',  27 'CONN27'
       28 'MWENGUI-ELF',       29 'MBYA-ELF',           30 'CONN30'
       31 'TCHIBOBO-TRITON-B', 32 'K8',                 33 'GAMBA '           /;

Parameter
   cap(k)        'capacity of type k oil pipe'
                 / 2 5, 3 10, 4 25, 5 50, 6 100 /
   pipecost(k)   'monetary units for type k capacity'
                 / 2 10, 3 15, 4 25, 5 40, 6 65 /
   p(n)          'production at each node'
                 / 1  5, 2  7, 3  5, 4  6, 5   5, 6  4, 8  7, 9  3, 10 5
                   11 4, 12 3, 13 6, 14 9, 16  5, 18 6, 19 5, 20 4, 21 6
                   22 3, 23 8, 26 5, 28 5, 29 10, 31 6, 32 6             /
   edgedist(n,n) 'generalized distance of each edge'
                 / 1 .2  3.50, 1 .3  1.90, 1 .4  5.40, 2 .3  3.70, 2 .7  1.15
                   3 .4  4.90, 3 .5  2.50, 3 .7  2.60, 3 .33 4.80, 4 .5  5.30
                   4 .6  4.00, 5 .6  4.30, 5 .8  2.70, 5 .9  2.10, 5 .33 3.75
                   6 .8  2.60, 7 .33 1.60, 8 .9  2.20, 8 .10 2.20, 9 .12 2.30
                   9 .33 1.60, 10.11 2.00, 10.13 2.80, 10.33 5.30, 11.12 1.10
                   11.13 1.80, 12.13 2.50, 12.14 1.20, 12.33 3.00, 13.14 2.10
                   13.16 3.20, 14.15 1.20, 14.16 5.30, 15.16 6.30, 15.17 2.10
                   15.33 1.65, 16.17 4.80, 17.19 7.30, 17.24 2.70, 18.19 1.50
                   19.20 1.80, 19.21 0.90, 19.23 3.00, 20.21 1.30, 20.26 2.20
                   20.29 4.80, 21.22 2.50, 21.23 2.80, 21.26 2.90, 22.23 0.80
                   23.24 2.40, 23.25 3.00, 23.26 5.00, 23.29 3.70, 24.25 0.90
                   24.29 4.50, 25.29 3.30, 25.30 0.90, 26.27 1.20, 26.28 2.80
                   26.31 2.50, 27.28 2.10, 27.31 1.50, 28.29 1.30, 28.31 3.00
                   29.30 2.60, 29.31 4.00, 30.32 0.90                         /;

Set
   regnode(n) 'non-port nodes'
   port(n)    'port'
   arc(n,n)   'arcs in the network'
   kk(k)      'reduced set of pipe line types';

Parameter dist(n,n) 'the distance of the arcs';

dist(m,n) = edgedist(m,n) + edgedist(n,m);
arc(m,n)$dist(m,n) = yes;

* Last node is the port
port(n)$(card(n) = ord(n)) = yes;
regnode(n)    = yes;
regnode(port) =  no;
arc(port,n)   =  no;

kk(k)     = yes;
kk('1')   = no;
kk('2')   = no;
pipecost1 = pipecost('2');
cap1      = cap('2');

* Adjust data for removed pipe line type
pipecost(kk) = pipecost(kk) - pipecost1;
cap(kk)      = cap(kk) - cap1;

nw(n) = yes;

Set
   s     'solvers'    / cbc, scip, gurobi, cplex, xpress /
   mtype 'model type' / mip /
   ss(s) 'solvers available';

ss(s) = SolverCapabilities(s,'mip');

Parameter h(s) 'handle';

ccoil.solveLink = %solveLink.AsyncGrid%;
ccoil.resLim    = 60;

option limRow = 0, limCol = 0, solPrint = silent, optCr = 0, optCa = 0;

loop(ss,
   if(sameas('cbc',    ss), option mip = cbc);
   if(sameas('cplex',  ss), option mip = cplex);
   if(sameas('gurobi', ss), option mip = gurobi);
   if(sameas('scip',   ss), option mip = scip);
   if(sameas('xpress', ss), option mip = xpress);
   solve ccoil minimizing cost using mip;
   h(ss) = ccoil.handle;
);

Parameter rep, haveSolution / 0 /;

$eolCom //
* Now collect
repeat
   loop(ss$handlecollect(h(ss)),
      rep(ss,'solveStat') = ccoil.solveStat;
      rep(ss,'modelStat') = ccoil.modelStat;
      rep(ss,'resUsd'   ) = ccoil.resUsd;
      rep(ss,'objVal')    = ccoil.objVal;
      display$handledelete(h(ss)) 'trouble deleting handles';
      h(ss) = 0;
      haveSolution$(ccoil.modelStat = %modelStat.Optimal% or ccoil.modelStat = %modelStat.IntegerSolution%) = 1;
   );
   if(haveSolution = 0, display$sleep(0.25) 'was sleeping for 1/4 second');
until haveSolution = 1 or card(h) = 0 or timeelapsed > 70;

display rep;

* We might have some solver processes still running. If the grid
* directory is the scratch directory, we better wait for the jobs to
* terminate otherwise we will have trouble removing the scratch
* directory which happens automatically when GAMS terminates.

$ifthen "%gams.scrdir%"=="%gams.griddir%"
repeat
   loop(ss$handlecollect(h(ss)),
      rep(ss,'solveStat') = ccoil.solveStat;
      rep(ss,'modelStat') = ccoil.modelStat;
      rep(ss,'resUsd'   ) = ccoil.resUsd;
      rep(ss,'objVal')    = ccoil.objVal;
      display$handledelete(h(ss)) 'trouble deleting handles';
      h(ss) = 0;
   );
   display$sleep(card(h)*0.25) 'was sleeping some time';
until card(h) = 0 or timeelapsed > 70;
display rep;
$endif

abort$(haveSolution = 0) 'We did not find an integer solution';