$title Oil Pipeline Design Problem using BCH Facility (BCHOIL,SEQ=288)

$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

Michael Bussieck, Hua Ni
Technical Note: Solving an Oil Pipeline Design Problem with the GAMS
Branch-and-Cut Facility
Technical report, GAMS Development Corp. 2003.

Keywords: mixed integer linear programming, branch and cut and heuristic facility,
          pipeline designment, network optimization
$offText

$onEcho > oilbase.inc
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';

* Data structure for the cut generation
Set
   ss          'index for mip solutions' / 1*100 /
   dsh(ss,n,n) 'the descendant structure of previous integer solutions';

Scalar
   siter 'current solution';

Alias (n,nn,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 oilbase / all /;
$offEcho

$include oilbase.inc
$include bchoil_d.inc
$echo heurcnt = 0; > pwl.ind

execute_unload 'net.gdx', n k kk port regnode arc p cap dist pipecost cap1 pipecost1;
siter = 1;
execute_unload 'dsh.gdx', ss siter dsh;

$ifThenI %system.mip% == cplex $set solver cplex
$else
$abort 'BCH Facility not available for MIP solver %system.mip%.'
$endIf

$onEcho > %solver%.opt
userHeurCall bchoil_h.inc optCr 0 resLim 10 lo=2 lf=bchoil_c.log o=bchoil_h.lst --mipsolver=%system.mip%
userHeurFirst 5
userHeurObjFirst 5
userHeurFreq 20
userHeurInterval 1000

userCutCall bchoil_c.inc lo=2 lf=bchoil_c.log o=bchoil_c.lst --mipsolver=%system.mip%
userCutFirst 0
userCutFreq 0
userCutNewInt yes
$offEcho

$ifI %system.mip% == cplex $echo varsel 3 >> cplex.opt

nw(n) = yes;
oilbase.optFile = 1;
solve oilbase minimizing cost using mip;