// $Id$
#include "flopc.hpp"
using namespace flopc;
#include "OsiCbcSolverInterface.hpp"
#include "CoinFloatEqual.hpp"


namespace Aircraft {
    enum {a, b, c, d, numA};
} 

int main() {

  /*The objective of this model is to allocate aircrafts to routes to maximize
  the expected profit when traffic demand is uncertain. Two different
  formulations are used, the delta and the lambda formualation.

  Dantzig, G B, Chapter 28. In Linear Programming and Extensions.
  Princeton University Press, Princeton, New Jersey, 1963.
  */
  {
    enum {route_1, route_2, route_3, route_4, route_5, numRoutes};
    const int numDemandStates = 5;

    MP_set i(Aircraft::numA); // aircraft types and unassigned passengers
    MP_set j(numRoutes);      // assigned and unassigned routes
    MP_set h(numDemandStates);// demand states 

    double ddval[5][5] = {{200,     220,    250,    270,    300},
    { 50,     150,      0,      0,      0},  
    {140,     160,    180,    200,    220},
    { 10,      50,     80,    100,    340},
    {580,     600,    620,      0,      0}};

    double lambdaval[5][5] =
    {{.2,     .05,    .35,    .2,     .2},
    {.3,     .7,    0.0,    0.0,    0.0},
    {.1,     .2,     .4,     .2,     .1},
    {.2,     .2,     .3,     .2,     .1},
    {.1,     .8,     .1,    0.0,    0.0}};


    double cval[4][5] =
    {{18,         21,         18,          16,           10},
    {0,          15,         16,          14,           9},
    {0,          10,          0,          9,            6},
    {17,         16,         17,          15,           10}};

    double pval[4][5] =
    {{16,         15,          28,          23,          81},
    {0,         10,          14,         15,          57},
    {0,          5,           0,           7,          29},
    {9,         11,          22,          17,          55}};

    MP_data dd(&ddval[0][0],j,h); //    dd.value(&ddval[0][0]);
    MP_data lambda(&lambdaval[0][0],j,h); //lambda.value(&lambdaval[0][0]);
    MP_data c(&cval[0][0],i,j); //     c.value(&cval[0][0]);
    MP_data p(&pval[0][0],i,j); //     p.value(&pval[0][0]);

    c.display("c");

    MP_data 
      aa(i),      // aircraft availiability 
      k(j),       // revenue lost (1000 per 100  bumped) 
      ed(j),      // expected demand
      gamma(j,h), // probability of exceeding demand increment h on route j
      deltb(j,h); // incremental passenger load in demand states;

    aa(Aircraft::a) = 10;  aa(Aircraft::b) = 19;  
    aa(Aircraft::c) = 25;  aa(Aircraft::d) = 15;

    k(route_1) = 13;
    k(route_2) = 13;
    k(route_3) =  7;
    k(route_4) =  7;
    k(route_5) =  1;

    ed(j) = sum(h, lambda(j,h)*dd(j,h));

    MP_index hp;

    gamma(j,h) = sum( h(hp).such_that(hp >= h), lambda(j,hp));

    deltb(j,h) = pos(dd(j,h)-dd(j,h-1));

    ed.display("ed");
    gamma.display("gamma");
    deltb.display("deltb");
    aa.display("aa");

    MP_variable
      x(i,j),   // number of aircraft type i assigned to route j
      y(j,h),   // passengers actually carried
      b(j,h),   // passengers bumped
      oc,       // operating cost
      bc;       // bumping cost

    MP_constraint
      ab(i),    // aircraft balance
      db(j),    // demand balance
      yd(j,h),  // definition of boarded passangers
      bd(j,h),  // definition of bumped passangers
      ocd,     // 
      bcd1,     // bumping cost definition: version 1
      bcd2;     // bumping cost definition: version 2


    ab(i) =   sum(j, x(i,j)) <= aa(i);
    ab.setName("aircraft balance");

    db(j) =  sum(i, p(i,j)*x(i,j)) >= sum( h.such_that(deltb(j,h)>0), y(j,h));
    db.setName("demand balance");

    yd(j,h) = y(j,h) <= sum(i, p(i,j)*x(i,j));
    yd.setName("definition of boarded passengers");

    bd(j,h) = b(j,h) == dd(j,h) - y(j,h);
    bd.setName("definition of bumped passengers");

    ocd() =     oc() == sum(i*j, c(i,j)*x(i,j));

    bcd1() =    bc() == sum(j, k(j)*(ed(j)-sum(h, gamma(j,h)*y(j,h))));

    bcd2() =    bc() == sum(j*h, k(j)*lambda(j,h)*b(j,h));

    MP_model m1(new OsiCbcSolverInterface), m2(new OsiCbcSolverInterface);

    y.upperLimit(j,h) = deltb(j,h);

    y.upperLimit.display("y upper");

    m1.add(ab).add(db).add(bcd1).add(ocd);
    m1.minimize(oc() + bc());

    assert(m1->getNumRows()==11);
    assert(m1->getNumCols()==47);
    assert(m1->getNumElements()==96);
    assert(m1->getObjValue()>=1566.03 && m1->getObjValue()<=1566.05);

    y.display("y first model");
    ab.display("ab");
    db.display("db");
    bcd1.display("bcd1");
    ocd.display("ocd");

    m2.add(ab).add(yd).add(bd).add(bcd2).add(ocd);
    y.upperLimit(j,h) = m2->getInfinity();

    m2.minimize(oc() + bc());

    assert(m2->getNumRows()==56);
    assert(m2->getNumCols()==72);
    assert(m2->getNumElements()==219);
    
    // Optimal objective value m1: 1566.04218913
    // Optimal objective value m2: 1566.04218913 (like m1)
    assert(m2->getObjValue()>=1566.03 && m2->getObjValue()<=1566.05);

    CoinRelFltEq eq;
    assert( eq(m2->getObjValue(),1566.04218913) );
    assert( eq(m1->getObjValue(),1566.04218913) );

    y.display("y second model");
  }
  cout<<"All tests completed successfully"<<endl;

}

