Set Sities /NE , SE , BOS , EWR , BWI , ATL , MCO /;
Set D_CITY(Sities) / NE , SE /;
Set W_CITY(Sities) / BOS , EWR , BWI , ATL , MCO /;

Alias(Sities,Sities_1);

Set DW_LINKS(Sities,Sities_1) / NE.BOS , NE.EWR , NE.BWI ,
                                SE.EWR , SE.BWI , SE.ATL , SE.MCO /;
Parameter p_supply / 450 / ;
* amount available at plant

Parameter w_demand(Sities) /  BOS  90,  EWR 120,  BWI 120,  ATL  70,  MCO  50 /;
* amounts required at warehouses

Parameter  pd_cost / NE 2.5 ,  SE 3.5 /;
Parameter  pd_cap /  NE 250 ,  SE 250 / ;

Parameter dw_cost(sities,sities_1) /  NE.BOS   1.7 ,  NE.EWR     0.7 ,
                                      NE.BWI   1.3 ,  SE.EWR     1.3 ,
                                      SE.BWI   0.8 ,  SE.ATL     0.2 ,
                                      SE.MCO   2.1 /;

Parameter dw_cap(sities,sities_1)  /  NE.BOS   100 ,  NE.EWR     100 ,
                                      NE.BWI   100 ,  SE.EWR     100 ,
                                      SE.BWI   100 ,  SE.ATL     100 ,
                                      SE.MCO   100 /;


Positive Variables DW_Ship[Sities,Sities_1] , PD_Ship[Sities] ;
* packages to be shipped
Variables Total_Cost ;

Equation Eq_check ,
         Eq_P_Balance ,
         Eq_D_Balance(Sities) ,
         Eq_W_Balance(Sities_1) ,
         Def_obj ;

Eq_check.. p_supply =e= sum{Sities$W_CITY(Sities), w_demand[Sities]};

Eq_P_Balance..
  sum{Sities$D_CITY(Sities), PD_Ship[Sities]} =e= p_supply;

Eq_D_Balance(Sities)$D_CITY(Sities)..
                      PD_Ship[Sities] =e= sum{Sities_1$DW_LINKS(Sities,Sities_1),
                                                      DW_Ship[Sities,Sities_1]};

Eq_W_Balance(Sities_1)..
                      sum{Sities$DW_LINKS(Sities,Sities_1),
                               DW_Ship[Sities,Sities_1]} =e= w_demand[Sities_1];

Def_obj..
Total_Cost =e=  sum{Sities$D_CITY(Sities),
                                          pd_cost[Sities] * PD_Ship[Sities]} +
                sum{(Sities,Sities_1)$DW_LINKS(Sities,Sities_1),
                           dw_cost[Sities,Sities_1] * DW_Ship[Sities,Sities_1]};

PD_Ship.up[Sities] = pd_cap[Sities] ;
DW_Ship.up[Sities,Sities_1] = dw_cap[Sities,Sities_1] ;

Model net3node /all/;

Solve net3node using nlp minimazing total_cost ;

Display total_cost.l ;