Set CITIES /NE , SE ,  BOS , EWR , BWI , ATL , MCO , PITT  /;
Set D_CITY(CITIES) /  NE , SE  / ;
Set W_CITY(CITIES) / BOS , EWR , BWI , ATL , MCO / ;
Set p_city(CITIES) / PITT /;

Alias(CITIES,CITIES_1);

Set DW_LINKS(CITIES,CITIES_1) / NE.BOS , NE.EWR , NE.BWI ,
                                SE.EWR , SE.BWI , SE.ATL , SE.MCO /;

Set Add(CITIES,CITIES_1); Add(CITIES,CITIES_1) = yes$((p_city(CITIES))and(D_CITY(CITIES_1)));
Set LINKS(CITIES,CITIES_1);  LINKS(CITIES,CITIES_1) = DW_LINKS(CITIES,CITIES_1)+ Add(CITIES,CITIES_1) ;


Parameter p_supply; p_supply = 450 ;
* amount available at plant
Parameter Supply(CITIES);  Supply(CITIES)$p_city(CITIES) = p_supply ;

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

Parameter cost(CITIES,CITIES_1) /  PITT.NE    2.5 ,  PITT.SE    3.5 ,
                                   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 /    ;
* shipment costs/100 packages

Parameter capacity(CITIES,CITIES_1) /  PITT.NE        250 ,  PITT.SE        250 ,
                                       NE.BOS         100 ,  NE.EWR         100 ,
                                       NE.BWI         100 ,  SE.EWR         100 ,
                                       SE.BWI         100 ,  SE.ATL         100 ,
                                       SE.MCO         100 / ;
* max packages that can be shipped



Positive Variable Ship[CITIES,CITIES_1] ;
* Ship -> packages to be shipped

         Variable Total_Cost ;

Equation Eq_Balance(CITIES) , Eq_check , Def_obj ;

Eq_Balance(CITIES)..    supply[CITIES] +
                        sum{CITIES_1$LINKS(CITIES_1,CITIES), Ship[CITIES_1,CITIES]} =e=
                        w_demand[CITIES] +
                        sum{CITIES_1$LINKS(CITIES,CITIES_1), Ship[CITIES,CITIES_1]} ;

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

Def_obj.. Total_Cost =e=  sum{(CITIES,CITIES_1)$LINKS(CITIES,CITIES_1),
                                 cost[CITIES,CITIES_1] * Ship[CITIES,CITIES_1]};

Ship.up[CITIES,CITIES_1] = capacity[CITIES,CITIES_1]

Model net2 /all/;

Solve net2 using lp minimizing total_cost ;