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set D_CITY;
set W_CITY;
set DW_LINKS within (D_CITY cross W_CITY);
param p_supply >= 0; # amount available at plant
param w_demand {W_CITY} >= 0; # amounts required at warehouses
check: p_supply = sum {j in W_CITY} w_demand[j];
param pd_cost {D_CITY} >= 0; # shipment costs/1000 packages
param dw_cost {DW_LINKS} >= 0;
param pd_cap {D_CITY} >= 0; # max packages that can be shipped
param dw_cap {DW_LINKS} >= 0;
var PD_Ship {i in D_CITY} >= 0, <= pd_cap[i];
var DW_Ship {(i,j) in DW_LINKS} >= 0, <= dw_cap[i,j];
# packages to be shipped
minimize Total_Cost:
sum {i in D_CITY} pd_cost[i] * PD_Ship[i] +
sum {(i,j) in DW_LINKS} dw_cost[i,j] * DW_Ship[i,j];
subject to P_Bal: sum {i in D_CITY} PD_Ship[i] = p_supply;
subject to D_Bal {i in D_CITY}:
PD_Ship[i] = sum {(i,j) in DW_LINKS} DW_Ship[i,j];
subject to W_Bal {j in W_CITY}:
sum {(i,j) in DW_LINKS} DW_Ship[i,j] = w_demand[j];
display dw_cost;
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