net3.mod

net3.mod

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];