net2.mod

net2.mod

param p_city symbolic;

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 {k in W_CITY} w_demand[k];

set CITIES = {p_city} union D_CITY union W_CITY;
set LINKS = ({p_city} cross D_CITY) union DW_LINKS;

param supply {k in CITIES} =
   if k = p_city then p_supply else 0;

param demand {k in CITIES} =
   if k in W_CITY then w_demand[k] else 0;

### Remainder same as general transshipment model ###

param cost {LINKS} >= 0;      # shipment costs/1000 packages
param capacity {LINKS} >= 0;  # max packages that can be shipped

var Ship {(i,j) in LINKS} >= 0, <= capacity[i,j];
                              # packages to be shipped

minimize Total_Cost:
   sum {(i,j) in LINKS} cost[i,j] * Ship[i,j];

subject to Balance {k in CITIES}:
   supply[k] + sum {(i,k) in LINKS} Ship[i,k]
      = demand[k] + sum {(k,j) in LINKS} Ship[k,j];