Delivered cost
Delivered cost (i to j) = production cost at plant i + transport cost from i to j
The first thing to build in any network-design problem. Allocate on this, never on production cost alone.
- production cost at i
- Cost of making one unit at plant i
- transport cost i to j
- Cost of moving one unit from plant i to market j
Network total cost
Total cost = SUM(fixed cost of open plants)
+ SUM(delivered cost i-to-j x units shipped i-to-j)
Costing any candidate network. Fixed cost is counted once per open plant, whatever volume it carries.
- fixed cost
- Facility cost incurred only if the plant runs
- units shipped
- The decision variable in each cell of the tableau
Penalty per unit
Penalty = second-cheapest delivered cost - cheapest delivered cost
When a plant is over capacity. Move markets off it in ascending order of penalty until the row fits.
- cheapest
- Lowest delivered cost for that market, from the overloaded plant
- second-cheapest
- Next lowest delivered cost, from a plant with spare capacity
Plant closure test
Net saving = fixed cost avoided - SUM(units moved x penalty per unit)
Feasible only if remaining capacity >= total demand
Whenever total capacity comfortably exceeds total demand. Run the feasibility check first.
- fixed cost avoided
- The closed plant's facility cost
- penalty per unit
- Extra delivered cost at the receiving plant