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Sem 5 Prep
← OperationsNetwork design and the transportation model

Formulas for this chapter

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
Step 1 of 20
The ideaTheory

Five kitchens, six dinner parties

You have five kitchens and six dinner parties to cater. Each kitchen can only cook so much. Each kitchen costs a fixed amount to open at all, and costs a different amount to cook and to drive from.

Which kitchens do you open, and which party does each one feed?

That is the network-design problem. It is the fourth of the four location methods, and it is the only one that chooses several facilities at once.

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