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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 2 of 20
The real wordsTheory

The capacitated plant-location problem

Network designChoosing which plants to operate and how much each one ships to each market, so that total cost is minimised, subject to each plant's capacity and each market's demand being met.

Three cost pieces make the objective:

Total cost = SUM (fixed facility cost of each open plant) + SUM (production cost x units made at that plant) + SUM (transport cost x units shipped plant -> market)

Two constraint families: no plant ships more than its capacity, and every market's demand is fully met.

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