Shadow Prices: What One More Unit Is Worth

Lesson notes

Key points

• Every linear programme, called the primal, has a partner problem called the dual, built from the same numbers.
• Each dual variable is a shadow price: how much the optimal objective improves if one constraint's right-hand side rises by one unit.
• Strong duality says that at optimality the primal and dual objective values are exactly equal.
• So if blasting hours at a mine have a shadow price of zero, that resource is not binding and buying more adds nothing.

Definitions

Shadow price

Change in optimal objective per one-unit increase in a constraint's right-hand side, within its valid range.

Takeaway: Shadow prices tell you what one more unit of a resource is worth.

Dual problemShadow priceStrong dualityNon-binding constraint