Interpret the dual values of a pricing LP and decide what to do
A multi-SKU pricing LP over 64 candidate price vectors for a store brand, a national brand and a premium brand returns, per store-week, the optimal profit and these dual values for its constraints (all with profit per store-week as the objective):
| Scenario | Optimal profit | Dual: store-brand stock row (per unit) | Dual: margin floor row (per dollar of margin shortfall) |
|---|---|---|---|
| Stock limit 150 units, no floor | 2,739.77 | 0.473 | not present |
| Stock limit 150 units + portfolio margin floor 52% | 2,731.08 | 0.384 | 0.148 |
| No stock limit, no floor | 2,753.99 | none | none |
The store-brand unit margin is about 6 to 7 dollars. (a) Explain what the stock dual of 0.384 means, and why it is far below the unit margin. (b) The supply team offers a rush shipment of 20 extra units per store-week at a cost of 0.30 per unit; another offer is 0.50 per unit. Which do you take, and how far can you trust the dual? (c) The CFO asks for a 55 percent floor. What do the duals and a re-solve tell you? (d) Suppose a ladder constraint (the store brand must be priced below the national brand) is also in the model and has a dual of 0. What does it mean?
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