What the numbers reported by the model mean
The model doesn't just say what to do; it also says how much it is worth to change each thing. With a single example (a cream and a gel) we see the optimal value, activity, slack, shadow price, reduced cost, break-even, and elasticity.
Move the sliders: the numbers change just like in the model.
Moisturizing cream
Exfoliating gel
1 · Optimal value and activity
also: objective function (Z) · primal solution · variable valueWhat is the best that can be achieved, and by doing what?
The optimal value is the best possible profit under the business rules. The activity is how much of each thing the plan makes: 500 units of cream and 0 of gel. No other combination yields more.
2 · Active constraint and slack
also: limit · constraint activity · slackWhich rule is holding back the plan?
A constraint is active (or binding) when it is fully used (slack 0): it is the one preventing us from earning more. The one with slack does not get in the way. Here, inventory rules, not the market.
3 · Shadow price
also: shadow price · dual value · marginal value of a constraintIf I had one more unit of inventory, how much would I earn?
The shadow price (or dual value) is the slope of the profit: how much Z increases if a constraint is relaxed by one unit. Only active constraints have it. Note: it is valid within a range. Beyond 600 units, the market rules, and an additional unit of inventory is worth $0; now the shadow price belongs to demand.
4 · Reduced cost and break-even
also: reduced cost (of a variable) · equilibrium value · equilibrium priceWhy isn't gel being sold, and at what price would it be worth it?
The reduced cost of a variable that the plan leaves at zero tells us how much it would cost to force it. The break-even is the price (or cost) at which it starts to become profitable: here, $45. A variable that is already profitable (like the cream) has a reduced cost of 0 and no break-even.
5 · Price elasticity
also: elasticity of demand · price sensitivityIf I raise the price of the cream, how much sales do I lose?
The elasticity is how much the units sold change for every 1% increase in price (−2: raising the price by 1% lowers sales by 2%). If it is elastic (greater than 1 in absolute value), lowering the price increases revenue; if it is inelastic, raising the price increases it. The model measures it using the history of each product, and if you activate it, the demand of a scenario responds to its price.
How much of each thing to make?
- Activity: how much the plan makes (units to sell, buy, hold).
- Min / Max: the range within which it can move.
- Reduced cost: how much it would cost to force one more unit of something that is not profitable.
- Break-even: the price or cost at which it would start to be profitable.
What holds back the plan and how much is it worth to relax it?
- Activity: how much of the limit is used.
- Slack: how much is left over; 0 = active and binding.
- Shadow price: how much the plan would gain if the limit increased by one unit.
- Range: how far that value is valid before another rule takes over.
In a table
| Concepto | Other names | Answers | In the example | Where it is seen |
|---|---|---|---|---|
| Optimal value | Objective function, Z | What is the best possible outcome? | $30,000 | Results › header |
| Activity | Primal, variable value | How much to do? | 500 units of cream, 0 of gel | Activity report › Variables |
| Slack | Slack | How much is left of the limit? | Inventory 0 · demand 100 | Activity report › Constraints |
| Shadow price | Shadow price, dual value | How much is it worth to relax a rule? | $60 per unit of inventory | Constraints · Inventories |
| Reduced cost | Reduced cost | How much does it cost to force something? | −$5 per unit of gel | Activity report › Variables |
| Break-even | Equilibrium value or price | At what price does it become profitable? | Gel at $45 | Variables · Products |
| Elasticity | Price sensitivity | How much do sales drop if the price increases? | −2 → +10% price = −17% units | Products · Gantt · Excel |
The idea in one sentence
The optimal value tells us how much can be earned; the activity, what to do; the shadow price, which limit is worth expanding; the reduced cost and the break-even, what is not profitable and at what price it would be; and the elasticity, how the market reacts to price.