Decision Science must provide answers even if we face problems that are not fully quantified. Can you handle ambiguity?
George manages 100 acres of land. He faces an annual dilemma that is now compounded by climate volatility: He must commit to his planting and pre-selling contracts without knowing the weather. The coming summer could be severely wet or agonizingly dry, and George must choose a plan that secures the financial well-being of his company.
He plans to grow two crops.
The Pre-Sale Contract Parameters
George can pre-sell units of either crop before planting, guaranteeing a stable income stream at a price of $3.90 per unit for both Crop A and Crop B, provided he can deliver on his promises.
However, if George fails to deliver the contracted amount, he faces penalties:
- Pre-Sale Price (A & B): $3.90 per unit sold.
- Penalty for Shortfall (A): $1.50 per unit not delivered.
- Penalty for Shortfall (B): $1.45 per unit not delivered.
Scenario 1: The Heavy Rains (Wet Summer)
This scenario strongly favors Crop A.
Scenario 2: The Extended Drought (Dry Summer)
This scenario requires expensive inputs for Crop A but is ideal for Crop B.
The Decision Challenge
George must determine his plan for the 100 acres:
- Acreage Allocation: How many acres of Crop A and Crop B should be planted? Fractions of acres are allowed.
- Contract Commitments: How many units of Crop A and Crop B should be pre-sold?
Finally, George needs to make at least $50,000 to cover the other fixed costs of his business. What would you recommend that George should do given that we have no probabilities for either scenario?
You are probably thinking of maximizing the minimum profit. Good. But are there other options as well?
Seeker suggests making these allocations, using its proprietary multi-objective optimization:
For these profits:
This solution provides a rational compromise between maximizing the minimum profit and minimizing the maximum regret.
To maximize the minimum profit, we would set:
For a guaranteed profit of $131,314.
While this guarantee is appealing, we squander opportunity by being too paranoid. After all, if the weather is favorable (in our case: if it is wet), we could make much more profit. In fact, if we knew the weather, we would plant 100% Crop A for wet conditions and presell all 80,000 units for a total profit of $292,000. For dry conditions, we would plant Crop B and presell all 60,000 units for a total profit of $220,000.
We may therefore consider minimizing the maximum regret, which is the loss when compared to the maximum profit that we could achieve under the respective conditions.
For this model, we obtain these allocations:
For these profits:
We see that we take much more of the upside in wet conditions now, but this comes at the unquantified risk of ending up with only $106,000 in dry conditions.
One final option is to maximize the expected profit while assuming both scenarios were equally likely. In this case, we should only plant Crop A and presell 30,000 units, for these profits:
Let us compare the profit under all strategies for both scenarios:
We see how Seeker's multi-objective optimization finds a very favorable compromise between seizing the potential of wet weather conditions while effectively mitigating the risk of dry weather.
And this is what real-world decision science is all about: finding favorable compromises. Can your solver do that?