Attention, Revenue Mavericks in DS City! The clock is ticking in the concrete jungle, and we have 10,000 precious, pine-scented assets to sell before Christmas!
This isn't just about maximizing revenue; it's about navigating the chaos of three wildly different customer segments across three critical sales periods (P1: Nov 28-Dec 9, P2: Dec 10-Dec 19, P3: Dec 20-Dec 24).
🌟 Our "Luxury" 10,000 Tree Inventory Consists of Three Types
- Charlie Brown (CB) (3,500 trees): Inexpensive, poor-looking, and barely bears needles. Your tree if you are truly desperate or budget-conscious.
- Homer Simpson (HS) (5,500 trees): The average tree for the average family, complete with a complimentary donut holder (probably).
- Scarlett O'Hara (SO) (1,000 trees): Not actually better looking than the Homer, but grossly overpriced for the entitled customer who needs to feel special. Frankly, the profit margin here is criminal.
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📉 The High-Stakes Wager
Your job is the most stressful of the season: allocate our inventory to the three sales periods!
Do you satisfy the initial rush in early December, or do you hold back the inventory, betting that some desperate procrastination shoppers will pay the higher margins? Be careful; every tree left unsold on December 25th results in a heartbreaking $15 loss.
Challenge: Use the demand and profit data below to calculate the optimal allocation to maximize our total expected profit. Provided you haven't filled up on eggnog yet.
What is it going to be? Newsvendor formula? Integer Programming? Or will you solve it the right way and use Seeker in a Google Colab.
Keep in mind that inventory not sold in one period spills over into the next!
If you used a deterministic solver for this problem, you will likely have seen this solution:
The MIP solver probably also claimed that your expected profit will be $318,000. Alas, this is a usual MIP hallucination that utterly ignores the fact that demand is uncertain.
Since we face a $15 loss when trees are left over instead of making a profit, we have to be more cautious. The MIP solution would, in reality, only give us an average profit of about $306,450.
If we optimize using Seeker with its stochastic optimization capabilities, we obtain this solution:
We see how the solver moves more inventory upfront to avoid having grown trees that will not be sold. As a result, the Seeker solution gives us an expected profit of about $313,050. That is about $6,600, or 2.1% more than the solution provided by a deterministic solver, and should cover the gifts for the family. Courtesy of using Seeker.
The full Seeker model for this problem is given here.
Merry Christmas!
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