This is one of the most brainteaser cases in my classes
Till today very few talented students have solved it
The case is connecting finance and statistics, and opens the door to supply chain conversations about inventory, service level, and cost
You are the owner of the restaurant "Fuego" in Marbella, famous for the delicious take away roasted chickens that you sell for lunch
Every morning you have to decide how many chickens to roast to meet the demand of the day
You sell the roasted chicken for 13€
Each roasted chicken costs 4€
You give to charity any remaining roasted chickens not sold
You have a good friend working in consultancy, ensuring daily demand is normally distributed with a mean of 80 roasted chickens and a standard deviation of 16 roasted chickens
How many chickens should you roast?
Why are you so concerned about how many chickens to roast?
The more chickens you roast, the more chickens you can sell...
is sales maximization your ultimate goal?
Same, the more chickens you roast, the more chickens you may not sell...
Is charity donations your business?
What is the objective?
If demand is bigger than your production, you are facing potential lost sales, the bigger the gap, the bigger your potential profit lost
If production is bigger than demand, you are facing a direct hit in your profit, the bigger the gap, the bigger the hit
The chickens discussion is around balancing opportunity cost and waste
The uncertainty in your demand is not helping, but your demand is normally distributed, so...
It is symmetrical around its center
It is defined by two values: the mean and the standard deviation
The mean is a measure of central tendency
The standard deviation measures the dispersion relative to the mean, as follows:
68% of values are within 1 standard deviation of the mean
95% of values are within 2 standard deviations of the mean
Almost all values (99.8%) are within 3 standard deviations of the mean
Start guessing to roast 80 chickens
Then check if roasting an addional chicken pays off
What is the probability of selling that additional chicken?
What is the probability of not selling that additional chicken?
50% and 50%
If in 50% of the days you increase profit by 9€ and in the other 50% of the days you lose 4€, then roasting 81 chickens is a better decision than roasting 80 chickens
Let's have a closer look to the normal distribution
There should be a number of roasted chicken where the potential profit from one more chicken sold equals the potential hit of one roasted chicken not sold
How many chickens should you roast?
Now move further...
What are your average sales and profit?
What is your service level?
What is the cost of improving your service level to 99%?
More discussion cases arriving soon