Baker / Newspaper / Fresh product store dilemma

Problem: A small bakery sells fresh croissants every morning. Each croissant costs $1 to produce and is sold for $3. However, the bakery doesn’t know exactly how many customers will come each day.

Key Facts:

  • Demand is uncertain: On weekdays, the demand ranges, let's say from 50 to 100 croissants.
  • Leftover pastries are wasted: Unsold croissants cannot be resold the next day due to freshness requirements. They are thrown away, representing a loss.
  • Understocking means lost profit: If the bakery doesn’t have enough croissants to meet customer demand, it loses potential sales and risks disappointing customers.

The bakery owner needs to decide how many croissants to bake each morning, balancing the risks of:

  1. Understocking: Running out of croissants and missing potential profits.
  2. Overstocking: Baking too many croissants and wasting unsold ones.

How to solve it. 

Step 1. Check and improve data. If possible, for two weeks, each day, count:

  1. Note the moment of the hour when fresh croissants are going out-of-stock;
  2. Note the total number of customers by that hour and create an average of croissants sold per customer
  3. Note the total number of customers in the day (or up to the maximum hour they would buy croissants)
  4. Multiply the number from 3 with the average from 2 and mark it as a range of number (with a Minimum and a Maximum)

Step 2: Understand Costs

  • Cost of Overstocking (Co): For each unsold croissant, you as bakery, are loosing $1 (production cost).
  • Cost of Understocking (Cu): For each croissant not baked but demanded, you as bakery, are losing $2 in missed profit ($3 sale price - $1 production cost).

Step 3: Critical Ratio

Calculates the critical ratio to determine the optimal number of croissants to bake:

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This means the bakery should aim to bake enough croissants to meet 67% of the demand distribution.

Step 4: Forecast Demand

Supposing the demand ranges from 50 to 100 croissants and the fact that demand follows a normal distribution:

  • Mean demand (µ): 75 croissants
  • Standard deviation (σ): 15 croissants

Using an Excel formula ( =NORM.INV(0.67, 75, 15) ) the bakery determines the optimal bake quantity corresponding to the 67th percentile of the demand distribution, which is approximately 82 croissants.

Outcome of Decision:

If demand is 70 croissants:

The bakery bakes 82 croissants.
It sells 70 croissants, with 12 left unsold.
Total revenue = $3 × 70 = $210.
Total cost = $1 × 82 = $82.
Profit = $210 - $82 = $128.

If demand is 90 croissants:

The bakery bakes 82 croissants.
It sells all 82 croissants but misses the chance to sell 8 more.
Total revenue = $3 × 82 = $246.
Total cost = $1 × 82 = $82.
Profit = $246 - $82 = $164.
Missed profit from 8 croissants = $16.

Lessons the baker learned:

Balancing Risks:  Baking 82 croissants minimizes the combined risks of understocking and overstocking, though neither risk is eliminated completely. If the bakery over-produces, it absorbs the cost of waste. If it under-produces, it loses some potential profit.

Demand Forecasting is Key:  Better forecasting (e.g., analyzing weekday vs. weekend demand) can refine the decision. Keep data for longer and instead of 2 weeks of sales to analyze 10 past Mondays;

Extensions to Supply Chain Management: This scenario reflects supply chain problems for perishable products (e.g., fresh food, even fashion). Optimizing inventory levels using the critical ratio helps businesses avoid excessive waste while maintaining customer satisfaction.

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