
IKEA’s Poäng Chairs (for Q4-5)
Poäng chair is one of IKEA’s most popular products. Average weekly sales of this chair in each store is Normal with mean 20 units and standard deviation of 10 units. Each chair costs IKEA $10 to produce and is sold at a price $60.  You are managing the inventory of Poäng chairs at two locations: Mega Bang Na and EmSphere stores.
Q4.  If you order the inventory independently for each store, what is the total number of chairs to order each week across the two stores? Round up to the next integer.

To determine the weekly order quantity for the Poäng chairs across the two stores, we need to consider the weekly demand at each store, which is described by a normal distribution.

### Given information:
- Demand at each store is normally distributed with a **mean of 20 units** and a **standard deviation of 10 units**.
- The demand is **independent** for each store.
- We have **two stores**: Mega Bang Na and EmSphere.

### Solution:

Since the demand at each store is independent and normally distributed, the **total weekly demand across both stores** will also be normally distributed with:
1. A **mean** equal to the sum of the means for each store.
2. A **variance** equal to the sum of the variances for each store.

#### Step 1: Calculate the total mean demand
For each store, the mean weekly demand is 20 units. Thus, the total mean demand across the two stores is:
\[
\mu_{\text{total}} = 20 + 20 = 40
\]

#### Step 2: Calculate the total variance and standard deviation
For each store, the standard deviation of weekly demand is 10 units. Since demand is independent across stores, the variance for each store can be added together to find the total variance:
\[
\sigma_{\text{total}}^2 = 10^2 + 10^2 = 100 + 100 = 200
\]
The total standard deviation is then:
\[
\sigma_{\text{total}} = \sqrt{200} \approx 14.14
\]

#### Step 3: Determine the order quantity
Since demand follows a normal distribution, we want to round up the mean total demand across both stores to account for the expected weekly demand.

Thus, the total weekly order quantity across both stores should be:
\[
\lceil 40 \rceil = 40 \text{ units}
\]

### Answer:
The total number of chairs to order each week across the two stores is **40 units**.

Would you like more details on the calculation process or have any questions?

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Here are some additional related questions:
1. What would be the impact on the order quantity if the demand variability increased?
2. How would you adjust the order quantity if the cost per chair changed?
3. What would be the optimal order size if demand were not independent between the two stores?
4. How does the independence of demand at each location affect inventory management?
5. If we introduce a third store with similar demand, how would the total order quantity change?

**Tip:** In inventory management, accounting for variability in demand is crucial to avoid stockouts or overstocking.

If you order the inventory independently for each store, what is the total number of chairs to order each week across the two stores? Round up to the next integer.

Explore how to calculate the total weekly order quantity for IKEA's Poäng chairs at two locations, considering independent normal distributions of demand. With a mean of 20 units and standard deviation of 10 units, the solution reveals an optimal order of 40 units.

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