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Customer Order Manager Kenny has recieved a request from a customer on how many units of a certain product he could deliver in week 1. In their manufacturing facility, the company works with frozen time periods of six weeks. The production quantity is 10 000 units, the lead time to finish their products is 3 weeks and they use a safety time of 1 week. However, the lead time to most of their customers is within a week.

a. How many units can Kenny promise the customer in the first week?

b. what is the forecast for week 7 using moving average (n=6)?

c. What is the forecast for week 7 using exponential smoothing (α=0.3)?

Let's go through the questions one by one based on the data provided in the table.

### Part (a) How many units can Kenny promise the customer in the first week?

To determine how many units Kenny can promise in Week 1, we need to look at the **Available To Promise (ATP)** value for Week 1.

- **ATP** is calculated as the current inventory plus the production quantity minus the sum of all the orders (or reservations) up to the end of the time period.

From the table:

- **Forecast for Week 1:** 3,000 units
- **Reservations for Week 1:** 2,500 units
- **Planned Production:** 10,000 units
- **Projected Available Balance (PAB) at Week 1:** 6,000 units
- **ATP for Week 1:** 6,000 units

**Answer:** Kenny can promise up to 6,000 units to the customer in the first week.

### Part (b) What is the forecast for Week 7 using moving average (n=6)?

The moving average forecast for Week 7 involves calculating the average of the forecasts for the last 6 weeks.

Forecasts for Weeks 1 to 6:
- Week 1: 3,000
- Week 2: 3,500
- Week 3: 3,200
- Week 4: 3,900
- Week 5: 4,500
- Week 6: 3,800

The moving average forecast for Week 7 is calculated as:

\[
\text{Forecast for Week 7} = \frac{3000 + 3500 + 3200 + 3900 + 4500 + 3800}{6}
\]

Let me calculate this.

\[
\text{Forecast for Week 7} = \frac{21,900}{6} = 3,650 \text{ units}
\]

**Answer:** The forecast for Week 7 using a 6-period moving average is 3,650 units.

### Part (c) What is the forecast for Week 7 using exponential smoothing (α=0.3)?

Exponential smoothing forecast for Week 7 can be calculated using the formula:

\[
F_{t+1} = \alpha \times D_t + (1 - \alpha) \times F_t
\]

Where:
- \( F_{t+1} \) is the forecast for the next period (Week 7 in this case).
- \( D_t \) is the actual demand (or forecast) for the current period.
- \( F_t \) is the forecast for the current period.
- \( \alpha \) is the smoothing constant (0.3 in this case).

Using the forecast for Week 6 as the base:

\[
F_7 = 0.3 \times D_6 + 0.7 \times F_6
\]

Let me calculate this now.

- **Forecast for Week 6:** 3,800 units
- **Using the Week 6 forecast:** \( F_7 = 0.3 \times 3800 + 0.7 \times 3650 \)

\[
F_7 = 0.3 \times 3800 + 0.7 \times 3650 = 1140 + 2555 = 3,695 \text{ units}
\]

**Answer:** The forecast for Week 7 using exponential smoothing with \( \alpha = 0.3 \) is 3,695 units.

---

Would you like any more details or do you have any questions? 

### Relative Questions:
1. How is ATP typically used in manufacturing planning?
2. What is the significance of the safety time in production planning?
3. Why is exponential smoothing used over simple moving averages in forecasting?
4. How does the value of \( \alpha \) in exponential smoothing affect the forecast?
5. What might cause discrepancies between the ATP and actual deliverable units?
6. How does lead time influence production scheduling?
7. What are other methods to calculate forecasts aside from moving averages and exponential smoothing?
8. How could changing the production quantity impact ATP in future weeks?

### Tip:
Understanding the relationship between demand, forecast accuracy, and production planning is key to optimizing inventory management.

Explore how Kenny can promise units in Week 1, forecast Week 7 using moving average (n=6), and use exponential smoothing (α=0.3) for accurate production planning. Get detailed solutions and insights into manufacturing forecasting methods.

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