Math Problem Statement

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)?

Solution

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:

Forecast for Week 7=3000+3500+3200+3900+4500+38006\text{Forecast for Week 7} = \frac{3000 + 3500 + 3200 + 3900 + 4500 + 3800}{6}

Let me calculate this.

Forecast for Week 7=21,9006=3,650 units\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:

Ft+1=α×Dt+(1α)×FtF_{t+1} = \alpha \times D_t + (1 - \alpha) \times F_t

Where:

  • Ft+1F_{t+1} is the forecast for the next period (Week 7 in this case).
  • DtD_t is the actual demand (or forecast) for the current period.
  • FtF_t is the forecast for the current period.
  • α\alpha is the smoothing constant (0.3 in this case).

Using the forecast for Week 6 as the base:

F7=0.3×D6+0.7×F6F_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: F7=0.3×3800+0.7×3650F_7 = 0.3 \times 3800 + 0.7 \times 3650

F7=0.3×3800+0.7×3650=1140+2555=3,695 unitsF_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 α=0.3\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 α\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.

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Math Problem Analysis

Mathematical Concepts

Inventory Management
Production Planning
Forecasting

Formulas

Moving Average Forecast
Exponential Smoothing

Theorems

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Suitable Grade Level

Professional