# MGT 441 Homework #1: Step-by-Step Solutions --- ## Chapter 1 Question **Q: Why is it important to match supply and demand? If a manager believes that supply and demand will not be equal, what actions could the manager take to increase the probability of achieving a match?** ### **Answer:** **Importance of Matching Supply and Demand:** - **Reduces Costs:** Overstocking leads to excess inventory and increased holding costs, while understocking results in lost sales and dissatisfied customers. - **Improves Customer Satisfaction:** Meeting demand ensures customers receive products when needed, improving loyalty and reputation. - **Optimizes Resource Utilization:** Proper alignment prevents waste of resources, labor, and capital. **Actions Managers Can Take:** 1. **Adjust Production Schedules:** Increase or decrease production rates based on demand forecasts. 2. **Use Inventory Buffers:** Maintain safety stock to handle demand fluctuations. 3. **Flexible Workforce:** Hire temporary workers or offer overtime during peak periods. 4. **Demand Management:** Use promotions or discounts to influence demand. 5. **Subcontracting:** Outsource excess demand to third parties. 6. **Improve Forecasting:** Use advanced forecasting techniques for better accuracy. --- ## Chapter 3 Questions ### **National Scan, Inc. Sales Data:** | Month | Sales (000 units) | |-------|-------------------| | Feb | 21 | | Mar | 20 | | Apr | 17 | | May | 22 | | Jun | 20 | | Jul | 24 | | Aug | 22 | --- ### **a. Plot the Monthly Data** *(Since I can't draw here, plot the points on graph paper or Excel: Months on X-axis, Sales on Y-axis.)* --- ### **b. Forecast September Sales Volume** #### **(1) The Naive Approach** - **Forecast for September = August Sales = 22 (000 units)** --- #### **(2) Five-Month Moving Average** - Use sales from Apr, May, Jun, Jul, Aug: \[ \text{Five-Month Moving Average} = \frac{17 + 22 + 20 + 24 + 22}{5} = \frac{105}{5} = 21 (000 \text{ units}) \] --- #### **(3) Weighted Average** - Weights: Aug = .60, Jul = .30, Jun = .10 \[ \text{Weighted Average} = (.60 \times 22) + (.30 \times 24) + (.10 \times 20) = 13.2 + 7.2 + 2. = 22.4 (000 \text{ units}) \] --- #### **(4) Exponential Smoothing (\( \alpha = .20 \)), March forecast = 19** - **March actual:** 20, **March forecast:** 19 \[ \text{April forecast} = 19 + .2 \times (20 - 19) = 19 + .2 \times 1 = 19.2 \] \[ \text{April actual: 17} \implies \text{May forecast} = 19.2 + .2 \times (17 - 19.2) = 19.2 - .44 = 18.76 \] \[ \text{May actual: 22} \implies \text{June forecast} = 18.76 + .2 \times (22 - 18.76) = 18.76 + .648 = 19.408 \] \[ \text{June actual: 20} \implies \text{July forecast} = 19.408 + .2 \times (20 - 19.408) = 19.408 + .1184 = 19.5264 \] \[ \text{July actual: 24} \implies \text{August forecast} = 19.5264 + .2 \times (24 - 19.5264) = 19.5264 + .8947 = 20.4211 \] \[ \text{August actual: 22} \implies \text{September forecast} = 20.4211 + .2 \times (22 - 20.4211) = 20.4211 + .3158 = 20.7369 \] **September forecast ≈ 20.74 (000 units)** --- #### **(5) Linear Trend Equation** Let’s fit a simple linear trend: \( Y = a + bX \) - Assign numbers to months: Feb=1, Mar=2, ..., Aug=7 | X (Month) | Y (Sales) | |-----------|-----------| | 1 | 21 | | 2 | 20 | | 3 | 17 | | 4 | 22 | | 5 | 20 | | 6 | 24 | | 7 | 22 | - \( \bar{X} = 4 \) - \( \bar{Y} = \frac{146}{7} \approx 20.86 \) Calculate slope \( b \): \[ b = \frac{\sum (X - \bar{X})(Y - \bar{Y})}{\sum (X - \bar{X})^2} \] Calculate each term: - For each \( X \), \( (X-\bar{X}) \): -3, -2, -1, , 1, 2, 3 - For each \( Y \), \( (Y-\bar{Y}) \): .14, -.86, -3.86, 1.14, -.86, 3.14, 1.14 Now multiply each pair and sum: \[ \sum (X-\bar{X})(Y-\bar{Y}) = (-3)(.14) + (-2)(-.86) + (-1)(-3.86) + ()(1.14) + (1)(-.86) + (2)(3.14) + (3)(1.14) \] \[ = -.42 + 1.72 + 3.86 + + (-.86) + 6.28 + 3.42 = 13.99 \] \[ \sum (X-\bar{X})^2 = 9 + 4 + 1 + + 1 + 4 + 9 = 28 \] So, \[ b = \frac{13.99}{28} \approx .5 \] Intercept \( a \): \[ a = \bar{Y} - b\bar{X} = 20.86 - .5 \times 4 = 20.86 - 2 = 18.86 \] So, the equation: \[ Y = 18.86 + .5X \] September is Month 8: \[ Y = 18.86 + .5 \times 8 = 18.86 + 4 = 22.86 (000 \text{ units}) \] --- ### **c. Which method seems least appropriate? Why?** - **Naive Approach** seems least appropriate, as it doesn't account for recent changes, trends, or fluctuations, especially given the variability in the data (see your plot). --- ### **d. What does use of the term "sales" rather than "demand" presume?** - It presumes that all demand was met, and there were no stockouts or unmet needs. If some demand couldn't be met due to inventory shortages, then sales understate true demand. --- ## **Final Summary** - **Matching supply and demand is crucial** for cost control, customer satisfaction, and efficient resource use. - **September sales forecasts:** - Naive: **22** - 5-Month Moving Average: **21** - Weighted Average: **22.4** - Exponential Smoothing: **20.74** - Linear Trend: **22.86** - **Naive method is least appropriate** due to ignoring trends and variability. - **"Sales" assumes all demand was met**, so actual demand could be higher if stockouts occurred. **Remember to plot the data for visual analysis.**

# MGT 441 Homework #1: Summary of Key Questions --- ## Chapter 1 Question Summary - Matching supply and demand is essential for minimizing costs, enhancing customer satisfaction, and optimizing resource utilization. Managers can take actions such as adjusting production schedules, maintaining safety stock, and improving demand forecasting to better align supply with demand. --- ## Chapter 3 Questions Summary ### Sales Data and Forecasting - Monthly sales data shows fluctuations in demand, with a peak in July at 24,000 units. Various forecasting methods yield different September sales predictions, with the naive approach forecasting 22,000 units and the linear trend forecasting 22.86, indicating variability in demand patterns. ### Method Appropriateness - The naive approach is considered least appropriate as it disregards trends and recent changes in sales data. It is critical to analyze data visually for better forecasting accuracy. ### Sales vs. Demand - The term "sales" implies that all customer demand was satisfied without stockouts, essentially underestimating actual demand if inventory shortages occurred. This distinction is crucial for understanding market dynamics and planning.