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## Calculations

For Problems 1 through 3, use the following time series data:

MONTH
DEMAND

1
148
2 166
3 155
4 163
5 152
6 220
7 223
8 218
9 237
10 211
1. Develop a three-period moving average forecast for periods 4-11. Calculate the MFE, MAD, and MAPE using data and forecasts for periods 4-10.
2. Develop a three-period weighted moving average forecast for periods 4-11. Use weights of 0.45, 0.35 and 0.2, with the most recent observation weighted higher. Calculate the MFE, MAD, and MAPE values using data and forecasts for periods 4-10. How do your results compare with those from Problem 1? Briefly explain why.
3. Develop two exponential smoothing forecasts: one with alpha = 0.3 and another with alpha = 0.7 for periods 2-11. Assume your forecast for period 1 was 150. Calculate the MFE, MAD, and MAPE values using data and forecasts for periods 2-10 for both forecasting models. Which model is a better fit? Why?.

4. You are given the task of forecasting demand for the ski outfit collection of Snowful Wear Inc. As anticipated, you observe that demand is highly seasonal. The following table gives the quarterly demand data (Sales in thousands of units) for the years 2012 to 2015.

Quarter 2012 2013 2014 2015
1 115 95 120 115
2 70 82 89 90
3 10 12 13 12
4 30 34 40 45

Using regression analysis, develop a forecasting model with quarterly seasonal indices for Snowful Wear. Forecast demand for each of the quarters for the year 2016.

5. You and a couple of friends from the MBA program decide to sell T-shirts during the Spring MBA Commencement to commemorate the event. The T-shirts sell for \$20, and cost \$9 to produce. After the commencement weekend, you think you can continue to sell them online but only at \$8 per T-shirt. In addition, for each T-shirt you sell online, you will incur a shipping cost of \$2. Suppose the demand for shirts can be approximated with a normal distribution and the mean demand is 80 shirts with a standard deviation of 20. What is the target service level? How many shirts should you produce?

6. One of the products sold by Office Min at its online store is the HP Deskjet XYZ23 printer. We know the following about this product:

Average monthly demand (assume 52 weeks per year): 60 printers
Standard deviation of weekly demand: 12 printers
Order lead time: 3 weeks
Standard deviation of order lead time: 0.3 weeks
Item cost: \$120 per printer
Cost to place an order: \$2 per order
Yearly holding cost per monitor: 40% of item cost
Desired service level during reordering period: 99% (z = 2.33)

a. What is the economic order quantity for this printer?
b. Calculate annual ordering costs and holding costs (ignoring safety stock) for the EOQ. What do you notice about the two?
c. Suppose Office Min currently orders 120 printers at a time. How much more or less would Office Min pay in holding and ordering costs per year if it ordered 12 printers at a time? Show your work.
d. What is the reorder point for the printer? How much of the reorder point consists of safety stock?
e. Because electronics becomes obsolete so quickly, Office Min is thinking about raising holding cost from 50% of item cost to a higher percentage. What will be the impact on the economic order quantity? Briefly explain your answer.

For parts f and g, use the following formula to consider the impact of safety stock (SS) on average inventory levels and annual holding costs:

f. (What is the annual cost of holding inventory, including the safety stock? How much of this cost is due to the safety stock?
g. Suppose Office Min is able to cut the lead time to a constant one week. What would the new safety stock level be? How much would this reduce annual holding costs?
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