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1. The quarterly sales data (number of copies sold) for a college textbook over the past 3 years are as follows in the Table below:
QUARTERLY SALES
Quarter Year 1 Year 2 Year 3
1 16 18 18
2 9 9 11
3 26 29 29
4 25 23 26
a) Compute seasonal indexes for the 4 quarters.
b) When does the textbook publisher experience the largest change in sales? Does this result appear to be reasonable? Explain.
c) Using the information on seasonality, compare a 4-quarter moving average to trend projection model and an exponential smoothing with a smoothing constant of 0.2.
d) Use the selected model to generate a forecast for sales for the first quarter of Year 4.
2. Sarita Uribe opened a new beauty products retail store. There are numerous items in inventory, and Sarita knows that there are costs associated with inventory. However, her time is limited so she cannot carefully evaluate the inventory policy for all products. Sarita wants to classify the items according to the dollars invested in them. The following table provides information about the 10 items that she carries:
ITEM NUMBER UNIT COST ($) DEMAND (UNITS)
E102 4 800
D23 8 1200
D27 3 700
R02 2 1000
R19 8 200
S107 6 500
S123 1 1200
U11 7 800
U23 1 1500
V75 4 1500
Use ABC analysis to classify these items into categories A, B, and C.
b) Develop a cycle policy if class A items are to be reviewed every 20 days, B items every 60 days, and C items every 120 days.
3. Barbara Brown is the purchasing agent for Central Valve Company, which sells industrial valves and fluid-control devices. One of their most popular valves is the Western, which has an annual demand of 4,000 units. The cost of each valve is $90.00, and the inventory carrying cost is estimated to be 10% of the cost of each valve. Barbara has made a study of the costs involved in placing an order for any of the valves that Central Valve stocks, and she has concluded that the average ordering cost is $25.00 per order. Furthermore, it takes about 8 days for an order to arrive from the supplier. During this time, the demand per week for Central valves is approximately 80.
a) What is the economic order quantity?
b) What is the reorder point? Develop an inventory policy with the reorder point.
c) What is the total annual inventory cost (carrying cost + ordering cost)
d) What is the optimal number of orders per year?
e) What is the optimal number of days between any two orders assuming there are 200 working days per year?
4. The EOQ is said to be a robust model. It is not affected by small changes in the key parameters of its models. These parameters are Demand, Holding cost, and ordering cost. Using the information from question 3 and allowing for changes of + 25% in these key parameters, show that the EOQ model is a robust model.
5. Use the exponential smoothing method to forecast for the 9th period for the time series data below
Period Actual
1 180
2 168
3 159
4 175
5 190
6 205
7 180
8 182
b. Develop a tracking signal to identify at which period the forecast is out of control. Use + 2 MAD as the control limit. Also, show a chart of tracking signal.
