Thomas Kratzer is the purchasing manager for the headquarters of a large insurance company chain with a central inventory operation. Thomas’s fastest-moving inventory item has a demand of 6,000 units a year. The purchasing cost of each unit is $16 (additional 5% discount applies if at lease 150 units ordered a time), and the inventory carrying cost is $3 per unit per year. The average ordering cost is $10 per order. It takes about 3 working days for an order to arrive. (This is a corporate operation, and there are 300 working days per year.) Answer the following questions, Q1~Q5. Note that you must include Excel formulas/calculations showing how you arrive at the answer. Q1: Assume that the demand is consistent throughout the year. What is the ROP? Note that stockouts and unnecessary inventory holding should be avoided at any times. Q2: Assume that the demand is consistent throughout the year. Based on the EOQ model, to minimize the costs of purchasing, ordering and inventory holding for the year, how many units should be ordered each time an order is placed? Q3: Following Q2, what is the total cost of purchasing, ordering and inventory holding expecetd for the year? Q4: The management recently obtained the real data (see below) of the demands during each reorder period (a reorder period = 3 working days). The management considers the above demands closely follow a normal distribution. To achieve a minumum 90% service level, a minimum new ROP (which should be whole number) should be used instead of the ROP used in Q1. This new ROP is expected to be higher than the ROP from Q1. What is the expected inventory holding cost to be added to the total inventory cost if the above new ROP is used in place of the ROP from Q1?

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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Thomas Kratzer is the purchasing manager for the headquarters of a large insurance company chain with a central inventory operation. Thomas’s fastest-moving inventory item has a demand of 6,000 units a year. The purchasing cost of each unit is $16 (additional 5% discount applies if at lease 150 units ordered a time), and the inventory carrying cost is $3 per unit per year. The average ordering cost is $10 per order. It takes about 3 working days for an order to arrive. (This is a corporate operation, and there are 300 working days per year.) Answer the following questions, Q1~Q5. Note that you must include Excel formulas/calculations showing how you arrive at the answer.

Q1: Assume that the demand is consistent throughout the year. What is the ROP? Note that stockouts and unnecessary inventory holding should be avoided at any times.

Q2: Assume that the demand is consistent throughout the year. Based on the EOQ model, to minimize the costs of purchasing, ordering and inventory holding for the year, how many units should be ordered each time an order is placed?

Q3: Following Q2, what is the total cost of purchasing, ordering and inventory holding expecetd for the year?

Q4: The management recently obtained the real data (see below) of the demands during each reorder period (a reorder period = 3 working days). The management considers the above demands closely follow a normal distribution. To achieve a minumum 90% service level, a minimum new ROP (which should be whole number) should be used instead of the ROP used in Q1. This new ROP is expected to be higher than the ROP from Q1.

What is the expected inventory holding cost to be added to the total inventory cost if the above new ROP is used in place of the ROP from Q1?

Demand (units)
during the
reorder period
59
57
48
48
70
75
68
58
60
76
58
57
71
38
60
37
65
43
68
38
50
49
52
53
67
44
54
45
69
53
47
48
49
54
44
52
72
52
57
67
51
57
52
58
67
65
43
49
50
63
61
66
50
67
56
52
51
75
80
50

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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