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The Green Monster baseball team has recently assigned a long-time employee, Mr. Ortiz, to the grounds crew. One of Mr. Ortiz's responsibilities is ordering the fertilizer needed to keep the grass playing field in top condition. The grounds crew uses fertilizer at a steady rate of 48 pounds per week. The fertilizer costs $12 per pound, and the supplier charges a fixed fee of $100 per order. The delivery lead-time is 2 weeks from the supplier. Green Monster's inventory holding cost is 0.5% per week.

9. If Mr. Ortiz chooses an order quantity of 120 pounds, what would be the time between two orders?
A. 0.5 week
B. 1.5 weeks
C. 2.5 weeks
D. 3.5 weeks

10. If Mr. Ortiz decides to place an order once every 10 weeks, what would be the average fertilizer inventory?
A. 120 pounds
B. 240 pounds
C. 480 pounds
D. 960 pounds

11. What is the optimal quantity of fertilizer Mr. Ortiz should order?
A. 40 pounds
B. 55 pounds
C. 400 pounds
D. 2884 pounds

12. Given a delivery lead time of 2 weeks, what should be the reorder point (i.e., level of inventory at which an order should be placed)?
A. 48 pounds
B. 60 pounds
C. 96 pounds
D. 120 pounds

13. Mr. Ortiz would like to reduce the order size to half its current value. Which of the following will achieve this?
A. Reduce the fixed fee to half its current value
B. Reduce the fixed fee to one fourth its current value
C. Increase the fixed fee to double its current value
D. Increase the fixed fee to four times its current value

14. Which of the following will reduce the total weekly cost as well as the order quantity?
A. Reduction in order quantity without any other change
B. Reduction in fixed fee and re-optimizing order quantity
C. Increase in holding cost and re-optimizing order quantity
D. It cannot be achieved

15. A retailer uses the Newsvendor model while deciding how much inventory to order to satisfy uncertain demand during a short season. Keeping everything else the same, if the demand faced by the retailer becomes more uncertain, which of the following may happen?
A. Cost of under-stocking (C_u) may increase
B. Cost of over-stocking (C_o) may increase
C. Optimal service level may increase
D. Order quantity may increase

Answer :

Mr. Ortiz should reduce the fixed fee and re-optimize the order quantity to reduce the total weekly cost and order quantity, but the cost of over-stocking may increase.

9. To determine the time between two orders, we divide the order quantity (120 pounds) by the usage rate (48 pounds per week), which results in 2.5 weeks.

10.The average fertilizer inventory can be calculated by multiplying the time between two orders (10 weeks) by the usage rate (48 pounds per week), resulting in 480 pounds.

11. The optimal quantity of fertilizer to order can be determined by considering the economic order quantity (EOQ) formula. Given the cost and holding cost parameters, the optimal quantity is 2884 pounds.

12. The reorder point is the level of inventory at which an order should be placed, considering the delivery lead time. It is calculated by multiplying the lead time (2 weeks) by the usage rate (48 pounds per week), resulting in a reorder point of 96 pounds.

13. To reduce the order size to half its current value, increasing the fixed fee to double its current value will lead to a decrease in the order quantity.

14. The reduction in fixed fee and re-optimizing the order quantity will result in a decrease in the total weekly cost as well as the order quantity.

15. If the demand faced by the retailer becomes more uncertain, the cost of over-stocking may increase as there is a higher risk of stocking excess inventory that might not be sold.

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