Question

The rising popularity of bubble and squeak as a breakfast item on the menu has resulted in a
steady demand for peas. Over the course of the past week, 228 customers have ordered the hearty
breakfast containing a cup of English peas. It costs $0.04 to hold a cup of peas in inventory for a
year and $3 to place an order. It takes two weeks to ship a container from England loaded with
peas. Assume that each year has 52 weeks.

What is the optimal order quantity?
A) 2670 cups
B) 17.8 cups
C) 1334 cups
D) 8.9 cups

What will be the average inventory if they order 1330 units each time?
A) 2660 cups
B) 1330 cups
C) 665 cups
D)333 cups

How many orders per year does the diner have to place if they order 1317 cups each time?
A) 18
B) 9
C) 5
D) 14

What is the cost of the inventory policy (holding cost + ordering cost) if the diner orders 8
times per year?
A) $53.64
B) $106.80
C) $26.70
D) $80.10

What is the average flow time if the diner orders 1334?
A) 8.76 weeks
B) 5.84 weeks
C) 2.93 weeks
D) 11.68 weeks

Answer 1

Weekly demand = 228 cups

Number of weeks per year = 52

Annual demand (D) = weekly demand × number of weeks per year = 228 × 52 = 11856 cups

Ordering cost (S) = $3

Holding cost (H) = $0.04

1)Optimal order quantity = √(2DS/H) = √[(2 × 11856 × 3)/0.04] = √(71136/0.04) = √1778400 = 1333.57 or rounded to 1334 cups

2) if order quantity (Q) = 1330 units, average inventory = Q/2 = 1330/2 = 665 cups

3) if order quantity (Q) = 1317 units

Number of order per year = D/Q = 11856/1317 = 9

4) if the number of orders per year = 8

Order quantity (Q) = D/number of orders per year = 11856/8 = 1482 units

Annual ordering cost = (D/Q)S = (11856/1482)3 = $24

Annual holding cost = (Q/2)H = (1482/2)0.04 = 29.64

Total cost of the inventory policy = Annual ordering cost + Annual holding cost = $24+$29.64 = $53.64

5) if order quantity (Q) = 1334

Average flow time = (Q/D) number of weeks per year= (1334/11856)52 = 5.84 weeks