Question

1: A museum of natural history opened a gifl shop which operates 52 weeks per year. managing invertories has become a problem.Top-selling SKU is a bird feeder. sale are 18 uits per week, the supplier charges $60 per unit. Ordering cost is $45. annual holding cost 25 percernt of a feeder's value. management chose a 390-unit lot size

what is the annual cycle-inventory cost of the current policy of using a 390-unit lot size?

would a lot size of 468 be better?

2 : For the bird feeders in Example 1, calculate the EOQ and its total annual cycle-inventory cost. how frequently will orders be placed if the EOQ is used?

3: suppose that you are reviewing the inventory policies on an $80 item stocked at a hardware store. the current policy is to repleish inventory by ordering in lots of360 units. additional information is:

D= 60 units per week, or 3,120 units per year

S=$30 per oder

H= 20% of selling price, or $20 per unit per year

what is the EOQ?

What is the total annual cost of the current policy( Q=360), and how does it compare with the cost with using the EOQ?

4: A company buys re-writable DVDs ( 10 disks/ box) from a large mail- order distibutor

the company uses approximately 5,000 boxes/ year at a fairly constant rate

the distributor offers the followig quantity discount schedule:

* if < 500 boxes are ordered, then cost =10/ box

* if > 500 but < 800 boxes are ordered, then cost = $ 9.50

* if > 800 boxes are ordered, then cost = $9.25

fixed cost of purchasing = $25,and the cost of capital = 12% per year. there is no storage cost.

5: The on-hand inventory is only 10 units, and the reorder point R is 100. there are no backorders but there is one open order for @00 units. should a new order be placed?

6: demand for chicken soup at a supermarket is always 25 cases a day and the lead time is always 4 day. the shelves were just restocked with chicken soup, leaving an on-hand inventoy of only 10 cases. no backorders currently existm but there is one open order in the pipelibe for 200 cases. what is the invetory position? should a new order be placed?

7: The Office Supply shop estimates that the average demand for a popular ball-point pen is 12,000 pens per week with a standard deviation of 3,000 pens. the current inventory policy calls for replenishment orders 156,000 pen. the average lead time from the distributor is 5 weeks, with a standard deviation of 2 weeks. if management wants a 95 percent cycle-service level, what should the reorder point be?  

Answer 1

PLEASE FIND ANSWERS TO FIRST 2 QUESTIONS :

Answer to question 1 :

We define annual cycle inventory = Annual ordering cost + annual inventory carrying cost

Annual ordering cost

= Ordering cost x Number of orders

= Ordering cost x Annual demand/ Order quantity

= Ordering cost x ( weekly demand x 52 weeks ) / Order quantity

= $45 x 18 x 52/ 390

= $108

Annual unit holding cost

= 25 percent of $60

= $15

Annual inventory holding cost

= Annual unit inventory holding cost x Average inventory

= $15 x Order quantity / 2

= $15 x 390/2

= $2925

Therefore, total cycle inventory = $108 + $2925 = $3033

For lot size of 468 :

Annual ordering cost

= Ordering cost x Number of orders

= Ordering cost x Annual demand/ Order quantity

= Ordering cost x ( weekly demand x 52 weeks ) / Order quantity

= $45 x 18 x 52/ 468

= $ 90

Annual unit holding cost

= 25 percent of $60

= $15

Annual inventory holding cost

= Annual unit inventory holding cost x Average inventory

= $15 x Order quantity / 2

= $15 x 468/2

= $ 3510

Therefore, total cycle inventory = $ 90 + $3510 = $3600

Answer to question number 2 :

Economic Order Quantity ( EOQ )

= Square root ( 2 x ordering cost x Annual demand / Annual unit inventory cost )

= Square root ( 2 x 45 x 18 x 52 / 15 )

= 74.93 ( 75 rounded to nearest whole number )

Annual ordering cost

= Ordering cost x Number of orders

= Ordering cost x annual demand/ EOQ

= $45 x 18 x 52 / 75

= $561.60

Annual holding cost

= Annual unit holding cost x Average inventory

= $15 x 75/2

= $562.5

Therefore , annual cycle inventory cost = $561.50 + $562.50 = $1124.10

Frequency at which orders should be placed if EOQ is used = EOQ/weekly demand = 75/18 = 4.17 weeks( rounded to 2 decimal places)

FREQUENCY AT WHOCH ORDER SHOULD BE PLACED IF EOQ IS USED = 4.17 WEEKS