Question

Sam's Cat Hotel operates 52 weeks per year, 7 days per week, and uses a continuous review inventory system. It purchases kitty litter for $10.75 per bag. The following information is available about these bags. Demand = 95 bags/week Order cost = $58/order Annual holding cost = 25 percent of cost Desired cycle@service level = 90 percent Lead time = 4 weeks (28 working days) Standard deviation of weekly demand = 16 bags Current on-hand inventory is 315 bags, with no open orders or backorders. a. What is the EOQ? What would be the average time between orders (in weeks)? b. What should R be? C. An inventory withdrawal of 10 bags was just made. Is it time to reorder? d. The store currently uses a lot size of 490 bags (i.e., Q = 490). What is the annual holding cost of this policy? Annual ordering cost? Without calculating the EOQ, how can you conclude from these two cal- culations that the current lot size is too large? e. What would be the annual cost saved by shifting from the 490-bag lot size to the EOQ?

Answer 1

Answer:

Fact:

Weekly demand = 95/week

Annual Demand (D) = Number of week * Weekly Demand = 52*95=4940 Units

Ordering Cost (S) = $58 per order

Annual Holding Cost (H)= 25% of purchase cost = 15% of $10.75= $2.6875

Lead time (LT) = 4 weeks

Standard Deviation in weekly demand = 16

Stock in hand =315 units with no open or back order

A. EOQ ( economic order quanity )= Square root of ((2*D*S)/H) =Sqrt((2*4940*58)/2.6875)=461.76 units = 462 units

Total stock in hand = 315 units

Balance annual quantity to be ordered = 4940-315= 4625

Number of orders to be placed = balance annual order quantity / EOQ = 4625/462= 10 orders

Order interval = Total number of weeks in a year/number of orders = 52/10=5.2 weeks

B. Since only the demand has a variance and lead time is fixed we can use the below formula to find the R

R= (Average weekly demand* Lead time) + (Zscore for 90% service level * Standard deviation *Sqrt(Lead time))

R= 95*4+ (1.64*16*sqrt(4)= 380+52.48=432.48 = 432 unit Answer.

Note: Z score can be obtained from z score table for normal distribution.

C. Since the R is 432 units and on-hand inventory is only 315, from whihc furthe 10 units are consumed, hence the order must be placed.

D. Annual holding cost (HC) = (Holing cost per unit per year*order quantity)/2= (2.6875*490)/2  = $658

Ordering Cost = Number of orders * per order cost

In this case Q=490 hence the number of order = 4625/490=9.43=10 orders

Ordering Cost = Number of orders * per order cost = 10*$58=$580

Purchase price= Annual quantity requried * unit price = 4625*10.75= 49719

Total cost= Purchase cost +Ordering cost + Holding cost= 49719+580+658=50957

Since the Holding cost is very high than ordering cost, hence we can say that the lot size is large.

E. Total cost in EOQ model

Ordering cost = 10*58=$580

Holding cost = (2.6875*462)/2= $621

Purchase price= Annual quantity requried * unit price = 4625*10.75= 49719

Total cost= Purchase cost +Ordering cost + Holding cost= 49719+580+621=50920

A saving of $37 can be achieved by moving to EOQ model.