Question

Problem 1:

  

An ophthalmologist’s office operates 52 weeks per year. It purchases disposable contact lenses for $11.70 per pair. The following information is available about these lenses.

Demand = 90 pairs/week

Order cost = $54/order

Annual holding cost = 27% of purchasing cost

Desired cycle-service level = 80%

Lead time = 3 weeks

Standard deviation of weekly demand = 15 pairs

Current on-hand inventory is 320 pairs, with no open orders or backorders.

Part I   Currently, the company uses a continuous review system,

A) What is the EOQ? What would be the average time between orders (in weeks)?

B) What should be the safety stock? What should the reorder point be?

c) An inventory withdrawal of 10 pairs was just made. Is it time to reorder?

Answer 1

Answer

Desired cycle-service level = 80%. @ = +(100%- 80%)/2 = + 0.10

Standard deviation of weekly demand ()= 15 pairs

Considering the demand is normally distributed , we need to select the T distribution .

Formula to acheive T = ( X- )/(/ ) =

If the company chooses to review and replenishment inventory every 5 weeks, then n = 5 . degrees of freedom = n- 1 = 5-1 = 4

Consider the T distribution table for @ = + 0.10 and df= 4,

he value of T = 1.533

Formula to acheive T =1.533 = ( X- )/(/ ) = ( X-)/(15/ )

Where as X is the quantity to be required per week including safety stock. is given demand per week i.e 90

X- = 10.28 pairs extra stock required per week.

Answer 1 : So the extra stock required for 5 weeks =10.28*5 = 51.41 pairs=51 pairs ( rounded).

Answer 2 : Target inventory at each reveiv period of 5 weeks= demand for five weeks + safety stock = 90 ( demand per week) * 5 + 51= 501 pairs.

Answer 3: It’s time for the periodic review. With the current inventory of 320 pairs, the ordered quantity will be the economic ordered quantity

EOQ = ( 2*D*H/K)

whereas D is annual demand

H is the holding cost

K is the ordering cost

Annual Demand = 90 ( Demand per week) * 52 ( number of weeks) = 4680 pairs .Available inventory = 320.

So the net demand (D) = 4680-320 = 4360

Holding cost ( H) =  27% of purchasing cost = 27% * $11.70 = $ 3.159

K = $54 per order]

So putting the values in above EOQ formula

EOQ = ( 2*4360*3.159/54) = 22.58 pairs per order = 23 pairs.