Question

Problem 1. 

Given the following information, formulate an inventory management system. The item is demanded 50 weeks a year.

	Last Year
Item cost	$10.00
Order cost	$250.00
annual hold cost (%)	33%	of item cost
Annual demand	25,750
average demand	515	per week
Standard deviation of weekly demand	25	per week
lead time	1	week
service probability	95%

Answer 1

Answer a :

EOQ = (2*annual demand*ordering cost/holding cost per unit per year)^.5

EOQ = (2*25750*250/(33%*10))^.5

EOQ = 1975.2 or 1975 units

So, ordering quantity is 1975 units

----

Reorder point = weekly demand*lead time + Z*SD*(lead time)^.5

Value of Z at 95% = 1.645

Reorder point = 515*1 + 1.645*25*(1)^.5

Reorder point = 556.12 or 556 units

Answer b :

Annual holding & order cost = Annual ordering cost + annual holding cost

Annual holding & order cost = (25750/1975)*250 + (1975/2)*(33%*10)

Annual holding & order cost = $6518.24

Answer c :

if 2000 units are ordered,

Then,

Annual holding & order cost =(25750/2000)*250 + (2000/2)*(33%*10) = $6518.75

Since the benefit of $50 is greater than the slight increase in cost of holding & ordering by $.5, so the advantage should be taken of $50 break.

Total no. of orders = 25750/2000 = 12.87 orders

So, savings due to 2000 units order at a time = 12*50 = $600

Net savings = 600 + 6518.24 - 6518.75 = $599.49

Answer 2

The Quantity to be ordered, Q_opt is the optimum quantity that should be ordered normally termed as Economic Order Quantity (EOQ).

It is calculated as:

Qopt 2 DS H

Where, D is the annual demand, S is the ordering or set up cost and H is holding cost.

The reorder point is the sum of expected demand during the lead time and the safety stock. It is calculated as:

R=dL + 20

Where, R is the reorder point,
р
is the average daily demand, L is the lead time in terms of days, z is the number of standard deviations from a specified service probability and
7
is standard deviation of usage in lead time.

The annual demand is 25,750 units and annual holding cost is 33% of the purchase price which is $10. The cost of placing an order is $250.

Using EOQ model,

Qopt 2 DS H

Substitute the values in the above equation as follows:

Qope 2(25750)(250) (0.33)(10) = 1975 units

Hence, the optimal order quantity of cotton is 1975 units .

As per the problem, weekly demand is 515 units with lead time of 1 week and standard deviation, of 25 units per week.

7

Using excel and applying NORMSINV (0.95) we get the value of z as 1.64.

Substitute:

R = 515(1) +(1.64)(25) = 556 units

Hence, at the level of 556 units , new order must be placed.

Calculate the annual holding cost by multiplying average inventory i.e. Q/2 by the cost of storage per unit i.e. H. as follows:

Holding Cost 2 (H) 2

At optimal quantity Q of 1975 units,

Substitute the values in the above equation as follows:

Holding Cost 1975 -(0.33)(10) = $3,258.75 2

Hence, the annual holding cost is $3,258.75 .

Calculate the annual ordering cost by multiplying the actual number of orders placed i.e. D/Q by the cost of each order i.e. S as follows:

Ordering Cost 8 (S)

At optimal quantity Q of 1975 units,

Substitute the above values in the equation as follows:

Ordering Cost 25750 (250) = $3,259.49 1975

Hence, the annual ordering cost is $3,259.49 .

c)

If we get a price break of $50 with purchase quantity of 2000 units or more

Calculate the annual holding cost at optimal quantity Q of 2000 units as follows:

Holding Cost ol (H) 2 2000 -(0.33)(10) 2 = $3,300

Hence, the annual holding cost is $3,300.

Calculate the annual ordering cost at optimal quantity Q of 2000 units as follows:

Ordering Cost 8 (S)

So, at optimal quantity Q of 2000 units,

Substitute:

Ordering Cost 25750 (250) = $3,218.75 2000

Hence, the annual ordering cost is $3,218.75.

Calculate the total cost with discount as follows:

Total annual cost with discount = Annual holding cost + Annual ordering cost -(Odering cost after price break ~ Number of orders) = 3,300+ 3,218.75 - 50x 25,750 2,000 = 6,518.75 -643.75 = $5,875 75-[*

Calculate the total cost without discount as follows (from part b ):

Total annual cost without discount = Annual holding cost + Annual ordering cost = 3,258.75 + 3259.49 = $6,518.24

Since the total cost incurred with discount is lesser as compared to the total cost without discount, the advantage should be taken with price break.

Calculate the annual amount that will be saved as follows:

Saving in Ordering Cost Total annual cost without discount - Total annual cost with discount = 6,518.24 -5,875 = $643.24

Therefore, the amount of $643.24 will be saved annually.