Question

A food processor uses approximately 27,000 glass jars a month for its fruit juice product. Each jar costs $10.8. Because of storage limitations, a lot size of 4,000 jars has been used. Annual holding cost is 20% of a jar’s price, and reordering cost is $60 per order.

The company operates an average of 20 days a month.

Answer the following questions, showing calculation steps:

How many times a year an order size of 4000 is placed?

What is the total cost of Q=4000? (Include ordering, holding and purchase cost)

What is optimal order quantity and its total cost?

What penalty is the company incurring by its present order size?

The manager would prefer ordering 10 times each month but would have to justify any change in order size. One possibility is to simplify order processing to reduce the ordering cost. What ordering cost would enable the manager to justify ordering every other day (i.e., 10 times a month)?

Given the discount offers, would you change your order size from your EOQ level and Why? Show all the steps.

Order size=Q	Price per unit
Q<4999	P=$10.8
5000<= Q <6000	P=$10
Q>= 6000	P=$9.5

Answer 1

PLEASE FIND BELOW ANSWERS TO FIRST 4 QUESTIONS :

Total cost for Q = 4000:

Annual demand = D = 27000 glass jars/ month x 12 months = 324000 glass jars

Annual unit holding cost = Ch = 20% of $10.8 =$2.16

Ordering cost = Co = $60

Annual ordering cost = Ordering cost x Number of orders = Co x annual demand/ order qty = $60 x 324000/ 4000 = $4860

Annual inventory holding cost = Ch x Average inventory = Ch x Order quantity /2 = $2.16 x 4000/ 2 = $4320

Total cost = Annual ordering cost + annual inventory holding cost = $4860 + $4320 = $9180

Optimal order quantity :

Optimal order quantity = Square root ( 2 x Co x D/ Ch ) = Square root ( 2 x 60 x 324000/ 2.16 ) = 4242.64 ( 4243 rounded to nearest whole number )

Annual ordering cost = Ordering cost x Number of orders = Co x annual demand/ order qty = $60 x 324000/ 4243 = $4581.66

Annual inventory holding cost = Ch x Average inventory = Ch x Order quantity /2 = $2.16 x 4243/2 = $4582.44

Total cost = Annual ordering cost + annual inventory holding cost = $4581.66 + $4582.44 = $9164.10

Penalty company is incurring :

Penalty incurred by company by following present order size

= $9180 - $9164.10

= $15.9

Ordering cost :

When ordering every other day , order quantity =Daily demand x 2 = 27000/20 x 2 = 2700

Let the corresponding ordering cost =C

Therefore, as per formula for optimum order quantity :

2700 = Square root ( 2 x C x D/Ch)

Or, 2700 = Square root ( 2 x C x324000/ 2.16 )

Or, 2700 = Square root ( 300000 x C )

Or, 300000 x C = 7290000

Or, C = 7290000/300000

Or, C = 24.3

ORDERING COST SHOULD BE $24.3