Question

Consider a product with a daily demand of 600 units, a setup cost per production run of $200, a monthly holding cost per unit of $5.00, and an annual production rate of 300,000 units. The firm operates and experiences demand 300 days per year.
Required:
a. What is the optimum size of the production run?
b. What is the average holding cost per year?
c. What is the setup cost per year?
d. What is the total cost per year if cost of each unit is 10 dollars?
e. Suppose that management mistakenly used the basic EOQ model to calculate the batch size instead of using the POQ model. How much money per year has that mistake cost the company?

Answer 1

Answer:

a. 3,795 units

b. $1,897.50

c.  $2,845.80

d. $42,693.80

Explanation:

Optimum size for the Production ran is the size that minimizes Set-up costs and Holding costs.

Optimum size for the Production = √ (2 × Annual Production × Set-up cost) / Holding Cost per unit

Optimum size for the Production = √ (2 ×  600 × 300 × $200) / $5.00

                                                       = 3,794.73 or 3,795 units

Average Holding Cost = Optimum size for the Production / 2

                                     =  3,795 units / 2

                                     =  $1,897.50

Set - up Cost = Total Annual Production / Optimum size for the Production × Set - up cost per unit

                     = ((600 × 300) / 3,795)× $5.00

                     = $237.15

Annual cost = $237.15 × 12

                    = $2,845.80

Total Cost Calculation

Purchase Price (3,795 × $10)  = $37,950.50

Holding Cost                            =    $1,897.50

Set - up Cost                            =   $2,845.80

Total Cost                                 = $42,693.80

POQ = Optimum size for the Production / Annual Demand

        = 3,795 units / (300 × 600)

        = 0.021