Question

Consider a product with a daily demand of 400 units, a setup cost per production run of $100. Monthly holding cost are 15%. Unit cost is $55.75. The company has an annual production rate of 292,000 units. The firm operates and experiences demand 365 days per year.

a. What is the production quantity?

b. What is the maximum inventory level that the company is capable of having on hand?

c. What is the cost of managing the inventory?

d. What is the number of setups?

e. What is the total cost, including the unit cost?

Answer 1

Answer:

a. 2643

b. 1321

c. 5524.77

d. 55.25

e. $8,156,074.321

Explanation:

Data provided in the question:

Production = 292,000

Daily demand, d = 400

Annual demand, D = 400 × 365 = 146,000

Production rate, P = 292000 ÷ 365 =800

set-up cost, Cs = $100

Holding cost, Ch = $55.75 × 15% = $8.3625

Now,

a) Economic production quantity, EPQ = $\sqrt{\frac{2\times D\times Cs}{Ch}\times(\frac{p}{(p-d)})}$

Or

= $\sqrt{\frac{2\times 146,000\times 100}{8.3625}\times(\frac{800}{(800-400)})}$

= 2642.64 ≈ 2643

b. Maximum inventory level that the company is capable of having on hand, $I_{max}$

= EPQ × [ 1 - (d ÷ p) ]

= 2642.64  × [ 1 - (400 ÷ 800) ]

= 1321.32 ≈  1321

c. Cost of managing the inventory

= $Ch\times(\frac{I_{max}}{2})$

= 8.3625 × [ 1321.32 ÷ 2 ]

= 5524.77

d. Number of setups

= [ Annual demand ] ÷ EPQ

= 146,000 ÷ 2642.64

= 55.25

e. Total cost including the unit cost

= Setup cost + Holding cost + Unit cost

= ( [ 146000 ÷ 2642.64 ] × 100 ) + ( [ 2642.64 ÷ 2 ] × 8.3625 ) + ( 146000× 55.75 )

= $8,156,074.321