Question

A producer of electronic parts wants to take account of both production rate and demand rate in deciding on its lot sizes. A particular $50 part can be produced at a rate of 100 units per day, and the demand rate is 20 units per day. Assuming there are 300 days in a year. The firm uses a carrying charge of 24% a year, and the setup cost is $200 each time the part is produced.

Required:
a. What lot size should be produced?b. If the production rate is ignored, what would the lot size be? How much does this smaller lot size cost the firm on an annual basis?

Answer 1

a) Optimal lot size = 1,118.03

b) Annual total cost = $46.51

Explanation:

As per the data given in the question,

a) Daily holding cost = $50 × 24% ÷ 300 = $0.04

Optimal lot size = Sqrt (2 × Demand rate × Setup cost ÷ (Daily holding cost × ( 1 - Demand rate ÷ Production cost)))

= Sqrt(2 × 100 × $200 ÷ ($0.04 × (1 - 20 ÷ 100)))

= $1,118.03

b) If the production rate is ignored then optimal lot size :

= Sqrt (2 × 20 × $200 ÷ 1)

= 89.44

Annual total cost = Setup cost+ holding cost

= (Demand rate ÷ Optimal lot size) × Setup cost + (Optimal lot size ÷ 2) × holding cost

= (20 ÷ 89.44) × $200 + 89.44 ÷ 2 ×$0.04

= $44.72 + $1.79

= $46.51