Electric Scissors Production Optimization: Finding the Perfect Batch Size

How many scissors should Jan produce in each batch?

Given the annual demand of 8,000 scissors, an average production rate of 150 scissors per day, and a daily demand of 40 scissors, what is the optimal batch size for Jan's small company?

Answer:

Jan should produce 2,697 scissors per batch.

When determining the optimal batch size for production, Jan should consider several factors such as the setup cost, annual demand, production rate, and holding cost per pair of scissors. By using the Economic Production Quantity (EPQ) formula, Jan can calculate the batch size that minimizes total production and inventory costs.

The EPQ formula is given as:

Q = √[2KD / h(1 - x)]

Where:

K = setup cost ($100)

D = annual demand (8,000 scissors)

h = annual holding cost per pair of scissors (30 cents)

x= annual demand / annual production rate

Plugging in the values:

x = 8,000 / (150 x 200) = 0.267

Q = √[(2 x $100 x $8,000) / [$0.30 x (1 - 0.267)]]

Q = √($1,600,000 / 0.22) = 2,696.8 ≈ 2,697 scissors per batch

Therefore, Jan should produce 2,697 scissors in each batch to optimize production efficiency and minimize costs.