Question

A company has orders for approximately 100,000 units of a product that it can sell at a price of €150.00 per unit. The company operates 300 days per year. It costs €5.00 to store one unit of the product for one month.

The company manufactures other products, and it must set up the manufacturing system for a production order for the product, which costs €300. The product can be produced at a rate of 600 per working day.

Determine:

1. The Economic Order Quantity
2. The annual cost of producing the product
3. The number of production runs required each year (1 Mark)
4. The length of the cycle (time between production runs) (1 Mark)
5. The number of days each production run will last  (1 Mark)

Answer 1

Annual Demand = 100,000

Selling Price = €150.00

Operating Days = 300 days per year

Holding Cost = €5.00/unit

Setup Cost = €300

Rate of production = 600/day

Demand rate = 100000/300 = 333.33

X= 1-(Demand rate/production rate) = 1-(333.33/600) = 0.445

EOQ = (2*Annual Demand*Setup Cost/(holding cost*X))^0.5 = (2*100000*300/(5*0.445))^0.5 = 5192.9 rounded to 5193

Annual Cost of Producing the product = No. of production runs * Set up cost

No. of production runs = Annual Demand / EOQ = 100000/5193 = 19.26

Annual Cost or producing the product = 19.26*300 = 5778

Length of Cycle = No. of working days in a year / No. of production runs per year = 300/19.26 = 15.58 days

Number of days each production will last = EOQ/rate of production = 5193/600 = 8.65 days