Andre Greipel is the owner of a small company that produces heart rate monitors.
ID: 450063 • Letter: A
Question
Andre Greipel is the owner of a small company that produces heart rate monitors. The annual demand is for 2,800 heart rate monitors, and Andre produces these devices in batches. On average, Andre can produce 150 monitors per day during the production process. Demand for monitors has been about 50 monitors per day. The cost to set up the production process is $600, and it costs Andre $0.75 to carry 1 monitor in inventory for one year. How many monitors should Andre produce in each batch?
a)What is the optimal economic production quantity?
b)On average, how many setups are required per year?
c)What is the total cost per year (holding plus setup)?
Explanation / Answer
Annual Demand = 2800 Consumption rate is uniform throughout the year. Per day Demand = 50 units/day The firm can produce at a rate of 150 units / day Carrying cost is $0.75 per unit / year Setup cost for production run is $600 / setup EPQ = 2SD / H * p / p - u where, S is the Set Up Cost D is the Annual Demand P is the Production rate U is demand rate per day H is Carrying Cost EPQ = 2*600*2800 / 0.75 * 150 / 150-50 = 2116.601*1.2247 = 2592.296 or 2592 units b. Set up requried per year = Annual Demand / EPQ = 2800 / 2592 = 1.08 Run Time = EPQ/Production Rate = 2592 / 150 = 17.28 days The run time is 17.28 days Production per day is 150 units Consumption Per day is 50 units hence, Inventory added is 100 per day (150-50) Maximum Inventory = 17.28*100 = 1728 c. Annual Holding Cost = Holding Cost per unit * Max Inv /2 = 0.75 * 1728/2 = 648 Annual Set Up Cost = Annual Demand / EPQ * Set Up cost = 2800/2592 * 600 = 648 Total Cost = $1296