El Computer produces its multimedia notebook computer on a production line that has an annual capacity of 16,000 units. The cost to set up the production line is $2345, and the annual holding cost is $20 per unit. Current practice calls for production runs of 50 notebooks computers each month. 1. What is the optimal production lot size? 2. How many production runs should be made each year? What is the recommended cycle time? 3. Would you recommend changing the current production lot size policy from the monthly 500 unit production runs? Why or why not? What is the projected savings of your recommendation?
To determine the optimal production lot size, we can use the Economic Order Quantity (EOQ) formula. The EOQ formula is given by:
EOQ = sqrt[(2DS)/H]
Where:
D = Annual demand
S = Setup cost per production run
H = Holding cost per unit
Let's calculate the optimal production lot size step-by-step:
1. Calculate the Annual Demand (D):
Since the current practice calls for production runs of 50 notebook computers each month, the annual production run is 50 * 12 = 600 units.
2. Calculate the Setup Cost per Production Run (S):
Given that the cost to set up the production line is $2345, which is incurred for each production run.
3. Calculate the Holding Cost per Unit (H):
The annual holding cost is $20 per unit.
Now that we have the necessary values, let's calculate the EOQ:
EOQ = sqrt[(2 * D * S) / H]
= sqrt[(2 * 600 * 2345) / 20]
≈ sqrt[282,000]
Therefore, the optimal production lot size is approximately 530 units.
Now, let's move on to the next question:
2. Calculate the Number of Production Runs and Recommended Cycle Time:
To find the number of production runs, we can divide the annual demand (D) by the optimal production lot size.
Number of Production Runs per Year = D / EOQ
= 600 / 530
≈ 1.13 (round to 1)
Since we can't have fractional production runs, we should take only one production run per year, producing approximately 530 units.
Recommended Cycle Time = 1 year / Number of Production Runs per Year
= 1 year / 1
= 1 year
Therefore, it is recommended to have one production run per year with a cycle time of 1 year.
Now, let's address the final question:
3. Would you recommend changing the current production lot size policy from the monthly 500 unit production runs? Why or why not? What is the projected savings of your recommendation?
Given that the projected optimal production lot size is approximately 530 units, we can observe that it is quite close to the current production lot size of 500 units. Therefore, changing the current production lot size policy may not be necessary.
However, if El Computer chooses to adopt the optimal production lot size of 530 units per year, there can be potential savings in holding costs. Let's calculate the projected savings:
Savings = Total Holding Cost with Current Lot Size - Total Holding Cost with Optimal Lot Size
Total Holding Cost with Current Lot Size = 500 * $20 = $10,000 (per month)
Total Holding Cost with Optimal Lot Size = 530 * $20 = $10,600 (per year)
Projected Savings = Total Holding Cost with Current Lot Size - Total Holding Cost with Optimal Lot Size
= $10,000 - $10,600
= -$600
Hence, if El Computer chooses to switch to the optimal production lot size of 530 units per year, the projected savings would be -$600, meaning a potential increase in holding costs by $600.