A toy manufacturing makes its own wind-up motors, which are then put into its toys. While the toy manufacturing process is continous, the motors are intermittent flow. Data on the manufacture of the motors appears below.
Annual demand (D)=50,000 units
Set-up cost(S)=$85 per batch
Carry cost=$.20 per unit per year
Daily subassembly production rate=1,000
Daily subassembly usage rate=200
a. To minimize cost, how large should each batch of subassemblies be?
b. Approximatley how many days are required to produce a batch?
c.How long is a complete cycle?
d. What is the average inventory for this problem?
e.What is the total inventory cost (rounded to the nearest dollar) of the optimal behavior in this problem?
^^^
thats if Setup cost (S) = $65 per batch
and Carrying cost = $.10 per unit per year
Solution for (a)
To find the answers to the questions, we need to calculate various parameters and use some formulas. Let's go step by step:
a. To minimize cost, we need to determine the optimal batch size for subassemblies. The Economic Order Quantity (EOQ) formula can help us with this. The formula for EOQ is:
EOQ = sqrt((2DS) / H)
Where:
- D is the annual demand (50,000 units)
- S is the setup cost per batch ($85)
- H is the carrying cost per unit per year ($0.20)
Plugging in the values:
EOQ = sqrt((2 * 50,000 * $85) / $0.20)
EOQ = 1,322 units (rounded to the nearest whole unit)
Therefore, each batch of subassemblies should be approximately 1,322 units to minimize cost.
b. To find the number of days required to produce a batch, we need to divide the batch size by the daily subassembly production rate:
Number of days = Batch size / Daily production rate
Number of days = 1,322 units / 1,000 units per day
Number of days = 1.322 days (rounded to the nearest day)
Approximately 1.322 days are required to produce a batch.
c. The complete cycle is the time it takes to produce a batch and use it up. The time can be calculated by dividing the batch size by the daily subassembly usage rate:
Complete cycle = Batch size / Daily usage rate
Complete cycle = 1,322 units / 200 units per day
Complete cycle = 6.61 days (rounded to the nearest day)
Therefore, a complete cycle is approximately 6.61 days.
d. The average inventory can be calculated using the EOQ formula, assuming half of the batch is in inventory at any given time:
Average inventory = EOQ / 2
Average inventory = 1,322 units / 2
Average inventory = 661 units
The average inventory for this problem is approximately 661 units.
e. The total inventory cost can be calculated by multiplying the average inventory by the carrying cost per unit per year:
Total inventory cost = Average inventory * Carrying cost per unit per year * Batch size
Total inventory cost = 661 units * $0.20/unit/year * 1,322 units
Total inventory cost = $17,458 (rounded to the nearest dollar)
The total inventory cost of the optimal behavior in this problem is approximately $17,458.