Montegut Manufacturing produces a product for which the annual demand is 10,000. Production averages 100 per day, while demand is 40 per day. Holding costs are $1.00 per unit per year;set-up costs $200.00. If they wish to produce this product in economics batches, what size batch should be used? What is the maximum inventory level? How many order cycles are there per year? How much does management of this good in inventory cost the firm each year?
To determine the optimal batch size, maximum inventory level, number of order cycles per year, and management cost, we need to consider the Economic Order Quantity (EOQ) model.
1. Batch Size (Q):
The EOQ formula is given by:
Q = √((2DS)/H)
where:
D = Annual demand (10,000 units)
S = Setup cost per order ($200)
H = Holding cost per unit per year ($1)
By plugging in the values, we can calculate the batch size (Q) as follows:
Q = √((2 * 10,000 * 200) / 1)
= √(4,000,000)
≈ 2,000 units
Therefore, the optimal batch size should be 2,000 units.
2. Maximum Inventory Level:
The maximum inventory level can be calculated by multiplying the batch size with the number of production days required to finish the batch. In this case:
Number of production days = Batch size / Production per day
= 2,000 / 100
= 20 days
Maximum Inventory Level = Batch size * Number of production days
= 2,000 * 20
= 40,000 units
Therefore, the maximum inventory level should be 40,000 units.
3. Order Cycles per Year:
The number of order cycles per year can be calculated by dividing the annual demand (D) by the batch size (Q).
Order Cycles per Year = D / Q
= 10,000 / 2,000
= 5 order cycles per year
Therefore, there will be 5 order cycles per year.
4. Management Cost:
The management cost is the sum of the setup costs and holding costs.
Management Cost per Year = Setup cost per order + (Holding cost per unit * Annual demand)
= 200 + (1 * 10,000)
= $10,200
Therefore, the management cost for this product in inventory will be $10,200 per year.
In summary:
- The optimal batch size should be 2,000 units.
- The maximum inventory level should be 40,000 units.
- There will be 5 order cycles per year.
- The management cost for this product in inventory will be $10,200 per year.