A repair and maintenance company is engaged in providing service to a particular brand of popular vehicle. It uses 8000 units of a moving parts per year as replacements of the old parts. Each part costs Rs. 250/-. The setup costs are estimated at Rs. 100 and the inventory carrying cost is the average of such inventory at 20% of the price. Supply of the part is at the rate of 80 per day. Calculate the following :
(i)Optimal order quantity
(ii)Optimal number of set ups,
(iii)Total variable costs based on optimal policy.
Assume 310 working days in a year
To calculate the optimal order quantity, optimal number of setups, and total variable costs based on the optimal policy for the repair and maintenance company, we can use the Economic Order Quantity (EOQ) model from Operations Research. The EOQ model helps in determining the most cost-effective order quantity for a company to minimize its total inventory costs.
(i) Optimal Order Quantity (Q):
The EOQ formula is given as:
\[Q = \sqrt{\frac{2DS}{H}}\]
Where:
- D = Annual demand (8000 units)
- S = Setup cost per order (Rs. 100)
- H = Holding cost per unit per year (20% of the price, which is 0.20 * 250 = Rs. 50)
Substituting the values into the formula:
\[Q = \sqrt{\frac{2 * 8000 * 100}{50}}\]
\[Q = \sqrt{320000}\]
\[Q ≈ 566.95\]
Rounded to the nearest whole number, the optimal order quantity (Q) is approximately 567 units.
(ii) Optimal Number of Setups (N):
The number of setups can be calculated by dividing the annual demand by the optimal order quantity:
\[N = \frac{D}{Q}\]
\[N = \frac{8000}{567}\]
\[N ≈ 14.08\]
Since you cannot have a fraction of a setup, you should round up to the nearest whole number. Therefore, the optimal number
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