Model Answer
0 min readIntroduction
Inventory management is a critical component of operations management, aiming to balance the costs of holding inventory with the risks of stockouts. Effective inventory control directly impacts a company’s profitability and customer satisfaction. Two key concepts in this regard are the Economic Order Quantity (EOQ), which determines the optimal order size to minimize total inventory costs, and the Reorder Point (ROP), which indicates when to place a new order to avoid stockouts. This answer will calculate the optimal order quantity and reorder point, given a lead time and desired service level, making necessary assumptions where data is missing.
Economic Order Quantity (EOQ) Calculation
The Economic Order Quantity (EOQ) is the order quantity that minimizes the total inventory costs, which include ordering costs and holding costs. The formula for EOQ is:
EOQ = √(2DS / H)
Where:
- D = Annual Demand
- S = Ordering Cost per Order
- H = Holding Cost per Unit per Year
Since the annual demand (D), ordering cost (S), and holding cost (H) are not provided in the question, we will assume the following values for demonstration purposes:
- D = 10,000 units
- S = ₹50 per order
- H = ₹5 per unit per year
Therefore:
EOQ = √(2 * 10,000 * 50 / 5) = √(200,000) = 447.21 units
Rounding this to the nearest whole number, the optimal order quantity is 447 units.
Reorder Point (ROP) Calculation
The Reorder Point (ROP) is the inventory level at which a new order should be placed. It is calculated as follows:
ROP = (Lead Time * Daily Demand) + Safety Stock
Where:
- Lead Time = Time between placing an order and receiving it (in days)
- Daily Demand = Average daily demand
- Safety Stock = Extra inventory held to buffer against unexpected demand fluctuations or delays in lead time.
We are given a lead time of 3 days. We need to calculate daily demand and safety stock.
Calculating Daily Demand
Daily Demand = Annual Demand / Number of Working Days
Assuming 250 working days in a year:
Daily Demand = 10,000 / 250 = 40 units per day
Calculating Safety Stock
Safety Stock is determined by the desired service level. A 99% service level means that there is a 1% chance of a stockout. To calculate safety stock, we need to know the standard deviation of daily demand. Without this information, we will use a simplified approach based on the Z-score corresponding to a 99% service level.
The Z-score for a 99% service level is approximately 2.33 (obtained from standard normal distribution tables). We will assume a standard deviation of daily demand to be 5 units (this is an assumption for demonstration).
Safety Stock = Z-score * Standard Deviation of Daily Demand * √(Lead Time)
Safety Stock = 2.33 * 5 * √3 = 2.33 * 5 * 1.732 = 20.14 units
Rounding this to the nearest whole number, the safety stock is 20 units.
Calculating Reorder Point
ROP = (Lead Time * Daily Demand) + Safety Stock
ROP = (3 * 40) + 20 = 120 + 20 = 140 units
Therefore, the reorder point is 140 units.
Conclusion
In conclusion, based on the assumed values for annual demand, ordering cost, and holding cost, the optimal order quantity is 447 units. With a lead time of 3 days and a desired service level of 99%, the reorder point is calculated to be 140 units. It is crucial to remember that these calculations are highly sensitive to the input parameters. Accurate demand forecasting, cost analysis, and consideration of lead time variability are essential for effective inventory management and minimizing total costs.
Answer Length
This is a comprehensive model answer for learning purposes and may exceed the word limit. In the exam, always adhere to the prescribed word count.