Question

The demand for a commodity is 100 units per day. Every time an order is placed, a fixed cost of Rs 400 is incurred and the holding cost is Rs 0.08 per unit per day. If the lead time is 13 days, then the economic lot size and the reorder point are in units

• A. 800 and 130
• B. 840 and 100
• C. 890 and 300
• D. 1000 and 300

Hint:

Always ensure your time units are fully uniform! Here, demand is units/day and holding cost is Rs/unit/day. Because they match, you do not need to convert them into annual figures. For ROP, remember: if Lead Time Demand > $Q$, subtract $Q$ repeatedly until the value is less than $Q$. \[ 1300 - 1000 = 300 \]

Answer 1

The Correct Option is D

Concept: The classical Economic Order Quantity (EOQ) model determines an optimal purchase lot size that minimizes total variable inventory costs (comprising setup/ordering costs and carrying/holding costs). The standard formula for economic lot size is: \[ Q^* = \sqrt{\frac{2 \cdot D \cdot C_o}{C_h}} \] Where: * $D$ = Demand rate (units per time period) * $C_o$ = Fixed cost per individual order placed (ordering cost) * $C_h$ = Holding cost per unit per time period (holding cost) The Reorder Point (ROP) represents the inventory level at which a replenishment order must be triggered, calculated as: \[ \text{ROP} = \text{Demand rate } (d) \times \text{Lead time } (L) \] *Note: If the inventory remaining during the lead time exceeds one full order cycle, we adjust for the replenishment cycle via the modulo operator to determine the physical hand-count level.*

Step 1: Extract variables and compute the Economic Lot Size ($Q^*$).
From the question statement, we harvest the parameters normalized on a daily baseline: * Daily Demand, $D = 100\text{ units/day}$ * Ordering Cost, $C_o = \text{Rs. } 400\text{ per order}$ * Holding Cost, $C_h = \text{Rs. } 0.08\text{ per unit per day}$ Let us substitute these expressions directly into the economic lot size equation: \[ Q^* = \sqrt{\frac{2 \times 100 \times 400}{0.08}} \] \[ Q^* = \sqrt{\frac{80000}{0.08}} \] To eliminate the decimal denominator, multiply the numerator and denominator by 100: \[ Q^* = \sqrt{\frac{8000000}{8}} = \sqrt{1000000} = 1000\text{ units} \]

Step 2: Calculate the Reorder Point ($\text{ROP}$).
We are given that the lead time $L = 13\text{ days}$. First, we find the gross demand consumption accumulating across this lead period: \[ \text{Total Lead Time Demand} = D \times L = 100\text{ units/day} \times 13\text{ days} = 1300\text{ units} \] Since our order size ($Q^* = 1000\text{ units}$) is smaller than the total lead time demand ($1300\text{ units}$), it implies that an additional order must have already been placed while a previous order was outstanding. The physical inventory level on hand that triggers the alert is calculated by evaluating the total lead time demand modulo the economic order quantity: \[ \text{ROP} = (D \times L) \pmod{Q^*} \] \[ \text{ROP} = 1300 \pmod{1000} = 300\text{ units} \] Hence, the economic lot size is $1000\text{ units}$ and the reorder point is $300\text{ units}$, aligning with Option (4).