Question

Sun Pharma Ltd. has an annual demand of 4000 units for one of its medicines. For this the production company has to bear setting up and order processing cost of Rs. 900. The cost of manufacturing is Rs. 800 per unit. The cost of carrying is 10% p.a. Based on this data, compute the Economic Batch Quantity.

Hint:

$$\text{At EBQ, Total Setup Costs} = \text{Total Carrying Costs}$$ You can double-check this: $$\text{Number of Batches} = \frac{4000}{300} = 13.33 \implies \text{Total Setup Cost} = 13.33 \times 900 = \text{Rs. } 12,000$$ $$\text{Average Inventory} = \frac{300}{2} = 150 \text{ units} \implies \text{Total Carrying Cost} = 150 \times 80 = \text{Rs. } 12,000$$ Because both costs are equal, the solution of 300 units is mathematically verified.

Answer 1

Step 1: Identifying the Variables and Equation Parameters:
The Economic Batch Quantity (EBQ) is a mathematical model used in batch costing systems to determine the most cost-efficient size of a production run. It balances setting-up costs against inventory carrying costs. We extract the given parameters from the problem: Annual Demand (D) &= 4,000 units per annum
Setup & Processing Cost per batch (S) &= Rs. 900
Manufacturing Cost per unit (C) &= Rs. 800
Carrying Cost percentage &= 10% per annum

Step 2: Calculating Unit Carrying Cost per Annum ($C_h$):
The inventory carrying cost represents the holding cost per unit per year. It is calculated by multiplying the unit manufacturing cost by the carrying rate: C_h &= C \times i
C_h &= Rs. 800 \times 10%
C_h &= Rs. 80 per unit per annum

Step 3: Applying the EBQ Formula and Computing Output:
The formula for Economic Batch Quantity is derived from the classic Wilson Economic Order Quantity model: EBQ = \sqrt{\frac{2 \times D \times S}{C_h}} Substituting our variables into this formula: EBQ &= \sqrt{\frac{2 \times 4,000 \times 900}{80}}
EBQ &= \sqrt{\frac{7,200,000}{80}}
EBQ &= \sqrt{90,000}
EBQ &= 300 units Therefore, Sun Pharma Ltd. should schedule its medicine manufacturing in batches of 300 units to minimize its total setup and holding costs.