Question

A food processing company uses 25,000 kg of corn flour every year. The quantity-discount price of corn flour is provided in the table below:

Quantity (kg)	Unit price (Rs/kg)
1 – 749	70
750 – 1499	65
1500 and above	60

 

The order processing charges are Rs. 500/order. The handling plus carry-over charge on an annual basis is 20% of the purchase price of the corn flour per kg. The optimal order quantity (in kg) is _______

Answer 1

Concept:

\(EOQ = \sqrt {\frac{{2D{C_0}}}{{{C_h}}}} = \sqrt {\frac{{2 \times 25000 \times 500}}{{\frac{{20}}{{100}} \times 60}}} = 1443.336\;kg\)

Total Inventory Cost = \(\sqrt {2D{C_0}{C_h}} \)

Calculation:

Given:

Demand = 25,000 kg, C₀ (ordering cost)= Rs. 500/order, C_h(holding cost)= 20% of unit cost

\(EOQ = \sqrt {\frac{{2D{C_0}}}{{{C_h}}}} = \sqrt {\frac{{2 \times 25000 \times 500}}{{\frac{{20}}{{100}} \times 60}}} = 1443.336\;kg\)

⇒ Quantity less than 1443.376 kg is not feasible

⇒ ∴ Checking for 750 – 1499 kg

Total annual cost = Direct cost + Total inventory cost

Total Annual Cost = Direct Cost + Total Inventory Cost

Total Inventory Cost = \(\sqrt {2D{C_0}{C_h}} \)

\(\therefore TAC = 25,000 \times 65 + \sqrt {2 \times 25000 \times 500 \times \frac{2}{{100}} \times 65} \)

Total Annual Cost = Rs. 16,43,027.75

For 1500 kg

\(Total Annual Cost = 25,000 \times 60 + \sqrt {2 \times 25000 \times 500 \times \frac{{20}}{{100}} \times 60} \)

Total Annual Cost = Rs. 15,17,320.50

So optimum order quantity is 1500 kg.