EOQ, total cost and reorder point numerical

Given

$D = 12000$ units/year, $S =$ Rs 300, $H = 0.20 \times 150 =$ Rs 30 per unit per year, 300 working days, $L = 10$ days.

(a) EOQ

$$Q^* = \sqrt{\frac{2DS}{H}} = \sqrt{\frac{2 \times 12000 \times 300}{30}} = \sqrt{240000} = 489.9 \approx 490\ \text{units}$$

(b) Orders and cycle time

$$N = \frac{D}{Q^*} = \frac{12000}{489.9} = 24.5\ \text{orders/year}$$ $$T = \frac{300}{24.5} = 12.2\ \text{working days}$$

(c) Annual ordering plus holding cost

Ordering cost $= 24.49 \times 300 =$ Rs 7,348; holding cost $= (489.9/2) \times 30 =$ Rs 7,348.

$$TC = 7348 + 7348 = \text{Rs } 14{,}697$$

(Purchase cost is $12000 \times 150 =$ Rs 1,800,000, so the total annual cost including purchase is Rs 1,814,697.)

(d) Reorder point

Daily demand $d = 12000/300 = 40$ units/day.

$$ROP = d \times L = 40 \times 10 = 400\ \text{units}$$

An order of 490 units is placed when the stock falls to 400 units.

(e) Order quantity of 600

$$TC_{600} = \frac{12000}{600}(300) + \frac{600}{2}(30) = 6000 + 9000 = \text{Rs } 15{,}000$$

Extra cost $= 15000 - 14697 =$ Rs 303 per year (about 2.1% higher).

Answer: EOQ = 490 units; 24.5 orders/year, every 12.2 working days; TC = Rs 14,697; ROP = 400 units; ordering 600 costs Rs 303 more per year.