A company has demand for 14000 units/year for a product. It can produce 1600 units/month. The set up cost is Rs. 400/set up. Inventory holding cost is Rs. 0.3 per unit per month. Decide the suitable inventory policy.

Demand D = 14000 per year

Set up costs Co = Rs. 400 per setup

Inventory carrying costs Ch = Rs. 0.3 per unit per month = Rs. 3.6 per year

Production capacity P = 1600 × 12 = 19200 per year

Economic Lot Size:

$Q* = \sqrt{\bigg(\dfrac{2.D.Co}{Ch}\bigg)} × \sqrt{\bigg({P}{P-D}\bigg)}= \sqrt{\bigg(\dfrac{2×14000×400}{3.6}\bigg)} × \sqrt{\bigg(\dfrac{19200}{19200-14000}\bigg)}= 3389.27 units$

Number of production runs per year: N = 14000/3389027 = 4.13 runs

$\text{Total inventory costs}$ $= \text{Holding costs + setup costs} = \dfrac{Q.Ch}{2} ×\bigg(\dfrac{1-D}{P}\bigg) + N×Co \\ = \dfrac{3389.27×3.6}{2} ×\bigg(\dfrac{1-14000}{19200}\bigg) + 4.13×400 = Rs. 3304.54$