A manufacturing company has a contract to supply 5000 bushes to an automobile factory per day. The company has capacity to manufacture 8000 bushes per day and holding cost of 1000 bushes is 8 paisa per day. Set up cost is Rs. 20. No shortages are allowed. What would be his frequency of production run? Sketch the inventory.

Demand (D) = 5000 bushes/day

Production capacity (P) = 8000 /day

Holding capacity for 1000 bushes $(C_h)$ $= \dfrac{8 paisa}{day} = \dfrac{8}{1000} * 100 \\ = 0.8 \text{paisa per bush}$

Set up cost $(C_0)$ = 20 per bush

No shortage allowed

Frequency of production run = ?

Sketch the inventory.

Economic lot size:

Q $= \sqrt{\dfrac{2DCo}{Ch}} * \sqrt{\dfrac{P}{(P-D)}} \\ = \sqrt{\dfrac{2*5000*20}{\bigg(\dfrac{8}{1000}\bigg)*\bigg(\dfrac{1}{1000}\bigg)}}* \sqrt{\dfrac{8000}{(8000-5000)}} \\ =5000*1.6329 \\ =8164.96 \\ =8165 units$

Frequency of production runs per day:

(N) $= \dfrac{D}{Co} \\ = \dfrac{5000}{20} \\ = 250 units$

Total inventory costs $\text{= Holding + setup costs} \\ = \dfrac{2 \times C_h}{2} \times \bigg(1- \dfrac{D}{p}\bigg)+ N*Co \\ = \dfrac{8165 \times 0.008}{2} \times \bigg(1- \dfrac{5000}{8000}\bigg)+ 250 \times 20 \\ = Rs. 5012.24$.