Question

A manufacture has to supply 80 units of his product every month to a customer. Capital cost is Rs. 800 per unit. Holding cost is 12% per year of capital cost. Shortages are not allowed. Cost of setting up machines for production is Rs. 300. How frequently should production be made so that inventory is most economical?

Answer 1

Given: 

R = 80 units per month and R = 80 × 12 

= 960 units per year. 

P = Capital cost = Rs. 800 per unit. 

I = Holding cost per unit per year = 12%. 

∴ C₁ = carrying cost per unit = PI = 800 × 12% = Rs. 96 per year. 

C₃ = Set up cost = Rs. 300 per order

Economic order quantity : 

∴ Q° = 77.46 = 77 order.

Reorder time is t° = \(\frac{Q°}{R} = \frac{77.46}{960}\) 

= 0.0807 years

i.e., t° =0.0897 × 365 = 29 days (approx) 

Frequency of order is n° = \(\frac{1}{t°}\)= 12.39 per year 

Minimum average cost is

C(Q°) =\(\sqrt{2C_1C_3R}\)

=\(=\sqrt{2 \times96 \times300 \times 960}\)

=7436.13

C(Q°) = Rs. 7436.13 per year