The component is manufacturer in the factory itself at the rate of 60 units per day, it costs Rs. 150 per unit and set up cost for each production run is Rs. 15,000. Inventory carrying cost is Rs. 10 per unit per day. If no shortages are allowed, decide the optimal ordering quantity and total estimated system cost. Sketch the inventory system.

Mumbai University > Mechanical Engineering > Sem 7 > Operations Research

Marks: 10 Marks

K = 60 units per day, R = 40 units per day, C1 = 10 per unit per day, C3 = 15000/ set up.

i. Optimal ordering Quantity :

q_0 = √(K/(K-R)) √((2C_3 R)/C_1 )

= √(60/(60-40)) √((2×15000×40)/10)

Optimal ordering cost = 600 units per setup

ii. Cost of the system:

C_0 = R×cost of unit + √(2RC_1 C_3 )∙√((K-R)/K)

= 40×120 + √(2×40×10×15000)∙√(20/60)

cost of the system = Rs.6800 per day