Question #296140

Neon lights in an industrial park are replaced at the rate of 100 units per day. The physical planet orders the neon lights periodically. It costs Rs.500 to initiate a purchase order. A neon light kept in storage is estimated to cost about Rs.20 per day. The lead time between placing and receiving an order is 12 days. Determine the optimum inventory policy for ordering the neon lights.


1
Expert's answer
2022-02-11T10:46:28-0500

Solution:

Size of order:

Q=2C2DC3Q=\sqrt{\frac{2C_2D}{C_3}}

Q=2C2DC3Q=\sqrt{\frac{2C_2D}{C_3}}

Demand D=100D=100 units per day

Ordering Cost C2=Rs.500C_2=Rs. 500 per order

Holding Cost C3=Rs.20C_3=Rs.20 per day

Lead Time L=12L=12 days


Q=250010020=70.7Q=\sqrt{\frac{2\cdot500\cdot100}{20}}=70.7 neonlights


The associate cycle length is:

t=Q/D=70.7/100=0.707t=Q/D=70.7/100=0.707 days

Because the lead time L=12L=12 days exceeds the cycle length t=0.707t=0.707 days, we must compute LeL_e

The number of integer cycles included in LL is

n=n= (largest integer 12/0.707=16\leq12/0.707=16 )

Thus,

Le=Lnt=1211.312=0.688L_e=L-nt=12-11.312=0.688 days

The reorder point thus occurs when the inventory level drops to

LeD=0.688100=68.8L_eD=0.688\cdot100=68.8 neonlights


The inventory policy for ordering the neon lights is order 100 units whenever the inventory order drops to 68.8 units. The daily inventory cost associated with the proposal inventory policy is

C2Q/D+C3Q/2=50070.7/100+2070.7/2=1414.2\frac{C_2}{Q/D}+C_3Q/2=\frac{500}{70.7/100}+20\cdot70.7/2=1414.2 days


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