19. 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.
Answers
Answer:
+0.02⋅1000/2=20 days
Step-by-step explanation:
Q=\sqrt{\frac{2C_2D}{C_3}}Q=
C
3
2C
2
D
Demand D=100D=100 units per day
Ordering Cost C_2=\$100C
2
=$100 per order
Holding Cost C_3=\$0.02C
3
=$0.02 per day
Lead Time L=12L=12 days
Q=\sqrt{\frac{2\cdot100\cdot100}{0.02}}=1000Q=
0.02
2⋅100⋅100
=1000 neonlights
The associate cycle length is:
t=Q/D=1000/100=10t=Q/D=1000/100=10 days
Because the lead time L=12L=12 days exceeds the cycle length t=10t=10 days, we must compute L_eL
e
The number of integer cycles included in LL is
n=n= (largest integer \leq12/10=1≤12/10=1 )
Thus,
L_e=L-nt=12-10=2L
e
=L−nt=12−10=2 days
The reorder point thus occurs when the inventory level drops to
L_eD=2\cdot100=200L
e
D=2⋅100=200 neonlights
The inventory policy for ordering the neon lights is order 100 units whenever the inventory order drops to 200 units. The daily inventory cost associated with the proposal inventory policy is
\frac{C_2}{Q/D}+C_3Q/2=\frac{100}{1000/100}+0.02\cdot1000/2=20
Q/D
C
2
+C
3
Q/2=
1000/100
100
+0.02⋅1000/2=20 days