Answer to Question #296140 in Math for Hamsa

Question

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.

Answer 1

Solution:

Size of order:

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

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

Demand $D=100$ units per day

Ordering Cost $C_2=Rs. 500$ per order

Holding Cost $C_3=Rs.20$ per day

Lead Time $L=12$ days

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

The associate cycle length is:

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

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

The number of integer cycles included in $L$ is

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

Thus,

$L_e=L-nt=12-11.312=0.688$ days

The reorder point thus occurs when the inventory level drops to

$L_eD=0.688\cdot100=68.8$ 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

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