Answer to Question #156917 in Operations Research for Kajal Kishor Chile

Question

Neon lights on a campus are replaced at the rate of 100 units perday. The physical plant orders the neon lights periodically. It costs BND 100 to initiate a purchase order. A neon light kept in storage is estimated to cost about BND 0.02 per day. The lead time between placing and receiving an order is 12 days. Determine the optimal inventory policy for ordering the neon lights

Answer 1

Size of order:

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

Demand $D=100$ units per day

Ordering Cost $C_2=\$100$ per order

Holding Cost $C_3=\$0.02$ per day

Lead Time $L=12$ days

$Q=\sqrt{\frac{2\cdot100\cdot100}{0.02}}=1000$ neonlights

The associate cycle length is:

$t=Q/D=1000/100=10$ days

Because the lead time $L=12$ days exceeds the cycle length $t=10$ days, we must compute $L_e$

The number of integer cycles included in $L$ is

$n=$ (largest integer $\leq12/10=1$ )

Thus,

$L_e=L-nt=12-10=2$ days

The reorder point thus occurs when the inventory level drops to

$L_eD=2\cdot100=200$ 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

$\frac{C_2}{Q/D}+C_3Q/2=\frac{100}{1000/100}+0.02\cdot1000/2=20$ days