Saferty Stock Problems
Problem 1:
Litely Corp sells 1,350 of its special decorator light switch per year, and places orders for 300 of these switches at a time. Assuming no safety stocks, Litely estimates a 50% chance of no shortages in each cycle, and the probability of shortages of 5, 10, and 15 units as 0.2, 0.15, and 0.15 respectively. The carrying cost per unit per year is calculated as $5 and the stockout cost is estimated at $6 ($3 lost profit per switch and another $3 lost in goodwill, or future sales loss). What level of safety stock should Litely use for this product? (Consider safety stock of 0, 5, 10, and 15 units)
Carrying cost equals zero.
Stockout cost:
Stockout cost:
(there is no shortage if 15 units are maintained)
Therefore: Minimum cost comes from carrying a 10-unit safety stock.
Problem 2:
A product has a reorder point of 110 units, and is ordered four times a year. The following table shows the historical distribution of demand values observed during the reorder period. Demand
Probability
100 .3 110 .4 120 .2 130 .1 Managers have noted that stockouts occur 30 percent of the time with this policy, and question whether a change in inventory policy, to include some safety stock, might be an improvement. The managers realize that any safety stock would increase the service level, but are worried about the increased costs of carrying the safety stock. Currently, stockouts are valued at $20 per unit per occurrence, while inventory carrying costs are $10 per unit per year. What is your advice? Do higher levels of safety stock add to total costs, or not? What level of safety stock is best?
Action
Safety stock cost
Stockout cost
Total cost
ROP=110 (SS=0)
0 =
$0
.2 x 10 x 20 x 4 =
$160
.1 x 20 x 20 x 4 =
$160
$0
$320
$320
ROP=120 (SS=10)
10 x $10 =
$100
.1 x 10 x 20 x 4 =
$80
$100
$80
$180
ROP=130 (SS=20)
Litely Corp sells 1,350 of its special decorator light switch per year, and places orders for 300 of these switches at a time. Assuming no safety stocks, Litely estimates a 50% chance of no shortages in each cycle, and the probability of shortages of 5, 10, and 15 units as 0.2, 0.15, and 0.15 respectively. The carrying cost per unit per year is calculated as $5 and the stockout cost is estimated at $6 ($3 lost profit per switch and another $3 lost in goodwill, or future sales loss). What level of safety stock should Litely use for this product? (Consider safety stock of 0, 5, 10, and 15 units)
Carrying cost equals zero.
Stockout cost:
Stockout cost:
(there is no shortage if 15 units are maintained)
Therefore: Minimum cost comes from carrying a 10-unit safety stock.
Problem 2:
A product has a reorder point of 110 units, and is ordered four times a year. The following table shows the historical distribution of demand values observed during the reorder period. Demand
Probability
100 .3 110 .4 120 .2 130 .1 Managers have noted that stockouts occur 30 percent of the time with this policy, and question whether a change in inventory policy, to include some safety stock, might be an improvement. The managers realize that any safety stock would increase the service level, but are worried about the increased costs of carrying the safety stock. Currently, stockouts are valued at $20 per unit per occurrence, while inventory carrying costs are $10 per unit per year. What is your advice? Do higher levels of safety stock add to total costs, or not? What level of safety stock is best?
Action
Safety stock cost
Stockout cost
Total cost
ROP=110 (SS=0)
0 =
$0
.2 x 10 x 20 x 4 =
$160
.1 x 20 x 20 x 4 =
$160
$0
$320
$320
ROP=120 (SS=10)
10 x $10 =
$100
.1 x 10 x 20 x 4 =
$80
$100
$80
$180
ROP=130 (SS=20)