Question

Demand for motor oil in an auto repair shop can be approximated by a Normal distribution and has a mean of 286 quarts per week with a standard deviation of 45 quarts per week. Company policy states motor oil should be in stock 98 percent of the time. Lead time is 3 days and the shop is open seven days a week (Hint: Work in terms of weeks for the following problems).

a. Calculate the ROP, rounding up to the nearest quart.

b. What would the order size be for a fixed-interval model using the previous information available as well as an order interval of 4 weeks and a supply of 537 quarts at the time of counting? Round up to the nearest quart.

c. Coming into work, the manager discovers a break-in has occurred. Several boxes of motor oil were stolen, leaving the shop with 136 quarts of oil. An order to replace the stolen oil is placed right away, which will be delivered in 3 days. What is the probability of stocking out?

Answer 1

Reorder point = demand during lead time + safety stock

= 286x3/7 +z x SD x (Lead time)^1/2

= 122.57+ 2.05 x45 x( 3/7)^1/2

= 122.57+60.39 = 283

b. If the oder is placed every 4 weeks, the order up to level

= demand during ( lead time + review time) + z x SD x (Lead time+ review time)^1/2

= 286 x( 3/7+4) + 2.05 x45 x( 3/7+4)^1/2

= 1266.57+194.09 =1461

If there are 537 already on hand the order size will be = 1461-537 =924

c

136 = dem. during lead time + SS

136 = 122.57 +  z x45 x0.6456

z = 136-122.57 / 29.45 =0.456

which gives probability of 0.676

Probability of stocking out = 1-0.676 = 0.324