Question

A small oil change shop uses an average of 80 litres of 5W40 synthetic oil per day. Usage tends to be normally distributed with a standard deviation of 8 litres per day. Lead time is four days, and the desired service level is 92 percent. What amount of safety stock is appropriate under each of these conditions:

a. Oil is reordered every 45 days.

b. A fixed order size of 2400 litres is used.

Answer 1

To calculate the appropriate safety stock, we use a formula that takes into account the desired service level, lead time, daily demand, standard deviation, and reorder quantity. For oil reordered every 45 days, we calculate the safety stock using the formula. For a fixed order size of 2400 litres, we calculate the daily demand, reorder quantity, and safety stock.

Step-by-step explanation:

In order to calculate the safety stock under different conditions, we need to use the formula:

Safety Stock = (Z * σ * √Lead Time) + (Z * σ * √Reorder Quantity / Daily Demand)

a. Oil reordered every 45 days:

1. Calculate the Z value corresponding to the desired service level of 92%.
2. Calculate the safety stock using the formula.

b. Fixed order size of 2400 litres:

1. Calculate the daily demand.
2. Calculate the reorder quantity using the fixed order size and the lead time.
3. Calculate the safety stock using the formula.