Exercise n

EXERCISE N.3
A product is stored in a warehouse. Its weekly demand is normally distributed with average value equal to 75 units and standard deviation equal to 17.8 units.
The order lead time is also normally distributed with average value equal to 2 weeks and standard deviation equal to 1 week.
The ordering cost is equal to 30€ per order and the yearly unit cost of holding inventory is equal to 0.40 €/unit.
The warehouse works 50 weeks per year.
The EOQ model is applied in order to manage the inventory level of the product at issue.
Calculate the optimal order quantity and the re‐order point so that there is a probability of 97.7% not to have stockouts during the order lead time.
Let us consider the same product as in Exercise 2 and apply now a fixed‐time period model in order to manage its inventory level.
The fixed time between inventory reviews is equal to 8 weeks.
Calculate the objective inventory level in order to have a service level equal to 97.7%.

Solution:

Given data:
D(weekly) = Weekly demand = 75 units
_D = 17.8 units
Order lead time = L = 2 weeks
_L = 1 week
Setup or Order cost = S= 30 €/order
Operational weeks= # of period = 50 weeks
Annual holding cost = H * # of periods = 0.4 €/unit
Probability of not having stock-out = P= 97.7%
Interval time of inventory reviews = T = 8 weeks
Fixed-time inventory management model.

For Fixed-time inventory management model, we have to define Objective level of inventory.

Objective level (OL) = d*(L+T) + SS

To define Safety stock the formula will change slightly, we must introduce the time interval between inventory reviews as following:

=

OL = d*(L+T)+SS = 75*(2+8) +188 = 938 units