Exercise n

EXERCISE N.1
A product is stored in a warehouse. Its daily demand is normally distributed with average value equal to 60 units and standard deviation equal to 7 units.
The order lead time is constant and equal to 6 days.
The ordering cost is equal to 10$ per order and the yearly unit cost of holding inventory is equal to 0.50 $/unit.
The warehouse works 365 days 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 95% not to have stockouts during the order lead time.
Table for k calculation:

K	Probability of no stockout	Probability of stockout		k	Probability of no stockout	Probability of stockout
0.00	0.5000	50.00%		2.00	0.9772	2.28%
0.25	0.5987	40.13%		2.25	0.9878	1.22%
0.50	0.6915	30.85%		2.50	0.9938	0.62%
0.75	0.7734	22.66%		2.75	0.9970	0.30%
1.00	0.8413	15.87%		3.00	0.9987	0.13%
1.25	0.8944	10.56%		3.25	0.9994	0.06%
1.50	0.9332	6.68%		3.50	0.9998	0.02%
1.75	0.9599	4.01%		3.75	0.9999	0.01%

Solution:

Given data:
D(daily) = Daily demand = 60 units
_D = 7 units
Order lead time = L = 6 days
Setup or Order cost = S= 10$/order
Operational days= #of period = 365 days
Annual holding cost = H * # of periods = 0.5 $/unit
Probability of not having stock-out = P=95%
EOQ inventory management model.

By applying EOQ model, we are able to determine the optimal quantity of items to be included in each order. Because, EOQ model follows variable interval for order placing, it requires rigorous (continuous) control and fixed quantity for each order.

= = 936 units/order

Next step is to calculate the re-order point. In order to compute the re-order point we have to apply a formulation that considers the probabilistic demand during lead time and deterministic (constant) lead time.

Re-order point = d * L + Safety stock (SS) = 60 [units/day] * 6 [days] + 28 units = 388 units

= 1.625 *7 [units]* = 28 units

Value of k for 95 % is not given in the table. So that, we have to get an arithmetic average of k(93.32%) and k(95.99%)

EXERCISE N.2
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.

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%
EOQ inventory management model.

By applying EOQ model, we are able to determine the optimal quantity of items to be included in each order. Because, EOQ model follows variable interval for order placing, it requires rigorous (continuous) control and fixed quantity for each order

= = 750 units/order

Next step is to calculate the re-order point. In order to compute the re-order point we have to apply a formulation that considers the probabilistic demand during lead time and probabilistic lead time.

Re-order point = d * L + Safety stock (SS) = 75 [units/week] * 2 [week] + 159 units = 309 units

=

The value of k for 97.7 % is given in the table and it is equal to 2.