Planning and Management Techniques
Inventory Control Theory – Selected exercises
1. The (uniform) demand of a given product is 30 units per month. The fixed cost of initiating the
production is 15 m.u. (monetary units). The cost of production of one unit is 1 m.u. and the holding cost
of the stock is 0.3 m.u. per unit per month.
a) Assuming that stockout is not allowed, calculate when the production should take place and the
amount that should be produced.
b) Assuming that the cost of stockout is 3 m.u. per month, calculate when the production should take
place and the amount that should be produced.
5. A company produces an item at a rate of 2000 units per week. The holding cost of the stock is 2 m.u.
(monetary units) per unit per week. The fixed cost of placing an order is 120 m.u. The weekly demand
(considered uniform) is 1500 units. The company will not allow stockout to occur.
The company is considering two different policies for stock management:
Ai – produce items to a maximal level of 1500 units;
Aii – produce items to a maximal level of 3600 units.
a) Determine which of the two policies is the most favorable.
b) Determine the optimal policy.
6. A company needs 15000 units of a certain product per year. The supplier has the following price
policy, according to the order quantity:
3300 m.u. (monetary units) per unit
3200 m.u. per unit
3000 m.u. per unit
if Q<2500
if 2500Q<5000
if Q5000
The fixed cost of ordering is 20000 m.u. The holding cost of the stock is 20% of the unit cost for ordering
quantities between 2500 and 5000 units
What is the optimal ordering policy that the company should follow?
7. Assume that in the model where stockout is allowed, it has been established that the quantity level
after the (instant) replenishment should be 80% of the order quantity. Obtain the optimal value for Q.
8. The weekly demand of a certain item is according to the following table:
Demand
(unit/week)
6
8
10
12
14
Probability
0.15
0.20
0.30
0.20
0.15
a) If the reorder lead time is 1 week, calculate the safety stock, the probability of stockout per cycle and
the average number of stockout units per cycle for order levels of 10, 12 and 14.
b) Assuming independence of the demand in 2 consecutive weeks and that the reorder lead time is 2
weeks, calculate the safety stock, the probability of stockout per cycle and the average number of
stockout units per cycle for order levels of 20, 24 and 28.
12. A company wishes to adopt the policy of fixed-order quantity and reorder level model to manage
the stock of a certain item, for which the monthly demand is random following a normal distribution
with an average of 2500 units and a standard deviation of 930 units. The reorder lead time is random,
with an average of 15 days and a standard deviation of 3 days.
a) What is the stockout probability if the company establishes a safety stock of 500 units? Calculate the
reorder level and the average value of stockout units per cycle.
b) Calculate the safety stock for a probability of stockout of 0.02. What are the corresponding reorder
level and the average value of stockout units per cycle?
c) What is the order quantity in each of the cases a) and b), for a service level of 95%? What are the
corresponding times between successive orders?