In the following a typical Inventory Management Test is considered. Elementay questions regarding EOQ, Reorder Point, Fill Level, Cycle Service Level are considered.

Also a chart showing the Inventory Time curve of a Periodic Review, order Point Policy (R,s,S) is shown.




A paint company follows an inventory  policy Continuous Review (s, Q) to control the level of inventories.

For a particular paint, historical data show a normal distribution of monthly demand, with average 28 pieces / month and a standard deviation of 8 pieces / month.

The lead time to supply the warehouse is approximately 14 weeks.

Each can of paint costs 6 €.

The unmet demand goes in back-order with an estimated  cost of 10 € /can.

Setup  costs A are 15 € / order and the carry costs of replenishment are 30% per year.

A) Determine the optimal lot size and reorder point of the paint.

B) Determine the optimal level of safety stock.

C) What is the reorder point if you want to avoid stock-out in 90% of cases

D) Determine the fill rate reached following the Inventory policy in a) and c).

E) Answer the points A), B), C), D) when orders of paints are lauched each month.

F) Suppose you have the following monthly demand:


Month demand

Month Demand (cans)
January 37
February 33
March 26
April 31
May 12
June 40


If the Inventory level at the beginning of January is equal to 26 cans of paint, determine the number of cans of paint ordered in 6 months, following the policy (R, s, S), where R and S are those of point E and s is the one found in A).