A particular model of Inventory Management where Periodic Review is equal to the Lead Time. In particular conditions about EOQ are discussed and difference performance measurements considered: Cycle Service Level, Fill Rate.



A hardware shop order screws and bolts from a local supplier every second week R. Lead Time, LT of the supplier is 2 weeks. 14 mm Bolts average demand is 150 units/week, and safety stocks are equal to 3 days of supply. Considering a 5 working days per week and 50 weeks/year:

a) What is Q=averaged quantity of Bolts ordered?

b) Indicating with A the setup costs in €/order, r the currying costs in €/€-year and v the bolt cost in €/unit, under what conditions Q=EOQ?

c) what is the maximum level of the Inventory Position during and Inventory Cycle?

d)If an order must be placed whn the inventory level is 130 units, what this the order quantity?

e) Determine the  standard deviation of demand during (LT+R)  if the Cycle Service Level P1= 90%

f) considering the above value, what is the Fill Rate P2 in the case of complete backorder?

g) and in the case of complete back order?

h)what is the reduction of safety stocks if we adopt a (s,Q) continuous review, fixed quantity Inventory Policy with the same P1?


Solution to point a)

Average quantity order each second week is 150 X 2 = 300 units/order

Solution to point b)

From EOQ formula it results:

Considering the known quantities, we obtain:


and then required conditions are:

Solution to point c)

On the average the maximum Inventory Position in a Inventory Cycle is at the beginning of the period, just after the order launch.

On the average at the begin of a Period the Inventory Level is equal to Safety Stock + the Average demand During Lead TIme. Safety stocks covers 3 days of demand, while Lead Time is 2 week. Inventory Position just before the order then , is equal to 2+2/5=2.4 weeks of demand, for a total of 2.4 X 150=360 items.

The average order is 300.

Inventory Position maximum is then 300 +360 =660 units

Solution to point d)

The up to Level S is 660 (see above). If at moment of the order stock level is =130 then the order is 660-130=530. Since next order takes 2 weeks and the average demand is 300 units/week there is an high probability to go in stock out.

Solution to point e)

if P1=90%, then k = 1.663 so:


Solution to point f)

Solution to point g)

 The 2 Fill Rate are the same. This because the value of ESPRC is very low respect to Q.

Solution to point h)

When we change from Periodic to Continuous Review, the standard deviation change from a time period LT+R to only LT.

Since in our case LT=R a. it is possible to say that:


and the the reduction in safety stock in continuous review respect periodic review is: