Question

A manufacturing company keeps stock of replacement parts for its critical equipment. The lead time for a rare $500 part is 2 months. The maintenance manager keeps close track of the inventory of these parts and places a new order whenever the stock reaches a certain threshold or reorder point. When they order, they place orders of 20 units at a time because the supplier has to make a special production run for it. From past history they estimate that the monthly demand for spares can be modeled as a Poisson distribution with a mean of 3.

a) Calculate the reorder point to achieve a fill rate of 95%.

b) Calculate the resulting average backorder level associated with this ordering policy.

c) Calculate the average monthly inventory cost assuming annual carrying cost of 24%.

Answer 1

Given Information	Data
Cost Price	$                         500
Re-Order Quantity	20
Average Monthly Demands	3
Annual Demand	36
Average Lead Time	2 Months
Carrying Cost [in $]	120
[24% * $500]
Assumption: It is assumed that Maximum and minimum demand / lead time are to be more than or less than average demand/ lead time given.
Level	Demand	Lead Time
Maximum	4 [Assumed]	3 Months [Assumed]
Average	3 [Given]	2 Months [Given]
Minimum	2 [Assumed]	1 Months [Assumed]
Solution to A.
	Units
Re-Order Level	11.40
[ Maximum Demand per day X Maximum lead time]*95%
Solution to B.
Minimum Level	5.40
[Re-Order Level-(Average Demand per day X Average Lead time]
Maximum Level	29.40
[Re-Order Level + Re- Order Quantity-(Minimum Demand per day X Minimum Lead time]
Average Back-Order Level
[Maximum Level+ Minimum Level]/2	17.40
OR
[Minimum Level+1/2*Re-Order Quantity]	15.40
Solution to C.	$
Average Monthly Inventory Cost [in $]	1,200
[Re-Order Quantity*1/2*Carrying cost per unit]