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%.
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] |
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