Mr. Beautiful an organization that sells weight training sets has an ordering co

Question

Mr. Beautiful an organization that sells weight training sets has an ordering cost of $35 for the BB-1 set ( BB-1 stands for Body Beautiful Number 1) The carrying cost for BB-1 is $5 per set per year. To meet demand, Mr. Beautiful orders large quantities of BB-1 5 times a year. The stockout cost for BB-1 is estimated to be $45 per set. Over the past several years, Mr. Beautiful has observed the following demand during the lead time for BB-1: Demand during lead time/Probability 40 0.1 60 0.2 80 0.2 100 0.2 120 0.2 140 0.1 The reorder point for BB-1 is 80 sets. What level of safety stock should be maintained for BB-1? The optimal qty of safety stock which minimizes expected total cost is ____ sets.

Explanation / Answer

Ordering Cost per Order = $ 35

Carrying cost per BB-1 for year = $ 5 Per year

No of orders = 5

Stockout cost is $ 45 per set

Redorder point = 80 Sets

Possible safety stock = Permissible demand- Re order Point

So the safety stock levels are 0, 20, 40, 60 Units for Mr. Beautiful at permissible demand of 80, 100,120, 140 Units respectively.

The Optimal Qty of sacfety stock which mimises Expected total cost is 60 units as the total costis mimimum at that level.

Relevant costs are calculated below

Safety stock
Level
(a) Demand realisations
Resulting in
stock out (b) Stock Out Units
c= (b-Reoreder Point of 80 - a) Probability of Stock out (d) Relevant stock out costs
e= (c* $ 45) No of orders
in a year (f) Expected Stock out costs
(d*e*f) Relevant carrying costs
= (a* 5) Total Relevant Costs 0 (80-80) 100 20 0.2 900 5 900 120 40 0.2 1800 5 1800 140 60 0.1 2700 5 1350 Total 5400 4050 0 4050 20 (100-80) 120 20 0.2 900 5 900 140 40 0.1 1800 5 900 Total 2700 1800 50 1850 40 (120-80) 140 20 0.1 900 5 450 Total 900 280 100 380 60 (140-80) Nil Nil Nil Nil 0 150 150 Total

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