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

Question

Mr. Beautiful, an organization that sells weight training sets, has an ordering cost of $40 for the BB-1 set (BB-1 stands for Body Beautiful Number 1). The canrying cost forBB-1 is $10 per set per year. To meet demand, Mr. Beautiful orders large quantities of BB-1 7 times a year. The stockout cost for BB-1 is estimated to be $40 per set. Over the past several years, Mr. Beautiful has observed the following demand during the lead time for BB-1: The reorder point for BB-1 is 120 sets. What level of safety stock should be maintained for BB-1?

Explanation / Answer

Given Ordering cost per order of the Body Beautiful number 1 = $ 40 per order

Carrying cost for BB-1 is $ 10 per set per year

No of orders placed for a year = 7 times a year

Stock out cost for BB-1 is $ 40 per set

The Reorder point for BB-1 is 120 sets.

Given the Estimated optimal quantity of safety stock which mimises the total cost is 77 Sets

Possible safety stock = Possible demand Less Reorder Point

So possible safety stock is 0 units, 10 Units , 20 Units , 30 Units

Safety stock of 30 units would miminise the total expected stock out and carrying cost (Anlaysis of relevant costsare given in the below table) of Mr.beautiful,

So the level of safety stock to be maintained is 30 Units

So new Reoreder point is = ROL + Safety stock = 120+ 30 = 150 Units

Relevant costs under Different safety stock situations are:

Total Relevant Costs (i= g+h)

Safety stock
Level
(a) Demand realisations
Resulting in
stock out (b) Stock Out Units
c= (b-Reoreder Point of 120 - a) Probability of Stock out (d) Relevant stock out costs
e= (c* $ 40) No of orders
in a year (f) Expexted Stock out costs
g= (d*e*f) Relevant carrying costs
h = (a* 10)

Total Relevant Costs (i= g+h)

0 (120-120) 130 10 0.2 400 7 560 140 20 0.2 800 7 1120 150 30 0.1 1200 7 840 Total 2400 2520 0 2520 10 (130-120) 140 10 0.2 400 7 560 150 20 0.1 800 7 560 Total 1200 1120 100 1220 20 (140-120) 150 10 0.1 400 7 280 Total 400 280 200 480 30 (150-120) Nil Nil Nil Nil 0 300 300

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