Problem 12.45 Question Help Mr. Beautiful, an organization that sells weight tra
ID: 381178 • Letter: P
Question
Problem 12.45 Question Help 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 $15 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 $10 per set. Over the past several years, Mr. Beautiful has observed the following demand during the lead time for BB-1: Time Probability 0.1 0.2 0.2 0.2 0.2 0.1 Demand During Lead 10 30 50 70 90 110 The reorder point for BB-1 is 50 sets. What level of safety stock should be maintained for BB-1? The optimal quantity of safety stock which minimizes expected total cost issets (enter your response as a whole number)Explanation / Answer
Carrying cost = $15 per set per year
Number of orders per year = 7
Stockout cost = $10 per set
Reorder point = 50 sets
Annual stockout cost = Sum of units short x Probability x Stockout cost per unit x Number of orders per year
The purpose is to find out the level of safety stock thst minimizes the sum of additional inventory carrying cost and stockout cost.
The total cost is minimum when safety stock is 40 sets.
The level of SS that should be maintained for BB-1 which minimizes expected total cost = 40 sets
Corresponding Reorder point = 50 + 40 = 90 sets
Safety stock Additional carrying cost Annual stockout cost Total cost 60 60 x 15 = 900 0 900 50 50 x 15 = 750 10 x 0.1 x 10 x 7 = 70 750 + 70 = 820 40 40 x 15 = 600 20 x 0.1 x 10 x 7 = 140 600 + 140 = 740 30 30 x 15 = 450 30 x 0.1 x 10 x 7 + 10 x 0.2 x 10 x 7 = 350 800 20 20 x 15 = 300 40 x 0.1 x 10 x 7 + 20 x 0.2 x 10 x 7 = 560 860 10 20 x 10 = 200 50 x 0.1 x 10 x 7 + 30 x 0.2 x 10 x 7 + 10 x 0.2 x 10 x 7 = 910 1110 0 0 60 x 0.1 x 10 x 7 + 40 x 0.2 x 10 x 7 + 20 x 0.2 x 10 x 7 = 1260 1260