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Weiss’s paint store uses a (q, r) inventory system to control its stock levels. for a particularly popular white latex paint, historical data show that the distribution of monthly demand is approximately normal, with mean 28 and standard deviation 8. replenishment lead time for this paint is about 14 weeks. each can of paint costs the store $6. although excess demands are back-ordered, the store owner estimates that unfilled demands cost about $10 each in bookkeeping and loss-of-goodwill costs. fixed costs of replenishment are $15 per order, and holding costs are based on a 30 percent annual rate of interest.
a. what are the optimal lot sizes and reorder points for this brand of paint?
b. what is the optimal safety stock for this paint?

Sagot :

ogorwyne

The optimal sizes of the brand of paint given a  mean of 28 and standard deviation of 8 is 81. The reorder point of the paint is 124 while the optimal safety stock is 26.

How to solve for the optimal size

mean = 28

sd = 8

Replenishment = 14 weeks

convert to months = 3.5 months

paint = $6

mean = 28 x 3.5

= 98

Find the standard deviation

= 8 x sqr(3.5)

= 14.966 = 15

Mean rate of demand

12 x 28 = 336

cost of holding = 30% x 6 = 1.8

unfilled demand = $10

EOQ = 2x 336 x 15 /1.8

= 5600

[tex]\sqrt{5600} = 75[/tex]

R0 = [tex]\frac{75*1.8}{10*336} = 0.04[/tex]

From the z table, 0.04 = 1.75

15x1.75x98 = 124.35

σLz = 0.242

Q1 = [tex]\sqrt{\frac{2*336}{1.8}(15+10)(0.2426) }[/tex]

= 81

81x1.8/10x336

= 0.043

How to solve for the reorder point

If R1 = 0.043  z value would be 1.75

15 x 1.75 + 98

= 124.3

R0 = R1

Q,R = (81, 124)

the optimal lot sizes  = 81.

reorder points = 124

How to solve for the optimal safety stock

R - mean

124 - 98

= 26

Read more on optimal safety stock https://brainly.com/question/14054595

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