Question

The inventory policy of a retail company is to hold only the highest sales volume items in its distribution center and to ship the remaining lower sales volume items direct from the respective manufacturers to its stores. This policy is intended to reduce transportation costs. Total annual sales of the company are $1 billion. It is known that half of this amount is accounted for by only 15% of the items. In addition, it is assumed that equation (8.1) in the text can be used to model the Pareto cumulative distribution. (a) If the company wants to stock the top selling 35% of the items in the distribution center, what is the expected value of these items in terms of annual sales? (b) On the other hand, if the company wants to stock only those items accounting for the top 75% of annual sales, what proportion of the items corresponds to this sales volume?

Answer 1

a. 75.3% is the expected percentage and this value corresponds to 753 million dollars

b. 34.62% of items corresponds to 75% of this sales volume

Explanation:

a. A =x(1-y)/(y-x)

X = 0.15, y = 0.50

A = 0.15(1-0.50)/(0.50-0.15)

= 0.15(0.5)/0.35

A = 0.2143

we have

x = 0.35

y = 0.35(1+0.2143)/(0.2143+0.35)

y = 0.425005/0.5643

y = 0.7531

y = 75.3%

75.3% is the expected percentage and this value corresponds to 753 million dollars

b. y = 0.75

find x

y = x(1+A)/(A+x)

x = yA/(1+A-y)

x = 0.75(0.2143)/1+0.2143-0.75)

x = 0.160725/0.4643

x = 0.3462

34.62% of items corresponds to 75% of this sales volume