Question

A mail-order house uses 18,000 boxes a year. Carrying costs are 60 cents per box a year, and ordering cost are $96. the folling price schedule applies.

Number of boxes	Price per box
1,000 to 1,999	$1.25
2,000 to 4,999	1.20
5,000 to 9,999	1.15
10,000 or more	1.10

A. What is the maximum level of inventory the company would have to plan for?

B. what is the average level of inventory the company would have to plan for?

C. Calculate the days of inventory metric for this company (assume a 365 day work year).

Answer 1

A mail order house uses ,D =18000 boxes per year

The carrying cost ,H =$.60 per yr

The odering cost ,S =$96

a.The optimal rdering quantity

q =Square Root 2DS/H

     =Square Root 2*18000 boxes * $96/$.6

     =Sqaure Root 3456000/.6

     =2400 boxes

There fore total cost of ordering with 2400 boxes per order would be

As 2400 boxes falls in the range of 2000 to 4999 boxes the price per box would be $1.2

Total Cost =Carrying Cost+Ordering Cost+Purchasing Cost

                =(q/s)h +(D/Q)S +PD

                =2400/2*.6 +18000/2400*96 +1.2*18000

                = 720+720+21600

                =$23040

Using an oder size of 10000 for a piece of $1.1 per box

      Total Cost =Carrying Cost +Ordering Cost +Purchasing Cost

                      =Q/2*H +D/Q*S +PD

                      = 10000/2*.60 +18000/10000*96+1.10*18000

                      = 3000+172.80+19800

                      =$22972.80

Using an oder size of 5000 for a piece of $1.15 per box.

Total Cost =Carrying Cost +Ordering Cost + Purchasing Cost

                =Q/2*H +D/Q*S +PD

               = 5000/2*.6 + 18000/5000*96 +1.15 * 18000

               =1500 +354.6 +20700

               = $22554.60

Therefore the minimum cost is for ordering 5000 boxes per order.

b.The average level of inventory if the order of boxes is 5000/2 =2500 .hence average level of inventory cost is $1500.

Here to calculate the inventory metric the cost of good sold have to be given which is missing from the problem.