#1 Work problem 1 pg 79. Note: use h= .15/365 and D = 365*d
#2 Work problem 2 pg 79-80. Note: use h = 0.25*50/52. Also note that the formula in the book is wrong. Should be Average Inventory = Q/2 + Z* *sqrt(L)
Question 1
EOQ = {2DS/H}1/2
D = 2000*365 = 730,000
S =50
H= (0.15/365)
EOQ = {(730000*2*50)/ 0.000411 = $421444.62
The number of times that the ATM need to be refilled will be given as: annual demand/ EOQ
= {(2000*365) /421444.62) = 1.73 times.
The average amount of cash in the ATM is given as:
EOQ/ 2 = 421444.62/2 = $210722
Question 1b
Total cost under old policy
Annual holding cost= $421466 /2 x (.15/365) = $86.60
Annual filling up cost =730000/421466 x 50 =86.60
Total annual cost = $173.2
Total cost under new Policy
Annual holding cost =$50000 /2 x (.15/365) =$10.27
Annual filling up cost = 730000/50000 x 50 = $730
Total cost = $740.27
Percentage increase
{740.27-173.2)/173.2} = 327.41%
Question 1c.
With the change towards the use of a single ATM location:
We have annual demand = 2*2000*365 = 1,460,000
Using the same EOQ model:
Amount that will minimize costs will be given as: {(2*1460, 000*50)/ 0.000411} ^0.5 = $596013
Number of times ATM needs to be replenished will be given as
= annual demand / EOQ
= 2920000/596042.51
= 2.44 times.
Average amount of cash that needs to kept = 596013/2 = $298007.
Question 1d
Old location total cost = 2{210733*.15/365+ 2*50) = 373.2
Total cost at the new location is = 298007(0.15/365) + 3*50 = 272.5
Comment: there is a decrease in cost because of shifting to one ATM in a new location.
Question 2
Using h as 0.2403
Weekly demand = 400
Annual demand is thus given as= 20800
Q* = √ (2DS/H) = {(20800*2*1000)/ 0.2403}^ 0.5 = 13155
R = mean *L + Zo* s.d * L^0.5
= (400*4) + (2.2368*150*2) = 2271
Average inventory = 13155/2 = 6577.5
When there is a shift towards the use of regional warehouse, we then have:
u=mean =100, lead time = 4 weeks
Ordering cost = 1000; standard deviation. = 75
Q = {(100*52*2*1000)/0.2403}^0.5 = 6578
R = µ*L + Z* s.d * L^1/2
= (100*4) + (2.24*75*2) =736
Total average inventory = 6578*50%= 3289
There is a decrease in the average inventory.
l3o0hd_s
Workproblem.docx
0
