Kezo System Problem

Decision Support systems and Applications 
Project

Esraa Mohamed Mohamed - 20130056
Eman Ehab Fathy - 20130085
Samiha Ashraf -  20130132

Supervised by 
Dr.Mohamed Saleh

Kezo systems problem

Kezo Systems has agreed to supply 500,000 PC FAX systems to Tarja Stores in 90 days at a fixed price.

A key component in the FAX systems is (\PAL chip"), one of which is required in each FAX system.

Kezo has bought these chips in the past from an American chip manufacturer AM Chips.

However, Kezo has been approached by a Korean manufacturer, KEC Electronics, which is offering a lower price on the chips. This offer is open for only 10 days, and Kezo must decide whether to buy some or all of the PAL chips from KEC.

-         Any chips that Kezo does not buy from KEC will be bought from AM.

-         AM Chips will sell PAL chips to Kezo for $3.00 per chip in any quantity.

-         KEC will accept orders only in multiples of 250,000 PAL chips, is offering to sell the chips for $2.00 per chip for 250,000 chips, and for $1.50 per chip in quantities of 500,000 or more chips.

However, the situation is complicated by a dumping charge that has been filed by AM Chips against KEC.

If this charge is upheld by the U. S. government, then the KEC chips will be subject to an antidumping tax.

This case will not be resolved until after the point in time when Kezo must make the purchase decision.

If Kezo buys the KEC chips, Kezo would have to pay any antidumping tax that is imposed.

Kezo believes there is a 60% chance the antidumping tax will be imposed. So 40 % chance the antidumping will not be imposed.

If it is imposed, then it is equally likely that the tax will be 50%, 100%, or 200% of the sale price for each PAL chip. So the probability for the three different tax is 0.33

Solution

Below we carry out step 1 of the decision tree solution procedure which (for this example) involves working out the total cost for each of the paths from the initial node to the terminal node.

Step 1

Path to terminal node 5 – kezo will purchase 250 chip from KEC and 250 chip from AM and there is no Antidumping tax.

The cost =(250 chip*2 $)+(250 chip*3 $)=1250 $

Path to terminal node 6 – kezo will purchase 250 chip from KEC and 250 chip from AM and there is an Antidumping tax by 50%

The cost = (250*2)+(250*3)+(50%*500 $)=1500  $

Path to terminal node 7 – kezo will purchase 250 chip from KEC and 250 chip from AM and there is an Antidumping tax by 100%

The cost = (250*2)+(250*3)+(100%*500 $)=1750 $

Path to terminal node 8 – kezo will purchase 250 chip from KEC and 250 chip from AM and there is an Antidumping tax by 100%

The cost = (250*2)+(250*3)+(200%*500 $)=2250 $

and then 

Path to terminal node 11 – kezo will purchase 500 chip from KEC and there is no Antidumping tax.

The cost = (500 chip *1.5 $) = 750 $

Path to terminal node 12 - kezo will purchase 500 chip from KEC and there is an Antidumping tax by 50%

The cost =(500*1.5)+(50% *750) = 1125 $

Path to terminal node 13 - kezo will purchase 500 chip from KEC and there is an Antidumping tax by 100%

The cost =(500*1.5)+(100% *750) = 1500 $

Path to terminal node 14 - kezo will purchase 500 chip from KEC and there is an Antidumping tax by 200%

The cost =(500*1.5)+(200% *750)= 2250 $

and finally the last branch 

Path to terminal node 15 – Kezo will purchase the 500 chip from AM.

The cost =(500 chip *3 $) = 1500 $

Terminal node          Total cost

5	1250 $
6	1500 $
7	1750 $
8	2250 $
11	750 $
12	1125 $
13	1500 $
14	2250 $
15	1500 $

We can now carry out the second step of the decision tree solution procedure where we work from the right-hand side of the diagram back to the left-hand side.

Step 2

Consider chance node 4 with branches to terminal nodes 6,7 and 8 emanating from it. The expected value for this chance node is given by 0.33(1500) + 0.33(1750) + 0.33(2250) = 5500/3 $.

Then chance node 3 with branches to terminal node 5 and 4. The expected value for this chance node is given by 0.4(1250) + 0.6(5500/3) =1600 $.

Consider chance node 10 with branches to terminal nodes 12,13 and 14 emanating from it. The expected value for this chance node is given by 0.33(1125) + 0.33(1500) + 0.33(2250) = 1625 $.

Then chance node 9 with branches to terminal node 11 and 10. The expected value for this chance node is given by 0.4(750) + 0.6(1625) =1275 $.

Hence at the initial decision node we have the three alternatives

(1) purchase 250 chip from KEC EV = 1600 $

(2) purchase all 500 chip from KEC EV = 1275 $

(3) purchase no chips from KEC (purchase it from AM) EV = 1500 $

So hence that the purchase all chips from KEC is the best alternative that give me least cost.

So Kezo will preferred to buy all chips from KEC.

You will find a video illustrate the problem and solve it HERE