DSS App. Project

DSS application

Decision tree

Supervisor: Dr. Mohammed Saleh

Real Problem

A small electronics company. In 6 months, a proposal is due for an electronic timing system for downhill skiing events in the 2018 Winter Olympic Games. For several years, this company has been developing a new form of “finish

beam” that records the time at which a ski racer crosses the finish line. A finish beam is a critical component in any ski timing system. They must be accurate to the millisecond and immune to poor weather. They must also be able to distinguish between a skier and a puff of snow crossing the beam, and they must maintain a wireless data link with

the starting gate in conditions which make radio transmission difficult (e.g. high mountains). When completed, theirs will be superior to anything currently on the market. But their progress in research and development has been slower than expected, and they are unsure about whether your staff can perfect the technology and produce the components in time to submit a proposal. they must make a decision about whether to press ahead with an accelerated schedule of research and development, taking into account your uncertainty about future events. Consider these facts:

•  The Olympic contract pays $100,000 to the winner.

•  If your R&D effort succeeds in developing the new beam (which will happen with probability p1), there is a good chance (probability p2) that your company will win the contract.

•   If you decide to accelerate the R&D schedule for the purposes of developing the new beam,       you will need to invest $20,000 in extra funds. With probability 1 − p1, this effort will fail to develop the
  new beam in time.

• new beam in time.

•   If you fail to develop the new beam, there is a small chance (probability p3) that they will still be able to win the same contract with their older beam of timing system that has already been developed. This involves no extra cost for research and development.their older beam model of timing system that has already been developed. This involves no extra cost for research and development.

at an additional production cost, above and beyond R&D costs.

This additional cost would be $5000 for the new beam of timing

system, and $4000 for the old beam model.

• Finally, if they win the contract, the finished product—whether the

• new or the old beam model—will cost an additional $2500 to produce,

• above and beyond the cost of building a prototype.

•          Making a proposal requires developing a prototype timing system

Solution:

Step 1

• at node 10 , they will invest $20000 , proposal additional cost $5000 for the new beam , and win $100,000 , and the cost to produce $2500 . -20,000-5000+100000-2500=$72,500
• at node 11 , they will invest $20000 , and proposal additional cost $5000 for new .         -20,000-5000=-25,000$
• at node 12 , they will invest $20,000. -20,000$
• at node 13 , they will invest $20,000 , proposal additional cost $4000 for the old beam , and win $100,000 , and the cost to produce $2500.  -20,000-4000+100000-2500=$73,500
• at node 14 , they will invest $20,000, proposal additional cost $4000 for the old.             -20,000-4000= -24,000$
• at node 15 , they will invest $20,000 , proposal additional cost $4000 for the old beam , and win $100,000 , and the cost to produce $2500.  -20,000-4000+100000-2500=$73,500
• at node 16 , they will invest $20,000, proposal additional cost $4000 for the old beam .    -20000-4000= -24,000$
• at node 17 , they will invest $20,000
• at node 18 , proposal additional cost $4000 for the old beam  , win $100,000 , and the cost $2500 to produce . -4000+100,000-2500 = $93,500
• at node 19 ,  proposal additional cost $4000 for the old beam . -4000$
• at node 20 , they will do nothing . 0

terminal node         total profit

          10                     72,500$

          11                     -25,000$

          12                     -20,000$

          13                     73,000$

          14                    -24,000$

          15                     73,500$

          16                    -24,000$

          17                     -20,000$

          18                     93,500$

          19                   -4000$

          20                        0

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

assume that p1=0.1 , p2=0.8 ,  p3=0.2

• For chance node 6 the EMV is = 72500p2+(1-p2)*-25000 = (72500*0.8)+(0.2*-25000) = 53000
• For chance node 7 the EMV is = 73000p3+(1-p3)*-24000 = (73000*0.2)+(-24000*0.8) = -4600
• and For node 12 , it's equal to -20000

the best decision at decision node 4 is to propose a new beam. with profit 53000$

• For chance node 8 the EMV is = 73500p3+(1-p3)*-24000 = (73500*0.2)+(-24000*0.8) = -4500
• and For node 17 , it's equal to -20000 

the best decision at decision node 5 is to not make a proposal . with loss -4500

• For chance node 2 the EMV is = .(node 4)p1 + (node 5)*(1-p1) = (53000*0.1)+(-4500*0.9) = 1250 

at node 9 

• For chance node 9 the EMV is = (93500*p3)+(-4000)(1-p3) = (93500*0.2)+(-4000*0.8) = 15500
• at node 20 , they will do nothing with 0$

the best decision at decision node 3 is to make a proposal for an old beam . with profit 15500

at the end , we support the company to not proceed with R&D and make a proposal for an old beam.

DSS Video