Seqlll'lItia( Decision Jt.faking

The dty of Metropolis is planningto constmct a street that will run through the city perpcndicuiarto the maineast-west street. The city planners have to make a choice between a moderl\vid;;: (4-lane) street that would cost P2M or a lesser-qualitynarrower stre.etthat would cost I)1M. We.shalldenote these two alternatives as WI and Nt. After 4 years. depending on whether the traffic

on the street turns out ot be light or heavy (LI or Ht), the city win have the option or wideningthe sircet. The probability ofthe~e traftlc conditions are estimated by city planners andec:.onomislsas P(Lt) =- 0.25andP(HI) = 075. JfWI is selected, maintenance .:xpcnscsduringthe tlrst 4 years wilibe P5,OOO or 1>75,000dependingon whether the traffic is light or heavy. ifNI issclct:ted,thesecost~are expectedtu be P30,OOOandPI50,000respectiveiy.Suppose ';treetW I is built. Then at the end of 4 years. no further work is required. Ifheavy traffic IScxp~,.il~nced;either a minor or majl,)rrepair must be made at costs of P 150,000 and 1'200,001.1respectively. If street"" I is built, then at the end of 4 years, if traffic hasbeenHght.either a

majy..)for rrtifor repair must bemade at costs ofP50.000 andPIOO.DOOrespectively. !ftral1k hasbeenheavy.a major repair mustbe madea1a c~stofP900,000. Trafficduringthe next (>ytarswillheclassifiedas lightor heavy(L2or H2). Theprobabilityofthese two events.condiiional nnthe tral1k condition in years 1-4 are given as follows:

P(L2/1, I) = 0.75 P(L2/H 1) = 0.10P(H2/LI) '== 0.25 f>(H2/HJ)=0.90

Mainten<1nL:Ccosts over years 5-10 will dep~nd on which street was built in year I. whai tvpe of"n~p<!irwa:; mad;~a! the end uryear 4, and tl.~ amount oftrat1lc during years 5-J()

-¥__"_'4_-

StreetYear I

WI

~-

NI

(a) Construct a decisiontree for this problem.

(b) Determine the nptimai sequential strategy for the city of Metropolis.

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Repair Traffic M aBJ1tcnann.'Year 5-10 \'enr s- W

None L2 200.000H2 2S0.000

Minor L2 ! <;()(lOIi

H2 !f).oon .

Major L2 12:"-oonH2 100.000

Minor 1.2 200.000 .H2 250,000

Major L2 17:\000H2 I50.000