1. Seqlll'lItia( Decision Jt.faking
The dty of Metropolis is planningto constmct a street that will run through the city perpcndicuiar
to the main east-west street. The city planners have to make a choice between a moderlvid;;: (4-
lane) street that would cost P2M or a lesser-qualitynarrower stre.etthat would cost I)1M. We.
shall denote 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 widening
the sircet. The probability ofthe~e traftlc conditions are estimated by city planners and
ec:.onomisls s P(Lt) =- 0.25andP(HI) = 075. JfWI is selected, maintenance .:xpcnscs during
a
the tlrst 4 years wili be P5,OOO or 1>75,000
depending on whether the traffic is light or heavy. if
NI is sclct:ted, hesecost~are expectedtu be P30,OOO PI 50,000respectiveiy.Suppose
t and ';treet
W I is built. Then at the end of 4 years. no further work is required. Ifheavy traffic IS
cxp~,.il~nced;either a minor or majl,)rrepair must be made at costs of P 150,000 and 1'200,001.1
respectively. If street"" I is built, then at the end of 4 years, if traffic hasbeenHght.either a
majy..)f rrtifor repair must bemade at costs ofP50.000 andPIOO.DOO
or respectively. !ftral1k has
beenheavy.a major repair mustbe madea1a c~stofP900,000. Trafficduringthe next (> ytars
willheclassified lightor heavy(L2 or H2). Theprobability
as ofthese two events. condiiional nn
the tral1k condition in years 1-4 are given as follows:
P(L2/1, I) = 0.75 P(L2/H 1) = 0.10
P(H2/LI) '== 0.25 f>(H2/HJ)= 0.90
Mainten<1nL:C costs over years 5-10 will dep~nd on which street was built in year I. whai tvpe of"
n~p<!ir a:; mad;~a! the end uryear 4, and tl.~ amount oftrat1lc during years 5 -J()
w
._._---- --
Street Repair Traffic M aBJ1t nann.'
c
-¥__"_'4_- Year I Year 5-10 'enr s- W
WI None L2 200.000
H2 2S0.000
Minor L2 ! <;()(lOIi
H2 !f).oon .
Major L2 12:"- on
o
~- H2 100.000
NI Minor 1.2 200.000 .
H2 250,000
Major L2 17:000
H2 I 50.000
(a) Construct a decision tree for this problem.
(b) Determine the nptimai sequential strategy for the city of Metropolis.