RESOT
are
are
are
are
in
This will be the “don’t hire” side, easy
Regret by columns(states of
nature) not rows
X
Z-score of -0.81 = 0.2090
This means there is about a 20.90% chance that
the project will be completed in 170 days or less.
Expected Value of Perfect Information (EVPI)
= (expected payoff under certainty EPC) – (the
expected payoff under risk EP)
Calculate the Expected Payoff under Certainty (EPC):
• Severe: Best route = Highway (25 minutes)
• Mild: Best route = Back roads (20 minutes)
• No Traffic: Best route = Bank Street (10 minutes)
EPC = (0.4×10) + (0.4×20) + (0.2×25) = 17 minutes
EVPI = EPC - EP
99% corresponds to a Z-score of 2.33
∴ 2.33 = X - 127
8.6022 , X = 197.04
Project should begin about 197 days earlier in order to be
completed on time with a 99% probability.
1
Decision2
node
Activity D is critical thus it is the one that should be crashed for one period
ES = Highest EF of Immediate Predecessors
EF = ES + t
LS = LF - t
LS = Lowest LS of Immediate Successor
Project Finish Time = Highest EF of last node OR the addition of t of 0 slack Activities
Slack (how long A can be delayed w/o extended completion time = LS - ES OR LF - EF
Activities with 0 Slack = critical Activities
Critical Path = made up of activities with 0 slack
States of nature node
LP 3 SENSITIVITY
MIXED
BIP
TRANSPORTATION
M
IF PROJECT 3 IS SELECTED, PROJECT 5 CANNOT BE SELECTED
X3 + X5 ≤ 1 (MUTUALLY EXCLUSIVE)
EXACTLY ONE OF PROJECTS 2 AND 3 MUST BE SELECTED
X2 + X3 = 1 (MULTIPLE CHOICE)
IF PROJECT 4 IS SELECTED, THEN PROJECT 2 MUST ALSO BE SELECTED
X4 ≤ X2 OR X2 ≥ X4 (CONDITIONAL/CONTINGENT)
IF PROJECT 1 IS SELECTED, PROJECT 5 MUST ALSO BE, AND VICE VERSA
X1 = X5 OR X1 - X5 = 0 (CO-REQUISITE)
NO MORE THAN 3 PROJECTS IN TOTAL MAY BE SELECTED
X1 + X2 + X3 +X4 + X5 ≤ 3
AT LEAST 2 OF THE FIRST PROJECTS MUST BE SELECTED
X1 + X2 + X3 ≥ 2
PROJECT 4 MUST BE SELECTED
X4 = 1
SELECT PROJECT 3 OR 5, OR BOTH
X3 + X5 ≥ 1
IF PROJECT 4 IS NOT SELECTED, THEN PROJECT 2 MUST ALSO NOT BE SELECTED.
X2 ≤ X4
IF SUPPLY WAS MORE THAN
DEMAND THEN IT’D BE
PROJECTS 3 AND 4 MUST BE SELECTED TOGETHER
X3 = X4
≤ XXX Supply and
=XXX DEMAND
PROJECT 3 OR 4 MUST BE SELECTED BUT NOT BOTH
X3 + X4 = 1
i
C
IF PROJECT 1 IS SELECTED, THEN PROJECT 2 AND 3 MUST ALSO BE SELECTED
X1 ≤ X2
X1 ≤ X3
ADD THEM TOGETHER, YOU GET — 2X1 ≤ X2 + X3
IF PROJECT 1 IS SELECTED, THEN PROJECT 2 OR 3, OR BOTH MUST ALSO BE SELECTED
X1 ≤ X2 + X3
PROJECT 1 CANNOT BE SELECTED IF BOTH PROJECTS 2 AND 3 ARE SELECTED
X1 + X2 + X3 ≤ 2
IF PROJECTS 2 AND 3 ARE SELECTED, THEN PROJECT 1 MUST BE SELECTED
X2 + X3 ≤ X1 + 1