This preview shows page 1. Sign up to view the full content.
Unformatted text preview: . All tasks with zero total float are critical.
. All critical tasks have zero free float.
. All critical tasks have zero total float.
Statements 2-4 are all true. Statement 1 is not true by the following example: C has
zero free float but 1 total float.
START A (5)
F=[5,5] F (11)
F=[24,25] D (8)
F=[13,13] G (1)
F=[14,25] END H (12)
F=[25,25] J. G. Carlsson, U of MN ISyE Lecture 7: PERT & CPM October 3/17, 2013 27 / 38 Crashing Crashing an activity refers to taking special costly measures to reduce the
duration of an activity below its normal value
E.g. “if we pay $50,000, we can reduce the duration of activity D from 8 to 7” Naturally, it is only worth considering crashing activities on the critical path
Crashing may change the critical path by reducing the duration of critical
activities J. G. Carlsson, U of MN ISyE Lecture 7: PERT & CPM October 3/17, 2013 28 / 38 Crashing as an LP
Suppose that each activity i can be crashed by paying pi to reduce the duration
by 1 day (or whatever time unit we like)
If we want to crash by xi days, then we pay pi xi
We have a given deadline that we have to meet: how can we crash in the
cheapest way possible?
pB = 3 C (8)
pC = 8 START D (11)
pD = 8 E (1)
pE = 4 A (5)
pA = 1 0
END F (12)
pF = 6 J. G. Carlsson, U of MN ISyE Lecture 7: PERT & CPM October 3/17, 2013 29 / 38 Crashing as an LP
Say we need to complete by 15 days:
minimize 10xA + 3xB + 8xC + 8xD + 4xE + 6xF
≥ 0 + 5 − xA
≥ yA + 3 − xB yC
yD ≥ yA + 8 − xC
≥ yB + 11 − xD yD
yF ≥ yC + 11 − xD
≥ yC + 1 − xE
≥ yC + 12 − xF yA , yB , yC , yD , yE , yF
xA , xB , xC , xD , xE , xF ≤ 15
≥0 yA , yB , yC , yD , yE , yF ≥0 Here the yi ’s represent completion times and the xi ’s represent how much we crash
J. G. Carlsson, U of MN ISyE Lecture 7: PERT & CPM October 3/17, 2013 30 / 38 Optimal solution At right, a “cost-duration tradeoff curve” J. G. Carlsson, U of MN ISyE Lecture 7: PERT & CPM October 3/17, 2013 31 / 38 PERT Networks
It is natural to try to take some uncertainty into account when designing
A PERT network estimates times based on three input values:
The optimistic time a occurs if execution goes extremely well
The most likely time m is just what it sounds like
The pessimistic time b occurs if execution goes extremely poorly ¯
The average duration time D and the variance ν are defined by
ν J. G. Carlsson, U of MN ISyE a + 4m + b
= Lecture 7: PERT & CPM October 3/17, 2013 32 / 38 PDM
The precedence diagramming method (PDM) is an extension of PERT/CPM in
which mutually dependent activities can be performed partially instead of
In PERT/CPM, we assume that an activity must be completely finished before we
can work on its successors
PDM generalizes this by allowing the following additional relationships:
SSAB (start-to-start) lead: activity B cannot start until activity A has been in progress
for at least SS time...
View Full Document
This document was uploaded on 02/23/2014 for the course MANAGMENT 2201 at University of Michigan.
- Spring '14