of 27
7/25/2019 Lecture 9- Decision Making(1)
1/27
Decision Making
Dr Anisur Rahman
7/25/2019 Lecture 9- Decision Making(1)
2/27
Decision Making
Decision makingis the cognitive process leadingto the selection of a course of action amongvariations.
Every decision making process produces a finalchoice.
Decision making is a reasoning process whichcan be rational or irrational, can be based on
explicit assumptions.
7/25/2019 Lecture 9- Decision Making(1)
3/27
Decision Making Tools
Allocation or Assignment umanresource planning!
E"uipment planning!
#roductivity comparison!
$nvestment!
Repair replacement %trategy
7/25/2019 Lecture 9- Decision Making(1)
4/27
uman Resources #lanning
Purpose: &o maintain an ade"uate and uniform supplyofsuitable experienced labour.
&o reduce overmanningduring downturns indemand
&o avoid sharp fluctuationin each trade.
Factors Influencing Demand & Supply of Labour
'ages ( Rewards )$ncentive
%kills
*ther factors such as +eographical location, working conditions,%ocial
7/25/2019 Lecture 9- Decision Making(1)
5/27
Allocation/Assignment Method
Assumptions:
1. No. of People (rows) = No. Tass (columns)
!. The num"ers within the matri# are the costs
associated with each particular tas.
$i# alternati%es are a%aila"le &' = &(!)(1) = .
Say you have three rushed tasks (T1), (T2) &(T3) and you have ADAMS, BROWN andCOOPER are available to perform tasks atdierent speed/ost)!
T1 T T!
"D"MS -- - /
#$%' 0 -1 --
(%%P)$ 2 -3 4
7/25/2019 Lecture 9- Decision Making(1)
6/27
T1T1 T2T2 T3T3ADAMSADAMS #11 #1$ #%
BROWNBROWN # #1' #11
COOPERCOOPER # #12 #
T1T1 T2T2 T3T3
ADAMSADAMS #* # #'
BROWNBROWN #' #2 #3
COOPERCOOPER #2 #* #'
%tep -5 Row operation select the lowest cost element in each row andsubtract this element from all elements in that row to develop a new matrix
%tep 35 6olumn operation select the lowest cost element in each row inthe new matrix and subtract this element from all elements in that row todevelop a new matrix
T1T1 T2T2 T3T3
ADAMSADAMS #* #% #'
BROWNBROWN #' #' #3
COOPERCOOPER #2 #3 #'
6heck each row andcolumn has at leastone 718! if not go step 3
7/25/2019 Lecture 9- Decision Making(1)
7/27
%tep 95 %trike off all the columns and rows that contain at least one :ero
with minimum number of hori:ontal and vertical lines T1T1 T2T2 T3T3
ADAMSADAMS #* #% #'
BROWNBROWN #' #' #3
COOPERCOOPER #2 #3 #'
%tep 5 6heck5 ; of lines < ; of =obs, if not means optimisation has not yetarrived. $n that case select the minimum uncovered element and subtractthis min element from all the uncovered elements to get a new matrixAnd strike off all the rows and columns again with minimum numbers ofhori:ontal and vertical lines
T1T1 T2T2 T3T3ADAMSADAMS #3 #$ #'
BROWNBROWN #' #' #3
COOPERCOOPER #' #1 #'
%tep 5 6heck ;>ines < ;=obs, if yes optimal solution arrived
7/25/2019 Lecture 9- Decision Making(1)
8/27
T1T1
T2T2
T3T3
ADAMSADAMS #3 #$ #'
BROWNBROWN #' #' #3
COOPERCOOPER #' #1 #'
%tep ?5 %elect the row@column with minumum ; of :ero, assign the row #erson tothe column obs corresponding to the :ero and strike off that column and row
%tep ?5 Do the same things for remaining rows and columns and assign the
corresponding #ersons to obs
T1T1 T2T2 T3T3
ADAMSADAMS
BROWNBROWN #' #'
COOPERCOOPER #' #1
Assign ob&9 to Adam
Assign ob&- to 6ooper
T1T1 T2T2 T3T3
ADAMSADAMS
BROWNBROWN #'
COOPERCOOPER
Assign ob&3 to Brown
&otal cost < /C-1C2 < 3?
7/25/2019 Lecture 9- Decision Making(1)
9/27
&he assignment is made as follows5-. %elect the row or column with fewest number of
:eroes in it
3. %elect an element in that row@column that is :ero
9. Assign the person in that row to that =ob in thecolumn
. Delete assigned row and column
?. Repeat the preceding procedure.
7/25/2019 Lecture 9- Decision Making(1)
10/27
ou can ha%e an optimal solution "* Maximising efficiency
Example:
The onl* difference is that *ou need to con%ert the matri# firstinto a minimising opportunit* costta"le and then proceed with
the pre%ious four steps as "efore.
&- &3 &9 &
ADA% 31 /1 ?1 ??
BR*' /1 91 01 4?
6**#ER 01 -11 21 01
DAF$% /? 01 4? 41
Efficiency
&- &3 &9 &
ADA% 01 1 ?1 ?BR*' 1 41 31 3?
6**#ER 31 1 -1 31
DAF$% 9? 31 3? 91
*pportunity 6ost
7/25/2019 Lecture 9- Decision Making(1)
11/27
T1 T! T& T+
A,AM$ +- - 1- 5
0N !- 2- - 2
300P4 !- - 1- !-
,A56$15 - 2 1-
T1 T! T& T+
A,AM$ !2 - 1- -0N 2 2- - -
300P4 2 - 1- 12
,A56$ 0 - 2 2
+ $traight lines co%ering all 7eros in the matri# 0ptimal $olution:
3ooper will definitel* perform Tas T! (1--8)
,a%is will perform Tas T1 (28)
rown Tas & (9-8) finall* Adams will perform Tas + (228)
7/25/2019 Lecture 9- Decision Making(1)
12/27
atrix Reduction Guestion
our compan* has one surplus truc in each of the towns A; ; 3;
,; and 4 and one deficit truc in each of the construction sites 1; !;
&; +; 2 and . The distance "etween the towns and the construction
sites in ilometres is shown in the matri# "elow (see Ta"le 1).
Assign the trucs from towns to construction sites to minimise the
total distance co%ered.
Site 1 Site Site ! Site * Site + Site ,
" -3 -1 -? 33 -0 0
# -1 -0 3? -? -/ -3
( -- -1 9 0 ? 2
D / - -1 -9 -9 -3
) 0 -3 -- 4 -9 -1
7/25/2019 Lecture 9- Decision Making(1)
13/27
4
7/25/2019 Lecture 9- Decision Making(1)
14/27
*wnership 6ost*wnership 6ost
'($')
1(31)
2(2')
3(11)
1(2) #12
2 (1) #22 #13
3 (1') #3' #21 #1'
$ ($) #3% #2 #1% #
Age at #urchase'
($')1
(31)2
(2')3
(11)
1(2) 3
2 (1) $
3 (1') 13 1' %
$ ($) 22 1 1*
Age at #urchase
aintenanceaintenance
6ost6ost
JearlyJearly
&otal 6ost&otal 6ost
'($')
1(31)
2(2')
3(11)
1(2) 1*
2 (1) 1$!* 1
3 (1') 1$!31$!3 1*!* 1%
$ ($) 1$!* 1*!3 1*!* 1%
Age at #urchase
7/25/2019 Lecture 9- Decision Making(1)
15/27
3omparing Producti%it*
Two e
7/25/2019 Lecture 9- Decision Making(1)
16/27
Equipment A
6t re
7/25/2019 Lecture 9- Decision Making(1)
17/27
Equipment #
6t re2;---
Profit = 2-;---
ou need to in%est !+-;--- to get 2-;--- per *ear for 1+.2 *ears
P = 2----#1+.2/!+---- = &.-!
Therefore; # is t$e best proposition.
7/25/2019 Lecture 9- Decision Making(1)
18/27
If you could some-o. determine precisely .-at .ould -appen as a result of
c-oosing eac- option in a decision/ making business decisions .ould be easy0 oucould simply calculate t-e 2alue of eac- competing option and select t-e one .it-t-e -ig-est 2alue0
In t-e real .orld/ decisions are not 3uite t-is simple0 4o.e2er/ t-e process ofdecision5making stillre3uires c-oosing t-e most 2aluable option55most 2aluablebeing/ in t-is case/ t-e option t-at -as t-e -ig-estExpected Monetary Value6)M78/a measure of probabilistic 2alue0
Suppose you are gi2en t-e opportunity to play a simple game0 " friend flips a coin0If it comes up -eads/ you .in 910 If it comes up tails/ you .in not-ing0 -at is t-e2alue of t-is game to you; Stated anot-er .ay/ -o. muc- .ould you pay to playt-is game;
)ac- time you play t-e game you -a2e a +< c-ance of .inning 91 and a +