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Assignment problem
transportation problem in general are concerned with
distributing any commodity from any group of supply
centers, called sources, to any group of receiving
centers, called destinations, in such a way as to
minimize the total distribution cost.
Assumptions:
Requirement assumption: each source has a fixed
supply of units, where this entire supply must be
distributed to the destinations. similarly, each destinationhas a fixed demand for units, where this entire demand
must be received from the source.
ASSIGNMENT PROBLEM
Characteristics & assumptions of transportation problem
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Assignment problem
Cost assumption: the cost of distributing units
from any particular source to any particular
destination is directly proportional to that number
of units distributed.therefore,this cost is just theunit cost of distribution times the number of
units distributed.
The feasible solutions property: A
transportation problem will have feasiblesolutions if and only if the sum of its supplies
equals the sum of its demands.
ASSIGNMENT PROBLEM
Characteristics & assumptions of transportation problem
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Assignment problem
The model:
The linear programming model hasconstraints for supply at each source and
demand at each destination. All constraints are equalities in a balancedtransportation model where supply equalsdemand.
Constraints contain inequalities inunbalanced models where supply does notequal demand.
Characteristics & assumptions of transportation problem
ASSIGNMENT PROBLEM
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Assignment problem
Shipping goods
Assigning plants to product
Profit maximization problem Overtime production
Production scheduling
ASSIGNMENT PROBLEM
Application of transportation problem
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Assignment problem
ASSIGNMENT MODEL
ASSIGNMENT PROBLEM
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Assignment problem
Assignment model is generally made on one-to-onebasis & if there are more jobs to do than can be done,one can decide which job to leave undone and whatresource to add.
In assignment model number of source is equal tonumber of destination ,supply at each source is unity(1)& demand at each destination is also unity(1), it isdifferent from transportation problem.
Unit allocated to cell is either 1 or 0 ,it is also differentfrom transportation model
However transportation algorithm is not very useful tosolve this model because of degeneracy.
ASSIGNMENT PROBLEM
Difference between transportation & assignment model
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Assignment problem
Assignment problem is completely degenerate form oftransportation model.
In n*n assignment problem, there will be n assignment
instead of 2n-1 assignment in transportation model.
Special structure of assignment model allows a moreconvenient and simple method of solution than
transportation model.
ASSIGNMENT PROBLEM
Difference between transportation & assignment model
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Assignment problem
Represent the assignment of n facilities ton jobs.Cij is cost of assigning ith facility to
jth job and Xij represents the assignment
of ith facility to jth job. If ith facility can be assigned to jth job,
xij=1,otherwise 0.
The objective is to make assignment thatminimize the total assignment cost ormaximize the total associated gain.
ASSIGNMENT PROBLEM
Structure & formulation of assignment model
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Assignment problem
Xij=0,if ith facility is not assigned to j th job,
Xij=1, if the ith facility is assigned to jth job.
Then the model is given by
Minimize z= CijXij
Subject to constraints Xij=1,i=1,2,3n(one
job is assigned to ith facility)
Xij=1,j=1,2,3,..n(one facilityassign to Jth job.
ASSIGNMENT PROBLEM
Structure & formulation of assignment model
J=1
n
i=1
n
J=1
i=1
n
n
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Assignment problem
& Xij=0 or 1.
ASSIGNMENT PROBLEM
Difference between transportation & assignment model
C11 C12 . C1n
C21 C22 C2n
C31 C32 C3n
Cn1 Cn2 Cnn
1
1
:
1
1 1 1
Jobs
1 2 n
1
2
:
n
facilities
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Assignment problem
Step 1: prepare the assignment table.
Step 2: convert assignment table into balanced problemby add dummy row or column if it is not balancedproblem.
Step 3:convert problem into minimization problem bysubtracting all the elements from the largest element if itis maximization problem.
Obtain reduced cost table:
(a) Subtract the minimum element in each row from all theelements of that row and then
(b) Subtract the minimum element in each column from allthe elements of that column.
ASSIGNMENT PROBLEM
Hungarian method
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Assignment problem
Step 5:Draw minimum number of lines to cover
all the 0s in the table.
Step 6:check the lines drawn equal to the orders
of the matrix or not. if not then, subtract the smallest uncovered elements
from all the uncovered elements and add it to
intersection of line. keep the remaining elements
unchanged & go to step 5 & then 6.
Step 7:get the optimum solution.
ASSIGNMENT PROBLEM
Hungarian method
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Assignment problem
A machine tool company decides to make
four subassemblies through four
contractors. each contractor is to receive
only one sub assembly. the cost of eachsubassembly is determined by the bids
submitted by each contractor and is show
in table in hundreds of rupees.
ASSIGNMENT PROBLEM
EXAMPLE-TRANSPORTATION PROBLEM
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Assignment problemASSIGNMENT PROBLEM
EXAMPLE-TRANSPORTATION PROBLEM
15 13 14 17
11 12 15 13
13 12 10 11
15 17 14 16
Contractors
1 2 3 4
S
u
ba
s
s
e
m
bli
e
s
1
2
3
4
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Assignment problem
Step III: (a) constraints on subassemblies are
X11+x12+x13+x14=1
X21+x22+x23+x24=1
X31+x32+x33+x34=1 X41+x42+x43+x44=1
(b) constraints on contractors are:
X11+x21+x31+x41=1
X12+x22+x32+x42=1
X13+x23+x33+x43=1
X14+x24+x34+x44=1
ASSIGNMENT PROBLEM
EXAMPLE-TRANSPORTATION PROBLEM
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Assignment problem
A school bus has to start from the school located
at A and return after picking up children from
B,C,D and E .the table below shows distances
between various pick-up points on differentroutes.the distance from A to B is 8 KM but from
B to A is 6 KM Because of one way streets and
other restrictions on movement between points.
as no of movement is possible from adestination to itself, these cells are marked with
dash.
ASSIGNMENT PROBLEM
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Assignment problem
A school bus has to start from the school located
at A and return after picking up children from
B,C,D and E .the table below shows distances
between various pick-up points on differentroutes.the distance from A to B is 8 KM but from
B to A is 6 KM Because of one way streets and
other restrictions on movement between points.
as no of movement is possible from adestination to itself, these cells are marked with
dash.
ASSIGNMENT PROBLEM
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Assignment problemASSIGNMENT PROBLEM
TO
A B C D E
A - 8 7 9 5
FROM B 6 - 11 5 5
C 15 11 - 6 14
D 9 5 6 - 8
E 7 3 6 4 -
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Assignment problem
Five workers are available to work with fivemachines. the respective cost associated witheach worker and machine assignment is given inthe table below. a sixth machine is available toreplace one of the existing machines and itsassociated costs are also given.
(a) determine, whether the new machine can beaccepted.
(b) determine the optimal assignment andsaving in cost.
ASSIGNMENT PROBLEM
Problem with dummy row or column
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Assignment problem
A company has a team of four salesmen
and there are four districts where the
company wants to start its business. after
taking into account the capabilities ofsalesman and the nature of district, the
company estimates that the profit per day
in rupees for each salesman in eachdistrict is as below.
ASSIGNMENT PROBLEM
Maximization problem
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Assignment problemASSIGNMENT PROBLEM
Maximization problem
1 2 3 4
A 16 10 14 11
B 14 11 15 15C 15 15 13 12
D 13 12 14 15
DISTRICT
SALESMAN
Find the assignment of salesmen to various district which will yield maximumprofit?
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Assignment problemASSIGNMENT PROBLEM
Maximization problem-2
A small garment making unit has five tailors switching five different types of
garments. the output per day per tailor and the profit for each type of
garment are given below
1 2 3 4 5A 7 9 4 8 6
B 4 9 5 7 8
C 8 5 2 9 8
D 6 5 8 10 10
E 7 8 10 9 9
Profit per garment 2 3 2 3 4
garments
tailors
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Assignment problemASSIGNMENT PROBLEM
Maximization problem-2
1. Which type of garment should be assigned to which tailor in order to maximize
profit, assuming that there are no other constraints?
2. If tailor D is absent for a specified period and no other substitute tailor is
available, what should be the optimal assignment?
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Assignment problem
Consider a manufacturing company that is thinking ofseveral alternative methods to increase its production tomeet the increase market demand.
step 1:list all the viable alternatives
1.expand the present plant
2.construct the new plant
3.subcontract production for extra demand.- these alternatives term as course of actions or simply
actions or strategies.
Decision theory approach
1DECISION THEORY
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Assignment problem
step 2:identify the expected future event
List all the future event they may occur. but it is very tough to
identifying that particularly which event will occur.
These future events are termed as state of nature
In our example state of nature are
- high demand
- moderate demand
- Low demand
- no demand
Decision theory approach
DECISION THEORY2
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Assignment problem
step 3:construct pay off table or conditional gain or profittable
- Make a pay off table for each possible combination ofalternative course of action and state of nature.
3
Decision theory approach
ALTERNATIVES STATE OF NATURE
HIGH MODERATE LOW NIL
EXPAND Rs.50000 Rs.25000 -25000 -45000CONSTRUCT 70000 30000 -40000 -80000
SUBCONTRACT 30000 15000 -1000 -10000
DECISION THEORY
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Assignment problem
Step 4 : select optimum decision criterion
Finally the decision-maker will choose criterionwhich results in largest payoff. the criterion may be
economic, quantitative or qualitativeetc.
DECISION THEORY 4
Decision theory approach
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Assignment problem
decision-making under conditions of certainty.
decision-making under conditions of uncertainty.
decision-making under conditions of risk.
5
Decision making environment
DECISION THEORY
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Assignment problem
- in this environment, only one state of nature exists foreach alternative i.e., there is complete certainty aboutthe future. it is easy to analyze the situation and makegood decisions.
- Decision-maker has perfect knowledge about the futureoutcomes, he simply choose the alternative havingoptimum pay-off.
6
Decision making under condition of certainty
DECISION THEORY
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Assignment problem
EXAMPLE:-
A company can manufacture two different products k1 andk2.the two products have to be processed through twomachines M1 & M2 whose available capacities in terms ofhours per week are 480 and 410 respectively. product k1 need
3 hours of M1 and 1 hour of M2 and product K2 requires 1hour of M1 and 2 hours of M2. find the number of units ofproducts K1 & K2 that can be manufactured every week byutilizing fully the available capacities of the machine.
7
MACHINES
PRODUCT TIMES
AVAILABILITY
M1 3 1 480
M2 1 2 410
Decision making under condition of certainty
DECISION THEORY
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Assignment problem
Let x be the number of units of k1 and y be the number
of units k2 that can be manufactured. then, as per the
given data we have the following simultaneous equation:
3x+y=480
X+2y=410
Solving we get x=110,y=150
Therefore 110 units of product k1 and 150 units of
product k2 can be manufactured.
8
Decision making under condition of certainty
DECISION THEORY
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Assignment problem
Example: Linear programming when resources required,
resources available, cost or profit per unit of the product
are know with certainty.
9
Decision making under condition of certainty
DECISION THEORY
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Assignment problem
Here, more than one states of nature exist but the
decision-maker lacks sufficient knowledge to allow him
assign probabilities to the various states of nature.
Under conditions of uncertainty, a few decision criteria
are available which could be of help to the decision-maker and a choice among them is determined by the
companys policy and attitude of the decision maker.
10
Decision making under condition of uncertainty
DECISION THEORY
Maximax criterion or criterion of optimism
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Assignment problem
Maximax criterion or criterion of optimism
Maximax criterion or criterion of optimism
11DECISION THEORY
ALTERNATIVES STATE OF NATURE
HIGH MODERATE LOW NIL
EXPAND Rs.50000 Rs.25000 -Rs.25000 -Rs.45000
CONSTRUCT 70000 30000 -40000 -80000
SUBCONTRACT 30000 15000 -1000 -10000
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Assignment problem
Maximax criterion or criterion of optimism
12
Maximax criterion or criterion of optimism
DECISION THEORY
Maximum of rows
50000
70000
30000
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Assignment problem
When dealing with costs ,the minimum of each
alternative is considered and the alternative which
minimizes the above minimum costs is selected. this is
called minimin criterion.
13
Maximax criterion or criterion of optimism
DECISION THEORY
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Assignment problem
To use this criterion, the decision-maker maximizes his
minimum possible payoffs.
14
Maximin criterion or criterion of pessimism or wald criterion
DECISION THEORY
ALTERNATIVES STATE OF NATURE
HIGH MODERATE LOW NIL
EXPAND Rs.50000 Rs.25000 -Rs.25000 -Rs.45000
CONSTRUCT 70000 30000 -40000 -80000
SUBCONTRACT 30000 15000 -1000 -10000
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Assignment problem 15DECISION THEORY
Maximin criterion or criterion of pessimism or wald criterion
Minimum of rows
-45000
-80000
-10000
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Assignment problem
This criterion developed by L.J.Savage.
Minimize our maximum regret.
16
Minimax regret criterion or savage criterion
DECISION THEORY
ALTERNATIVES STATE OF NATURE
HIGH MODERATE LOW NIL
EXPAND Rs.20000 Rs.5000 Rs.24000 35000
CONSTRUCT 0 0 39000 70000
SUBCONTRACT 40000 15000 0 0
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Assignment problem
Minimax regret criterion or savage criterion
17
Minimax regret criterion or savage criterion
DECISION THEORY
Maximum of row
35000
70000
40000
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Assignment problem
Hurwicz criterion (criterion of Realism)
This is also called as a weighted average criterion
This concept allow decision maker to take into
account both the maximum and minimum for each
alternative and assign them weights according to
his degree of optimism.
=degree of optimism
1-=degree of pessimismhere is called coefficient or index of
optimism
18
Hurwicz criterion (criterion of Realism)
DECISION THEORY
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Assignment problem
Step 1:choose appropriate degree of optimism
Step 2:Determine the maximum as well as
minimum of each alternative and obtain
P=.maximum+(1-).minimum Step 3:choose the alternative that yields
the maximum value of p.
19
Hurwicz criterion (criterion of Realism)
DECISION THEORY
H i it i ( it i f R li )
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Assignment problem 20
Hurwicz criterion (criterion of Realism)
DECISION THEORY
maximum of row minimum of row p
50000 -45000 31000
70000 -80000 40000
30000 -10000 22000
L l C it i C it i f R ti lit
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Assignment problem
This criterion assigns equal probabilities to
all the events of each alternative decision
and selects the alternative associated with
the maximum expected payoff.
If n denotes the number of events and Ps
denote the payoffs, then expected value
for strategy, say S1 is 1/n[p1+p2++Pn].
21
Laplace Criterion or Criterion of Rationality
DECISION THEORY
R li h i it i
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Assignment problem 22
Realism or hurwicz criterion
DECISION THEORY
Expected payoff
1000/4[50+25-25-45]=-1250
-5000
85000
D i i ki d diti f i k
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Assignment problem 23
Decision making under conditions of risk
DECISION THEORY
Most business decisions may have to be made underconditions of risk. here more than one states of natureexist and the decision-maker has sufficient information toassign probabilities to each of these states.
These probabilities could be obtained from the pastrecords or from simply the subjective judgment
E t d t l t d l it i
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Assignment problem 24
Expected monetary value or expected value criterion
DECISION THEORY
This criterion requires the calculation of the expected
value of each decision alternative which is the sum of the
weighted payoffs for that alternative ,where the weights
are the probabilities assigned to the states of nature that
can happen.
Step 1: construct a conditional payoff table listing thealternative decisions and the various states of nature.
Enter the conditional profit for each decision-event
combination along with the associated probabilities.
Step 2: calculate the EMV for each decision alternativeby multiplying the conditional profits by assigned
probabilities and adding the resulting conditional values.
Step 3: select alternatives that yields the highest EMV.
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Assignment problem 25DECISION THEORY
A news paper boy has the following probabilities ofselling a magazine:
No. of copies sold probabilities
10 .10
11 .15
12 .20
13 .25
14 .30
Cost of a copy is 30 paise and sale price is 50 paise.hecannot return unsold copies.how many copies should heorder?
Expected monetary value or expected value criterion
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Assignment problem 26DECISION THEORY
possible
demand probabilities
possible stock action
(no. of
copies)
10
copies
11
copies
12
copies
13
copies
14
copies
10 0.1 200 170 140 110 80
11 0.15 200 220 190 160 130
12 0.2 200 220 240 210 180
13 0.25 200 220 240 260 230
14 0.3 200 220 240 260 280
Conditional profit table
Expected monetary value or expected value criterion
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Assignment problem 27DECISION THEORY
Expected profit table
possibledemand probabilities possible stock action
(no. of
copies)
10
copies
11
copies
12
copies
13
copies
14
copies
10 0.1 20 17 14 11 8
11 0.15 30 33 28.5 24 19.5
12 0.2 40 44 48 42 36
13 0.25 50 55 60 65 57.5
14 0.3 60 66 72 78 84
total
expected
profit 200 215 222.5 220 205
Expected monetary value or expected value criterion
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Assignment problem 28DECISION THEORY
The newsboy must, therefore, order 12
copies to earn the highest possible
average daily profit of 222.5 paise
Expected monetary value or expected value criterion
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Assignment problem 29DECISION THEORY
An alternative approach is to minimize expected
opportunity loss. Step 1:prepare the conditional profit table for each
decision event combination and write the associatedprobabilities.
Step 2:for each event, determine the conditional
opportunity loss by subtracting the pay off from themaximum payoff for that event.
Step 3:clculate EOL for each decision alternative bymultiplying the COLs by the associated probabilities and
then adding the values. Step 4;select the alternative that yields the lowest EOL.
Expected opportunity loss criterion
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Assignment problem 30DECISION THEORY
Expected opportunity loss criterion
possible
demand probabilities possible stock action
(no. of
copies)
10
copies
11
copies
12
copies
13
copies
14
copies
10 0.1 200 170 140 110 80
11 0.15 200 220 190 160 130
12 0.2 200 220 240 210 180
13 0.25 200 220 240 260 230
14 0.3 200 220 240 260 280
conditional profit table
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Assignment problem 31DECISION THEORY
Expected opportunity loss criterion
conditional LOSS TABLE
possible
demand probabilities possible stock action
(no. of
copies)
10
copies
11
copies
12
copies
13
copies
14
copies
10 0.1 0 30 60 90 120
11 0.15 20 0 30 60 90
12 0.2 40 20 0 30 6013 0.25 60 40 20 0 30
14 0.3 80 60 40 20 0
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Assignment problem 32DECISION THEORY
Expected opportunity loss criterion
EXPECTED LOSS TABLE
possible
demand probabilities possible stock action
(no. of
copies)
10
copies
11
copies
12
copies
13
copies
14
copies
10 0.1 0 3 6 9 12
11 0.15 3 0 4.5 9 13.5
12 0.2 8 4 0 6 1213 0.25 15 10 5 0 7.5
14 0.3 24 18 12 6 0
EOL 50 35 27.5 30 45
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Assignment problem 33DECISION THEORY
Expected opportunity loss criterion
THE OPTIMUM STOCK ACTION IS THE ONE WHICH WILL MINIMIZE
EXPECTED OPPORTUNITY LOSSES;THIS ACTION CALLS FOR THESTOCKING OF 12 COPIES EACH DAY,AT WHICH POINT THERE IS
MINIMUM EXPECTED LOSS OF 27.5 PAISE.
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Assignment problem 34DECISION THEORY
EXPECTED VALUE OF PERFECT INFORMETION
possibledemand possible stock action
(no. of copies) 10 copies 11 copies 12 copies 13 copies 14 copies
10 200
11 220
12 240
13 26014 280
CONDITIONAL PROFIT TABLE UNDER CERTAINTY
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Assignment problem 35DECISION THEORY
EXPECTED VALUE OF PERFECT INFORMETION
EXPECTED PROFIT TABLE WITH PERFECT INFORMATION
market size
conditional
profit
probability of market
size expected profit
(no. of
copies
under
certainty with perfect
information
10 200 0.1 20
11 220 0.15 33
12 240 0.2 48
13 260 0.25 65
14 280 0.3 84
EPPI=250
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Assignment problemDECISION THEORY
EXPECTED VALUE OF PERFECT INFORMETION
EVPI=250-222.5=27.5So, EVPI is no more than 27.5
36
f
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Assignment problemDECISION THEORY
EMV for item that have selvage value
36
An ice-cream retailer buys ice cream at a cost of Rs.5per cup and sells it for Rs. 8 per cup; any remainingunsold at the end of the day can be disposed of at asalvage price of Rs.2 per cup. past sales have rangedbetween 15 and 18 cups per day; there is no reason tobelieve that sales volume will take on any othermagnitude in future. find the EMV if the sale history hasthe following probabilities:
Market size: 15 16 17 18
Probability: 0.1 0.2 0.4 0.3
EMV f it th t h l l
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Assignment problemDECISION THEORY
EMV for item that have selvage value
37
If CP denotes conditional profit. S the quantity in stockand D the market demand, then
CP=(8-5)S,WHEN D=>SAND
CP=8D-5S+2(S-D),WHEN D
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Assignment problemDECISION THEORY
EMV for item that have selvage value
38
possible stock action (alternative)
15 16 18
15 0.1 45 42 3616 0.2 45 48 42
17 0.4 45 48 48
18 0.3 45 48 54
Possible
demand
(event)
probabilities
Conditional profit table
EMV f it th t h l l
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Assignment problemDECISION THEORY
EMV for item that have selvage value
39
possible demand
(event) probabilities
possible stock action
(alternative)
15 16 17 18
15 0.1 4.5 4.2 3.9 3.6
16 0.2 9 9.6 9 8.4
17 0.4 18 19.2 20.4 19.2
18 0.3 13.5 14.4 15.3 16.2
EMV 45 47.4 48.6 47.4
EXPECTED PROFIT TABLE
EMV=Rs.48.6 for stock action of 17 ice cream cups each day
E l
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Assignment problemDECISION THEORY
Example
40
GM of calcutta motor is planning staffing of thedealershipps garage facilities in Ahmedabad. frominformation provided by the manufacturer and from othernearby dealership, he has estimated the number ofannual mechanic hours that the garage will be likely to
needed Hours 10000 12000 14000 16000
Probability 0.15 0 .25 0.4 0.2
The manager plans to pay each mechanic Rs.9 per hourand to charge customer Rs.16. mechanics will work a 40
hours per week and get an annual 2 week vacation.Determine how many mechanics Calcutta motor shouldhire?
Calculate EOL and EVPI also?
DECISION TREES
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Assignment problemDECISION THEORY
DECISION TREES
41
The decision problems discussed so far
with only single stage decision making. we
now consider situations that involve
multiple stages. they are characterized bya sequence of decision with each decision
influencing the next. such problems, called
sequential decision problems, areanalyzed best with the help of decision
trees.
DECISION TREES
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Assignment problemDECISION THEORY
DECISION TREES
42
A client asks an estate agent to sell three properties A,Band c for him and agrees to pay him 5% commission oneach sale. he specifies certain conditions. the estateagent must sell property A first, and this he must dowithin 60 days. if and when A is sold, the agent receives
his 5% commission on that sale. he can then either backout at this stage or nominate and try to sell one of theremaining two properties within 60 days. if he does notsucceed in selling the nominated property in that period,he is not given the opportunity to sell the other. if hedoes sell it in the period, he is given the opportunity to
sell the third property on the same conditions. Thefollowing table summarizes the prices, selling cost andthe estate agents estimated probability of making a sale.
DECISION TREES
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Assignment problemDECISION THEORY
DECISION TREES
43
Property Prices of
property
Selling
costs
Probability
of sales
A 12000 400 0.7
B 25000 225 0.6
C 50000 450 0.5
1)DRAW UP AN APPROPRIATE DECISION TREE FOR THE
ESTATE AGENT.2)WHAT IS THE ESTATE AGENTS BEST STRATEGY UNDER
EMV APPROACH.
DECISION TREES
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Assignment problemDECISION THEORY
DECISION TREES
44
Mr Sinha had to decide whether or not to drill a well on his farm. in his
village, only 40% of the wells drilled were successful at 200 feet of depth.some of the farmers who did not get water at 200 feet, drilled further upto
250 feet but only 20% struck water at 250 feet. cost of drilling is Rs.50
per foot. Mr. Sinha estimated that he would pay Rs.18,000 during a 5-
year period in the present value terms, if he continues to buy water from
the neighbor rather than go for the well which would have a life of 5
years. Mr. Sinha has three decision to make:(a)should he drill up to 200feet and (b) if no water is found at 200 feet, should he drill up to 250
feet?(c) should he continue to buy water from his neighbor?
Posterior probabilities and bayesian analysis
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Assignment problemDECISION THEORY
Posterior probabilities and bayesian analysis
45
In a preceding analysis of decision making under
probabilities used in the expected value criterion are usually obtained
from the past historical data. these probabilities are called priorprobabilities and the analysis that uses them to find expected payoffs is
known as prior analysis.
If the prior analysis results in high expected opportunity loss (EOL) or
EVPI,it may be desirable to obtain additional information through
sampling or experimentation or test research. prior probabilities may thenbe revised in the light of this additional information by using bayes
theorem to yield posterior probabilities or bayes probabilities.
Revised analysis of the problem using these probabilities is called
posterior analysis or bayesian analysis. this analysis gives a revised
value of EMV which is expected to be better than the EMV based on prior
analysis. the difference between the two should at least be equal to the
UTILITY THEORY
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Assignment problemDECISION THEORY
UTILITY THEORY
46
Think about the situation in which you have two option:-
(1)Get 10000 rupees fix
(2)5% chance of getting Rs.250000 and 95% chance of getting nothing
What is your answer?
The worth of money is different for different people and is also different in
different situations.
Each rupee is not equally valuable to an individual.
The determination of utility is subjective.it depends upon our attitude of
accepting risk.The utility theory approach attempts to determine a utility function or a
utility curve for a decision maker.
UTILITY THEORY
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Assignment problemDECISION THEORY
UTILITY THEORY
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Here function converts money into an arbitary utility measure.
Risk avoider: slope decrease as money values increase. firm with
unsound finansial position.
Risk neutral:expected utility give the same results as expected
return(EMV) analysis.
EXAMPLE:LARGE COMPANIES & GOVERNMENT.
Risk taker:curve increase faster than the money value.
In practice utility curve is a combinetion of risk taker and risk avoider
UNBALANCED ASSIGNMENT
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Assignment problem
UNBALANCED ASSIGNMENT
PROBLEM
You are given the information about the
cost of performing different jobs by
different persons. the job-person marking
(@) indicates that the individual involvedcannot perform the particular job. using
this information, state (i) the optimal
assignment of jobs, and (ii) the cost ofsuch assignment
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Traveling salesman problems
Mr Patel is a salesman with Delite
Manufecturing company. he wants to visit
six cities, say, 1,2,3,4,5 and 6,starting with
city 1where he is stationed. the distancesbetween various cities are given in the
table.Patel wants to develop a tour
through the five other cities and return tohis home city in such a way that he was to
travel a minimum distance.