```GROUP 5
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PALLAV
SUDHIR
PRITY BALA
ANUP
SARANSH
RAJAT
HIRNI
ANTHONY
CHETNA
ROGER
History Linear Programming
During the 1940’s and the army needed a way to plan expenditures and returns
in order to reduce costs and increase losses for the enemy. George B. Dantzig is
the founder of the simplex method of linear programming, but it was kept
secret and was not published until 1947 since it was being used as a war-time
strategy. But once it was released, many industries also found the method to be
highly valuable. Another person who played a key role in the development of
linear programming is John von Neumann, who developed the theory of the
duality and Leonid Kantorovich, a Russian mathematician who used similar
techniques in economics before Dantzig and won the Nobel prize in 1975 in
economics.
History Linear Programming
Dantzig's original example of finding the best assignment of 70 people to 70
jobs emphasizes the practicality of linear programming. The computing power
required to test all possible combinations to select the best assignment is quite
large. However, it takes only a moment to find the optimum solution by
applying the simplex algorithm. The theory behind linear programming is to
drastically reduce the number of possible optimal solutions that must be
checked. In the years from the time when it was first proposed in 1947 by
Dantzig, linear programming and its many forms have come into wide use
worldwide. Fourier in 1823 wrote a paper describing today's linear
programming methods, but it never made its way into mainstream use. A
paper by Hitchcock in 1941 on a transportation problem was also overlooked
until the early 1950s. It seems the reason linear programming failed to catch on
in the past was lack of interest in optimizing.
Linear Programming:
A methodology for identifying underutilized resources
Identifying underutilized resources is crucial for evaluating the
economic feasibility of downsizing. However, identification of these
resources is perhaps one of the most difficult and critical aspects of
downsizing. A quantitative technique that may be used to identify
potentially unproductive resources is linear programming (LP). LP may
be used to measure resource utilization and other economic attributes
of the firm's operations. For firms not contemplating downsizing, this
information may also be potentially useful for making management
aware of an organization's underutilized resources as well as their cost
to the firm.
Linear Programming:
A methodology for identifying underutilized resources
LP is used to model a firm's goals and its operating constraints. An
algorithm is then used to find an allocation of the firm's scarce
resources that maximizes the goal specified in the LP model.
Diminished product demand is a constraint facing many firms today
and is one of the primary reasons firms decide to downsize. LP may
also be used to determine departments that are currently understaffed.
Identifying these departments should help to prevent work force
reductions that would be harmful to the firm. Equally important,
identifying understaffed departments represents opportunities for
reallocating the unproductive resources of other departments to
applications that enhance the firm's financial performance.
Linear Programming:
A methodology for identifying underutilized resources
LP may be used to model a firm's business opportunities and resources.
The solution to the resulting set of equations may be used to identify
departments with unused resources. Equally important, the LP
solution aids in identifying areas within the firm's operations where
slack resources may be reallocated to use them productively. Finally, it
may be used to measure the profitability and resource utilization from
alternative marketing, financing, and production scenarios.
Identification of underutilized resources and measurement of their
cost is a starting point for evaluating the economic feasibility of
downsizing. While LP may be used to measure these variables,
downsizing involves much more than the mechanistic computation of
the benefits and cost of terminating the firm's employees. It involves
the future direction and capabilities of the corporation. However, LP
can serve as a useful technique for developing information for making
this critical decision.
HISTORY CPM/PERT
 CPM was developed by M.R.Walker of E.I.Du Pont de
Nemours & Co. and J.E.Kelly of Remington Rand, circa
1957, for the UNIVAC-I computer.
 first test was made in 1958, when CPM was applied to the
construction of a new chemical plant.
 In March 1959, the method was applied to a maintenance
shut-down at the Du Pont works in Louisville, Kentucky.
Unproductive time was reduced from 125 to 93 hours.
 PERT was developed primarily to simplify the planning
and scheduling of large and complex projects.
 It was developed by Bill Pocock of Booz Allen Hamilton
and Gordon Perhson of the U.S. Navy Special Projects
Office in 1957 to support the U.S. Navy's Polaris nuclear
submarine project.
PERT
PERT is a method to analyze the involved tasks in
completing a given project, especially the time needed
to complete each task, and identifying the minimum
time needed to complete the total project.
Conventions
 A PERT chart is a tool that facilitates decision making; The first





draft of a PERT chart will number its events sequentially in 10s
(10, 20, 30, etc.) to allow the later insertion of additional events.
Two consecutive events in a PERT chart are linked by activities,
which are conventionally represented as arrows (see the diagram
above).
The events are presented in a logical sequence and no activity
can commence until its immediately preceding event is
completed.
The planner decides which milestones should be PERT events
and also decides their “proper” sequence.
A PERT chart may have multiple pages with many sub-tasks.
PERT is valuable to manage where multiple tasks are occurring
simultaneously to reduce redundancy
Uncertainty in project scheduling
 During project execution, however, a real-life project will never
execute exactly as it was planned due to uncertainty. It can be
ambiguity resulting from subjective estimates that are prone to
human errors or it can be variability arising from unexpected
events or risks. And Project Evaluation and Review Technique
(PERT) may provide inaccurate information about the project
completion time for main reason uncertainty. This inaccuracy is
large enough to render such estimates as not helpful.
 One possibility to maximize solution robustness is to include
safety in the baseline schedule in order to absorb the anticipated
disruptions. This is called proactive scheduling. A pure proactive
scheduling is an utopia, incorporating safety in a baseline
schedule that allows to cope with every possible disruption
would lead to a baseline schedule with a very large make-span. A
second approach, reactive scheduling, consists of defining a
procedure to react to disruptions that cannot be absorbed by the
baseline schedule.
APPLICATION
 The PERT/cost system was developed to gain tighter control over
actual costs of any project. PERT\cost relates actual costs to
project costs. Job cost estimates are established from an activity
or a group of activities on the basis of a time network. Labor and
nonlabor estimates are developed for the network targeting the
control of time and costs and identifying potential areas where
time and cost can be traded off—all aimed at more effective,
efficient project management.
 As with all aspects of business, the Internet has become a
powerful tool with respect to PERT. Managers can now locate
PERT applications on the World Wide Web and apply them
directly to the appropriate manufacturing project. In most
instances, PERT diagrams are available that eliminate the
estimating process and make PERT a more useful and convenient
tool
CPM
 CPM is commonly used with all forms of projects,
including construction, aerospace and defense,
software development, research projects, product
development, engineering, and plant maintenance,
among others. Any project with interdependent
activities can apply this method of mathematical
analysis
Basic technique
The essential technique for using CPM is to construct a
model of the project that includes the following:
 A list of all activities required to complete the project
(typically categorized within a work breakdown structure),
 The time (duration) that each activity will take to
completion, and
 The dependencies between the activities
 Using these values, CPM calculates the longest path of planned
activities to the end of the project, and the earliest and latest that
each activity can start and finish without making the project
longer. This process determines which activities are "critical"
(i.e., on the longest path) and which have "total float" (i.e., can
be delayed without making the project longer).
 In project management, a critical path is the sequence of
project network activities which add up to the longest overall
duration. This determines the shortest time possible to complete
the project. Any delay of an activity on the critical path directly
impacts the planned project completion date (i.e. there is no
float on the critical path). A project can have several, parallel,
near critical paths. An additional parallel path through the
network with the total durations shorter than the critical path is
called a sub-critical or non-critical path.
SIMULATION MODELING
Overview
Is the process of building a mathematical or logical
model of a system or a decision problem, and
 experimenting with the model to obtain insight into
the system’s behavior or to assist in solving the
decision problem.
 It is an analysis tool used for the purpose of designing
planning and control of manufacturing systems.
 Simulation modeling may be defined as the concise
framework for the analysis and understanding of a
system.
 It is an abstract framework of a system that facilitates
imitating the behavior of the system over a period of
time.
 In contrast to mathematical models, simulation
models do not need explicit mathematical functions to
relate variables
 Simulation modeling techniques are powerful for
manipulation of time system inputs, and logic.
 They are cost effective for modeling a complex system,
and with visual animation capabilities they provide an
effective means of learning, experimenting and
analyzing real-life complex systems.
 They enable the behavior of the system as a whole to
be predicted
 Therefore ,they are suitable for representing complex
systems to get a feeling of real system.
 One of the greatest advantage of a simulation model is
that it can compress or expand time.
 Simulation models can also be used to observe a
phenomenon that cannot be observed at very small
intervals of time.
 Simulation can also stops continuity of the
experiment.
A Brief History of Simulation
 Simulation has been around for some time.
 Early simulations were event-driven and frequently
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military applications.
In the 1960’s Geoffrey Gordon developed the
transaction (process) based orientation that we are
now familiar with.
Gordon’s software was called General Purpose
Simulation System (GPSS).
GPSS was originally intended for analyzing time
sharing options on mainframe computers.
The software was included as a standard library on
IBM 360s and its use was quite widespread.
SIMULATION MODEL
 Usually, a simulation model is a computer model that
imitates a real-life situation.
 It is like other mathematical models, but it explicitly
incorporates uncertainty in one or more input
quantities
 When we run simulation, we allow these random
quantities to take various values, and we keep track of
any resulting output quantities of interest
 In this way, we are able to see how the outputs vary as a
function of the varying inputs
BENEFITS
 Does not require
simplifying assumptions
 Can deal with problems
not possible to solve
analytically
 Provides an experimental
laboratory: possible to
evaluate decisions/systems
without implementing
them
 Generally easier to
understand than analytical
models
LIMITATIONS
 Building models and
simulating is timeconsuming for complex
systems
 Simulation results /
simulated systems are
always approximations of
the real ones
 Does not guarantee an
optimal solution - lack of
 Should not be used
indiscriminately in place of
sound analytical models.
APPLICATIONS OF SIMULATIONAL
MODELING
 Simulation enables the study of, and experimentation
with, the internal interactions of a complex system, or
of a subsystem within a complex system.
 Informational, organizational, and environmental
changes can be simulated, and the effect of these
alterations on the model’s behavior can be observed.
Trends
 Virtual reality animations.



Curve fitting for input data.
Automatic detection of warm up
Output analysis modules (including replication).
 Bolt on “Optimizers” – Tools to search for optimal
settings of parameters.
APPLICATIONS IN HRM
 With the OB Representation model and simulation
system it is possible to simulate the organisational
performance under different conditions like varying
 The human resource planning and development can
be connected to organisational structure or tasks. It
makes possible the performance measurements of
employees in an organisations.
 From the results of the simulation process, the
decisions for the personnel planning process could be
made. Decision support could be realized through
different aspects.
 The user of the simulation are able to vary input
parameters for identifying critical levels of operation
experience, personnel skills or fit between expected
staff and necessary competencies.
 Research and applications of mathematical and
statistical models are the core of this program's
activities, whether the models represent structural
descriptions of human abilities, interests, or
temperaments; dynamic simulations of skill
acquisition, retention, and performance; or more
global models of human systems
 In addition, it makes possible to develop and evaluate
prescriptive models, including models that optimize
person-job matching based on aptitudes and interests,
or that guide the design of training systems to
maximize effectiveness within cost constraints.
 An important aspect is the evaluation of modeling and
simulation technology for competency mapping &
training
 Simulation Modeling is used in determination of the
steady-state manpower situation that would be
attained if a certain policy were to be maintained for a
prolonged period of time.
 It helps a manpower planner accurately identify the
age and rank structure that fits the organisational
framework required to fulfil the organizational goals.
HR FORECASTER
 A computer simulation such as HR Forecaster can
model a real-life or hypothetical situation on your
computer so that you can study how the system works.
the behavior of your workforce. The software packages
for running computer-based simulation
modeling makes the process modeling almost
effortless.
 HR Forecaster's simulation methods are especially
useful in studying systems with a large number of
coupled degrees of freedom and are useful for
modeling phenomena with significant uncertainty in
inputs, such as the calculation of risk.
 HR Forecaster uses computational algorithms for
simulating the behavior of various workforce variables,
either actual or scenario. It is distinguished from other
simulation methods by being nondeterministic in
some manner – usually by using random numbers (in
practice, pseudo-random numbers) – as opposed to
deterministic algorithms.
Markov Chains
Markov Analysis
Overview
 Markov analysis is a probabilistic technique.
 - It provides information about a decision situation.
 - It is a descriptive, not an optimizing technique.
 - Specifically applicable to systems that exhibit
probabilistic movements from one state (or condition) to
another.
History
Markov analysis analyzes the current behaviour of some variables. This
was first used by the Russian mathematician A. Markov to describe and
predict the behavior of gas particles in a closed container.
In operations research, it has been successfully applied to a wide
variety of situationsIt has been used in examining and predicting the behaviour of
customers in terms of their brand loyalty and their changing from one
brand to another.
It has also been used to the study the life of newspaper subscriptions.
Recently it has been used to study the customer’s account behaviour
i.e. to the study the customers as they change from ‘current account’
through ‘one month overdue’ to ‘two months over due’ to ‘bad debt’. In
all these applications, future behaviour has been predicted by
analyzing the present one.
Application in HRM
Determining Labor Supply Predicting Worker Flows and Availabilities
 Succession or Replacement Charts
Who has been groomed/developed and is ready for promotion right NOW?
 Human Resource Information Systems (HRIS)
An employee database that can be searched when vacancies occur.
 Transition Matrices (Markov Analysis)
A chart that lists job categories held in one period and shows the proportion of
employees in each of those job categories in a future period.
1.
“Where did people in each job category go?”
2.
“Where did people now in each job category come from?
 Personnel / Yield Ratios
How much work will it take to recruit one new accountant?
SUCCESSION PLANNING
REPLACEMENT CHART
FOR EXECUTIVE POSITIONS
POSITION REPLACEMENT CARDS
FOR EACH INDIVIDUAL POSITION
------------------------------------------------------------------------
POSITION
WESTERN DIVISION SALES MANAGER
DANIEL BEALER Western Division Sales Mgr
POSSIBLE CANDIDATES
POTENTIAL
SHARON GREEN
Now
GEORGE WEI
Training
HARRY SHOW
TRAVIS WOOD
PRESENT
CURRENT POSITION
Outstanding
PROMOTION
PERFORMANCE
Western Oregon Sales Manager
Outstanding
N. California Sales Manager
Outstanding
Needs
Idaho/Utah Sales Manager
Seattle Area Sales Manager
Satisfactory
Satisfactory
Needs Training
Questionable
HUMAN RESOURCE
INFORMATION SYSTEMS (HRIS)
PERSONAL DATA
Age, Gender, Dependents, Marital status, etc
EDUCATION & SKILLS
Languages spoken, Specialty skills
Ability/knowledge to operate specific machines/equipment/software
JOB HISTORY
Job Titles held, Location in Company, Time in each position, etc.
Performance appraisals, Promotions received, Training & Development
MEMBERSHIPS & ACHIEVEMENTS
Professional Associations, Recognition and Notable accomplishments
PREFERENCES & INTERESTS
Career goals, Types of positions sought
Geographic preferences
CAPACITY FOR GROWTH
Potential for advancement, upward mobility and growth in the company
Example for an Auto Parts
Manufacturer
MARKOV ANALYSIS
(STATISTICAL REPLACEMENT ANALYSIS)
TO: 
FROM:
A TRANSITION MATRIX
TOP
MID
TOP
.80
.02
MID
.10
.76
.04
.06
.78
LOW
SKILL
ASSY
LOW SKILLED ASSY
.18
.01
.10
.01
.15
.84
.05
.15
.88
.07
EXIT
MARKOV ANALYSIS – 2
(Captures effects of internal transfers)
(Start = 3500)
FROM/ TO: 
TOP
100
MID
LOW
SKILL
200
600
600
TOP
.80
.10
A TRANSITION MATRIX
MID
LOW SKILLED ASSY
.02
.76
.06
.04
EXIT
.18
.10
.78
.01
.15
.01
.84
.15
ASSY
2000
.05
.88
.07
--------------------------------------------------------END YR WITH: 100
190
482
610
1760 [358 left]
NEED RECRUITS ? 0
10
118
240*
368 tot
NEED LAYOFFS ?
(10)*
(10) tot
KEEP STABLE 100 200
600
600
2000 = 3500 Tot
MARKOV ANALYSIS – 3
(Anticipates Changes in Employment
Levels)
Employment needs are changing. We need a 10% increase in skilled
workers (660), and a 15% decrease in assembly workers (1700) by year’s
end.
------------------------------------------------------(Start = 3500)
A TRANSITION MATRIX
FROM/ TO: 
TOP MID
LOW SKILLED ASSY
EXIT
TOP
100
.80
.02
.18
MID
200
.10
.76
.04
.10
LOW
600
.06
.78
.01
.15
SKILL 600
.01
.84
.15
ASSY
2000
.05
.88
.07
--------------------------------------------------------END YR WITH: 100 190
482
610
1760 [358 left]
NEED RECRUITS ? 0
10
118
50*
NEED LAYOFFS ?
(60)*
NEW LEVELS 100 200 600
600
1700 = 3260 tot
Determining Labor Surplus or
Shortage
 Based on the forecasts for labor demand and supply,
the planner can compare the figures to determine
whether there will be a shortage or surplus of labor for
each job category.
 Determining expected shortages and surpluses allows
the organization to plan how to address these
challenges.
PERSONNEL / YIELD RATIOS
Past experience has developed these yield ratios for recruiting a Cost
Accountant:
FOR EVERY 12 APPLICATIONS RECEIVED, ONLY 1 LOOKS PROMISING ENOUGH TO
INVITE FOR AN INTERVIEW
OF EVERY 5 PERSONS INTERVIEWED, ONLY 1 IS ACTUALLY OFFERED A POSITION
IN THE ORGANIZATION
OF EVERY 3 JOB OFFERS MADE, ONLY 2 ACCEPT THE POSITION
OF EVERY 10 NEW WORKERS WHO BEGIN THE TRAINING PROGRAM, ONLY 9
SUCCESSFULLY COMPLETE THE PROGRAM
THUS:
100 APPLICATIONS MUST BE RECEIVED, so that
8.33 JOB INTERVIEWS CAN BE HELD, so that
1.67 JOB OFFERS CAN BE MADE, and
1.11 PEOPLE MUST BE TRAINED, so that we get
ONE NEW COST ACCOUNTANT!!!
Queuing Systems
The word queue comes, via French,
from the Latin cauda, meaning tail.
Queuing theory is the mathematical study of waiting lines,
or queues. The theory enables mathematical analysis of
several related processes, including arriving at the (back of
the) queue, waiting in the queue (essentially a storage
process), and being served at the front of the queue.
 Queuing theory is generally considered a branch of operations
research because the results are often used when making
service. It is applicable in a wide variety of situations that may be
encountered in business, commerce, industry, healthcare, public
service and engineering.
 The theory permits the derivation and calculation of several
performance measures including the average waiting time in the
queue or the system, the expected number waiting or receiving
service, and the probability of encountering the system in
certain states, such as empty, full, having an available server or
having to wait a certain time to be served.
APPLICATION IN HRM
Example: A Call Centre is a Queue.
In call centres, human resource costs account between 60% to 70% of
operating expenses. The managers have to reduce the labour cost, but
not to the detriment of the customers.
A call centre uses queuing systems to queue their customers' requests
until free resources become available. This means that if traffic
intensity levels exceed available capacity, customer's calls are not lost;
customers instead wait until they can be served. This method is used in
queuing customers for the next available operator.
A queuing discipline determines the manner in which the exchange
handles calls from customers. It defines the way they will be served, the
order in which they are served, and the way in which resources are
divided among the customers. Here are details of four queuing
disciplines:
 First in first out
This principle states that customers are served one at a time and that
the customer that has been waiting the longest is served first.
 Last in first out
This principle also serves customers one at a time, however the
customer with the shortest waiting time will be served first. Also
known as a stack.
 Processor sharing
Customers are served equally. Network capacity is shared between
customers and they all effectively experience the same delay.
 Priority
Customers with high priority are served first.
LIMITATIONS
 The assumptions of classical queuing theory may be
too restrictive to be able to model real-world situations
exactly. The complexity of production lines with
product-specific characteristics cannot be handled
with those models.
Goal Programming
 Goal programming is a branch of multiobjective
optimization, which in turn is a branch of multi-criteria
decision analysis (MCDA), also known as multiple-criteria
decision making (MCDM). This is an optimization
programme. It can be thought of as an extension or
generalisation of linear programming to handle multiple,
normally conflicting objective measures. Each of these
measures is given a goal or target value to be achieved.
Unwanted deviations from this set of target values are then
minimised in an achievement function. This can be a vector
or a weighted sum dependent on the goal programming
variant used.
History
 Goal programming was first used by Charnes, Cooper and
Ferguson in 1955, although the actual name first appear in a 1961
text by Charnes and Cooper. Seminal works by
Lee,Ignizio, Ignizio and Cavalier, and Romero followed.
Schniederjans gives in a bibliography of a large number of pre1995 articles relating to goal programming, and Jones and Tamiz
give an annotated bibliography of the period 1990-2000. A recent
textbook by Jones and Tamiz gives a comprehensive overview of
the state-of-the-art in goal programming.
 The first engineering application of goal programming, due to
Ignizio in 1962, was the design and placement of the antennas
employed on the second stage of the Saturn V. This was used to
launch the Apollo space capsule that landed the first men on the
moon.
Strengths and weaknesses
 A major strength of goal programming is its simplicity and ease of use.
This accounts for the large number of goal programming applications
in many and diverse fields. Linear Goal programmes can be solved
using linear programming software as either a single linear programme,
or in the case of the lexicographic variant, a series of connected linear
programmes.
 Goal programming can hence handle relatively large numbers of
variables, constraints and objectives. A debated weakness is the ability
of goal programming to produce solutions that are not Pareto efficient.
This violates a fundamental concept of decision theory, that is no
rational decision maker will knowingly choose a solution that is not
Pareto efficient. However, techniques are available. to detect when this
occurs and project the solution onto the Pareto efficient solution in an
appropriate manner.
 The setting of appropriate weights in the goal programming model is
another area that has caused debate, with some authors suggesting the
use of the Analytic Hierarchy Process or interactive methods for this
purpose.
APPLICATION IN HRM
A Scoring Model for Job Selection
 A graduating college student with a double major in
Finance and Accounting has received the following
three job offers:
 financial analyst for an investment firm in Chicago
 accountant for a manufacturing firm in Denver
 auditor for a CPA firm in Houston
 “The financial analyst position provides the best
opportunity for my long-run career advancement.”
 “I would prefer living in Denver rather than in Chicago
or Houston.”
 “I like the management style and philosophy at the
Houston CPA firm the best.”
 Clearly, this is a multicriteria decision problem.
 Considering only the long-run career advancement
criterion:
 The financial analyst position in Chicago is the best
decision alternative.
 Considering only the location criterion:
 The accountant position in Denver is the best decision
alternative.
 Considering only the style criterion:
 The auditor position in Houston is the best alternative.
 Steps Required to Develop a Scoring Model
Step 1: List the decision-making criteria.
Step 2: Assign a weight to each criterion.
Step 3: Rate how well each decision alternative
satisfies each criterion.
Step 4: Compute the score for each decision
alternative.
Step 5: Order the decision alternatives from highest
score to lowest score. The alternative with
the highest score is the recommended
alternative.
 Mathematical Model
Sj = S wi rij
i
where:
rij = rating for criterion i and decision alternative j
Sj = score for decision alternative j
 Step 1: List the criteria (important factors).
 Location
 Management
 Salary
 Prestige
 Job Security
 Enjoyable work
 Five-Point Scale Chosen for Step 2
Importance
Weight
Very unimportant
1
Somewhat unimportant
2
Average importance
3
Somewhat important
4
Very important
5
 Step 2: Assign a weight to each criterion.
Criterion
Location
Management
Salary
Prestige
Job security
Enjoyable work
Importance
Weight
Very important
Average importance
Somewhat important
Average importance
Somewhat unimportant
Somewhat important
Very important
5
3
4
3
2
4
5
 Nine-Point Scale Chosen for Step 3
Level of Satisfaction
Extremely low
Very low
Low
Slightly low
Average
Slightly high
High
Very high
Extremely high
Rating
1
2
3
4
5
6
7
8
9
 Step 3: Rate how well each decision alternative satisfies
each criterion.
Criterion
Location
Management
Salary
Prestige
Job security
Enjoyable work
Decision Alternative
Analyst Accountant
Auditor
Chicago
Denver
Houston
8
6
4
3
8
7
5
6
9
6
7
5
7
5
4
4
7
6
8
6
5
 Step 4: Compute the score for each decision alternative.
Decision Alternative 1 - Analyst in Chicago
Criterion
Weight (wi ) Rating (ri1)
wiri1
5
x
8
=
40
Location
3
3
9
Management
4
5
20
Salary
3
6
18
Prestige
2
7
14
Job security
4
4
16
Enjoyable work
5
8
40
Score
157
 Step 4: Compute the score for each decision
alternative.
Sj = S wi rij
i
S1 = 5(8)+3(3)+4(5)+3(6)+2(7)+4(4)+5(8) = 157
S2 = 5(6)+3(8)+4(6)+3(7)+2(5)+4(7)+5(6) = 167
S3 = 5(4)+3(7)+4(9)+3(5)+2(4)+4(6)+5(5) = 149
 Step 4: Compute the score for each decision alternative.
Criterion
Location
Management
Salary
Prestige
Job security
Enjoyable work
Score
Decision Alternative
Analyst Accountant
Auditor
Chicago
Denver
Houston
40
30
20
9
24
21
20
24
36
18
21
15
14
10
8
16
28
24
40
30
25
157
167
149
 Step 5: Order the decision alternatives from highest
score to lowest score. The alternative with the
highest score is the recommended alternative.
 The accountant position in Denver has the highest score
and is the recommended decision alternative.
 Note that the analyst position in Chicago ranks first in 4
of 7 criteria compared to only 2 of 7 for the accountant
position in Denver.
 But when the weights of the criteria are considered, the
Denver position is superior to the Chicago job.
Fuzzysets
Operations Research present state and future
trends are analyzed from the Fuzzy-Sets-based
methodologies
Every researcher in OR models knows that data in this
field of human science are deterministic or random or
uncertain. Of course, if measurements are available, the
scientist must use such strong data but, in many case, a lot
of data are weaker and subjectivity is necessary. To combine
in a good way, at the best, taking account the present level
of knowledge, it is what we can do. Fuzzy sets—and
specially, fuzzy numbers—is a good tool for the OR analyst
facing partial uncertainty and subjectivity. We are able to
associate with several hybrid operators, probabilistic and
uncertain data.
The goal: to build a model faithful at the best and
intelligible for the decision maker
Fuzzy-Sets-based models in
Operations Research
 fuzzy optimization,
 preference modelling,
 linguistic modelling and
 decision models
The role of Fuzzy-Sets-based
models
The role played by Fuzzy Sets in the field of OR is absolutely
essential, they allow us to model more than adequately those
situations in which certain ambiguity arises of a nonprobabilistic type, as well as in a large part of human beings'
reasoning mechanisms.
In fact, as Prof. L.A. Zadeh pointed out :
"A fundamental contribution of fuzzy logic is a methodology
for computing with words (CW) which mimics human
reasoning. It is this methodology that in one form or another is
already used in most of the applications of fuzzy logic. In coming
years, however, computing with words, based on fuzzy logic, is
likely to emerge as a field of key importance in its own right".
From this point of view, with which we all agree, and provided
that OR, and the interface OR-IT, is a rather wide field of work, it
is very difficult to forecast to any extent what will be the future
for each of the OR key topics
APPLICATION IN HRM
 Job assignment is one of most important functions in
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human resource management.
It presents a new model which optimizes the multiobjectives allocation problem by using fuzzy logic strategic.
The fuzzy experience evaluation matrix indicates the score
of certain employee on certain task. The values in the
matrix are based on the employee’s experience.
Fuzzy appraisal decision-making method provides fuzzy
synthesis appraisal matrix referring to individual
experience value.
Then Task-Arrange or Hungarian Algorithm provides the
final solution with the help of our proposed experience
matrix.
PREVIOUS MATHEMATICAL MODELS
The review of existing human resource allocation models
for a CPA firm shows that there are major shortcomings in
the previous mathematical models.
 linear programming models cannot handle multiple
objective human resource allocation problems for a CPA
firm.
 goal programming or multiple objective linear
programming (MOLP) cannot deal with the organizational
differentiation problems. To reduce the complexity in
computing the trade-offs among multiple objectives
The fuzzy solution can help the CPA firm make a realistic
decision regarding its human resource allocation problems
as well as the firm''s overall strategic resource management
when environmental factors are uncertain.
Forecasting techniques for
HRM
WHAT IS FORECASTING ?
Forecasting is the process of making statements
about events whose actual outcomes (typically) have
not yet been observed. A commonplace example might
be estimation of the expected value for some variable
of interest at some specified future date
WHY DO WEE NEED FORECASTING IN
HRM?
Human Resource Management has critical role to play in corporate
strategic plan. All the HR functions contribute positively to achieving
the objective. The main task of HR is to support other departments to
have the best people. Forecasting helps to match the requirements and
the availabilities of employees. Matching Human resources with
planned organizational activities for the present and the future is one
of the main problems faced by an organization. Human resources have
a certain degree of inflexibility, both in terms of their development and
their utilization. It takes several months to recruit, select, place, and
train the average employee; in the case of higher-echelon Management
personnel in large organizations, the process may take years. Decisions
on personnel recruitment and development are strategic and produce
long-lasting effects. Therefore, Management must forecast the demand
and supply of Human resources as part of the organization’s business
and functional planning processes. Long-term business requirements,
promotion policies, and recruitment (supply) possibilities have to be
matched so that Human resources requirements and availability
estimates (from both internal and external sources) correspond
sufficiently
Factors that an organization considers
before choosing a technique
 Organization's environment
 Organization size.
 Organization's budget
 Perceived uncertainty in labor markets and
economy
 Competition
THERE TWO BASIC DIFFERENTIATION
IN FORECASTING TECHNIQUES UESD
 Qualitative Forecasting Techniques
Qualitative forecasts are essentially educated guesses
or estimates by individuals who have some knowledge
of previous HR availability’s or utilization
 Technique Description
1. Nominal Group
A group of four or five participants is asked to present their views regarding
labor forecasts. These views are written down, with no discussion until all of
the members have advanced their positions. The group then discusses the
information presented and, subsequently, a final ballot is taken to determine
its judgment.
2. Delphi Technique
This technique calls for a facilitator to solicit and collate Written, expert
opinions on labor forecasts. After answers are received, a summary of the
information is developed and distributed t the experts, who are then requested
to submitted revised forecasts. experts never meet face-to-face, but rather
communicate through the facilitator.
3. Replacement Planning
Forecasting estimates are based on charting techniques, which identify current
job incumbents and relevant information about each of them. This
information typically includes a brief assessment of performance and
potential, age length of time in current position, and overall length of service.
4. Allocation Planning
This technique involves judgments about labor supply or demand by observing
the movement of employees through positions at the same organizational
level.
 Quantitative Forecasting Techniques
There are several quantitative methods for
determining labor supply and demand
Technique Description
1. Regression Model
Fluctuations in labor levels are projected using relevant
variables, such as sales.
2. Time-Series Model
Fluctuations in labor levels are projected by isolating trend,
seasonal, cyclical, and irregular effects.
3. Economic Model
Fluctuations in labor levels are projected using a specified
form of the production function.
4. Linear Programming Model
Fluctuations in labor levels are analyzed using an objective
function as well as organizational and environmental
constraints.
5. Markov Model
Fluctuations in labor levels are projected using historical
transition rates.
Other models
 Managerial Judgment :- This techniques is very simple. In
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this, manager sit together, discuss and arrive at a figure which
would be the future demand for labor. The technique may
involve a ‘bottom-to-top’ or ‘top-to-bottom’ approach
Trend Analysis:- Method which forecast employments
requirements on the basis of some organizational index
Ratio Analysis :- Another approach , Ratio analysis , means
making forecasts based on the ratio between.
Scatter Plot:- A graphical method used to help identify the
relationship between two variables. A scatter plot is another
option.
Computerized Forecast:- The determination of future staff
needs by projecting a firm’s sales, volume of production, and
personnel required to maintain this required volume of output,
using computers and software packages.
 Econometric Models:- Econometric models for
estimation Past statistical data are analyzed in the hope
that it will prove possible to describe precisely the
relationships between a number of variables in
mathematical and statistical terms.
 Nominal Group Technique :- The nominal group
technique is a decision making method for use among
groups of many sizes, who want to make their decision
quickly, as by a vote, but want everyone’s opinions taken
 H R Budget and Planning Analysis :- this approach is
through budget and planning analysis. When new ventures
complicate employment planning.
 Scenario Forecasting :-Scenario techniques is used to
explore the likelihood of possible future developments and
changes and to identify the interaction of uncertain future
trends and events.
 Work Study Technique :- Work study technique is based
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on the volume operation and work efficiency of personnel.
Delphi Technique:- This technique calls for a facilitator to
solicit and collate written, expert opinion on labor forecast.
developed and distributed to the expert, who are than
requested to submit revised forecast
Regression Analysis:- Regression analysis identifies the
movement of two or more inter-related series. It is used to
measure the changes in a variable as a result of changes in
other variables
Workload Analysis :- It is a method that uses information
about the actual content of work based on a job analysis of
the work.
Job Analysis :- Job analysis helps in finding out the
abilities or skil9ls required to do the jobs efficiently.
THANK YOU!
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