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**APPLICATION OF OPERATIONS RESEARCH IN HRM**

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**GROUP 5 PALLAV SUDHIR PRITY BALA ANUP SARANSH RAJAT HIRNI ANTHONY**

CHETNA ROGER

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**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.

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**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.

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**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.

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**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.

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**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.

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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.

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**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.

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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.

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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

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**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.

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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

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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

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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

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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.

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SIMULATION MODELING

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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.

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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

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**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

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**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.

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**A Brief History of Simulation**

Simulation has been around for some time. Early simulations were event-driven and frequently 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.

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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

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**Benefits Limitations 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 Building models and simulating is time-consuming for complex systems Simulation results / simulated systems are always approximations of the real ones Does not guarantee an optimal solution - lack of precise answers Should not be used indiscriminately in place of sound analytical models.

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**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.

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**Trends Virtual reality animations. Advanced statistical functions**

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.

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APPLICATIONS IN HRM With the OB Representation model and simulation system it is possible to simulate the organisational performance under different conditions like varying workload or unexpected critical incidents. 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.

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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.

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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

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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

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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.

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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. By changing variables, predictions may be made about the behavior of your workforce. The software packages for running computer-based simulation modeling makes the process modeling almost effortless.

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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.

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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.

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Markov Chains

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**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.

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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 situations- It 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.

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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. It answers two questions: “Where did people in each job category go?” “Where did people now in each job category come from? Personnel / Yield Ratios How much work will it take to recruit one new accountant?

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**SUCCESSION PLANNING REPLACEMENT CHART POSITION REPLACEMENT CARDS**

FOR EXECUTIVE POSITIONS POSITION REPLACEMENT CARDS FOR EACH INDIVIDUAL POSITION POSITION WESTERN DIVISION SALES MANAGER DANIEL BEALER Western Division Sales Mgr Outstanding Ready Now PRESENT PROMOTION POSSIBLE CANDIDATES CURRENT POSITION PERFORMANCE POTENTIAL SHARON GREEN Western Oregon Sales Manager Outstanding Ready Now GEORGE WEI N. California Sales Manager Outstanding Needs Training HARRY SHOW Idaho/Utah Sales Manager Satisfactory Needs Training TRAVIS WOOD Seattle Area Sales Manager Satisfactory Questionable

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**HUMAN RESOURCE INFORMATION SYSTEMS (HRIS)**

PERSONAL DATA Age, Gender, Dependents, Marital status, etc EDUCATION & SKILLS Degrees earned, Licenses, Certifications 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

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**Transition Matrix Example for an Auto Parts Manufacturer**

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**MARKOV ANALYSIS (STATISTICAL REPLACEMENT ANALYSIS)**

TO: A TRANSITION MATRIX FROM: TOP MID LOW SKILLED ASSY EXIT TOP MID LOW SKILL ASSY

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**MARKOV ANALYSIS – 2 (Captures effects of internal transfers)**

(Start = 3500) A TRANSITION MATRIX FROM/ TO: TOP MID LOW SKILLED ASSY EXIT TOP MID LOW SKILL ASSY END YR WITH: [358 left] NEED RECRUITS ? * tot NEED LAYOFFS ? (10)* (10) tot KEEP STABLE = Tot

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**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 MID LOW SKILL ASSY END YR WITH: [358 left] NEED RECRUITS ? * NEED LAYOFFS ? (60)* NEW LEVELS = tot

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**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.

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**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!!!

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Queuing Systems

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**The word queue comes, via French, from the Latin cauda, meaning tail.**

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**Queuing theory is the mathematical study of waiting lines, or queues**

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.

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Queuing theory is generally considered a branch of operations research because the results are often used when making business decisions about the resources needed to provide 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.

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**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:

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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.

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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.

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Goal Programming

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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.

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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 pre-1995 articles relating to goal programming, and Jones and Tamiz give an annotated bibliography of the period 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.

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**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.

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**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

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**The student made the following comments:**

“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.

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**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.

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**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.

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**Sj = S wi rij Mathematical Model i where:**

rij = rating for criterion i and decision alternative j Sj = score for decision alternative j

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**Step 1: List the criteria (important factors).**

Career advancement Location Management Salary Prestige Job Security Enjoyable work

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**Five-Point Scale Chosen for Step 2**

Importance Weight Very unimportant 1 Somewhat unimportant 2 Average importance 3 Somewhat important Very important

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**Step 2: Assign a weight to each criterion.**

Criterion Importance Weight Career advancement Very important 5 Location Average importance 3 Management Somewhat important 4 Salary Average importance 3 Prestige Somewhat unimportant 2 Job security Somewhat important 4 Enjoyable work Very important 5

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**Nine-Point Scale Chosen for Step 3**

Level of Satisfaction Rating Extremely low 1 Very low 2 Low 3 Slightly low 4 Average 5 Slightly high 6 High 7 Very high 8 Extremely high 9

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**Step 3: Rate how well each decision alternative satisfies each criterion.**

Analyst Accountant Auditor Criterion Chicago Denver Houston Career advancement Location Management Salary Prestige Job security Enjoyable work

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**Step 4: Compute the score for each decision alternative.**

Decision Alternative Analyst in Chicago Criterion Weight (wi ) Rating (ri1) wiri1 Career advancement x = 40 Location Management Salary Prestige Job security Enjoyable work Score

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**Step 4: Compute the score for each decision alternative. Sj = S wi rij **

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**Step 4: Compute the score for each decision alternative.**

Analyst Accountant Auditor Criterion Chicago Denver Houston Career advancement Location Management Salary Prestige Job security Enjoyable work Score

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**Step 5: Order the decision alternatives from highest**

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.

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Fuzzysets

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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

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**Fuzzy-Sets-based models in Operations Research**

fuzzy optimization, preference modelling, linguistic modelling and decision models

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**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 non-probabilistic 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

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APPLICATION IN HRM Job assignment is one of most important functions in human resource management. It presents a new model which optimizes the multi-objectives 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.

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**ADVANTAGE OF FUZZYSETS OVER 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.

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**Forecasting techniques for HRM**

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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

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**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

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**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

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**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

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**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.

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Quantitative Forecasting Techniques There are several quantitative methods for determining labor supply and demand

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**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.

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Other models Managerial Judgment :- This techniques is very simple. In 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.

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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 into traditional voting. 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.

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Work Study Technique :- Work study technique is based 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. After answer are received, a summary of the information is 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.

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