by: J. B. Nangpuhan II (MPA Student, Chonnam National University). Adviser: Dr. G. C. Jang, Policy Analysis and Evaluation.
I. Policy Analysis
A. Concepts
Policy analysis is determining which of various alternative policies will most achieve a given set of goals in light of the relations between the policies and the goals. Policy analysis can be divided into two major fields:
1. Analytical and descriptive – policy analysis attempts to explain policies and their development.
2. Prescriptive – policy analysis is involved with formulating policies and proposals, like, to social welfare.
B. Policy analysis is closely related to the following concepts: management science, policy evaluation, benefit-cost analysis, quantitative decision-making theory, forecasting.
II. Management Science
A. Concepts
Also called operations research, the application of the scientific approach to the analysis and solution of managerial decision problems.
B. Characteristics
1. A primary focus on managerial decision making.
2. The application of scientific approach to decision making.
3. The examination of the decision situation from a broad perspective, that is, the application of a systems approach.
4. The use of methods and knowledge from several disciplines.
5. A reliance on formal mathematical models (scientific models).
6. The extensive use of electronic computers.
C. Uses
Production, long-range planning, advertisements, sales, marketing, inventory, top management, research, etc.
D. Advantages
1. Systematic and logical approach to decision making.
2. Helps communication within the organization through consultation with experts in various areas.
3. Permits a thorough analysis of a large number of alternative options.
4. Enables evaluation of situations involving uncertainty.
5. Allows decision maker to judge how much information to gather in a given problem.
6. Increases the effectiveness of the decision.
7. Enables quick identification of the best available solution.
E. Limitations
1. Time-consuming.
2. Lack of acceptance by decision makers.
3. Assessments of uncertainties are difficult to obtain.
4. Evaluates the decision in terms of a sometimes oversimplified model of reality.
5. Can be expensive to undertake, relative to the size of the problem.
6. Studies may be shelved for various reasons, resulting in an unproductive expense.
III. Game Theory
A. Concepts
A scientific process of decision making under conflict or competition.
B. Characteristics
1. Two or more decision makers are involved and the consequences (payoff) to each depends on the courses of action taken by all.
2. Objectives do not coincide and may completely opposed.
3. Each party is trying to maximize his or her overall welfare at the expense of the others. The result is either win or loses.
C. Uses
Making strategies, international military conflicts, labor-management negotiations, potential mergers.
D. Assumptions and Formats
1. Two or more players are involved with the same, but opposing, objectives.
2. Simultaneous decisions are assumed in all game situations.
3. Each party is interested in maximizing his or her welfare at the expense of the other.
4. It is generally assumed that most instances involve repetitive situations, series of games.
5. The average payoff per play is termed the value of the game. A game whose value is zero is called a fair game.
6. It is assumed that each player knows all possible courses of action (finite number) open to the opponent as well as all anticipated payoffs.
E. Limitations
1. Concepts such as moves, strategies, complete information, payoff matrix, and simultaneous decisions are theoretical idealizations with intuitive meaning but very little practicability.
2. The two-person, zero-sum game, the only game model completely solved mathematically, is oversimplified.
3. Behavioral problems such as convincing the players of the best strategy may interfere with any analytical solution.
F. Why study game theory? Advantages
1. Game theory stimulates us to think about conflicts in a novel way.
2. Game theory leads us to see why the existing theory is inadequate.
3. The theory is applicable to almost any type of conflict (military, economic, political, and social).
4. The game formulation often helps explain much of the phenomenon being observed.
5. Game theory formulations and solutions may give decision makers a better understanding of the intricacies of life and help explain social behavior.
IV. Decision Analysis
A. Concepts
Decision theory, a quantitative decision analysis procedure applied to decision making, attempts to answer the following questions: what is the degree of risk that is assumed?, how does it relate to the available alternatives?, can the risk be reduced? Decision tables and decision trees are involved in this process.
B. Decision Tables
1. Also known as payoff table.
2. Characteristics of decision tables:
a. Decision making under certainty – complete information is assumed (deterministic).
b. Decision making under risk – partial information is assumed (probabilistic or stochastic decision situations).
c. Decision making under uncertainty – limited information is assumed.
3. The relationship between decision situation and different management science techniques:
V. Decision Trees
A. Concepts
A graphical presentation of decision tables in the form of a tree in a sequential or multiperiod decision process.
B. Advantages
1. Decision tree shows, at a glance, when decisions are expected to be made, what possible consequences are, and what the resultant payoffs are expected to be.
2. The results of the computations are depicted directly on the tree, simplifying the analysis.
C. Composition of a decision tree
1. Decision points – designated by a square, the decision maker must select one alternative course of action.
2. Chance points – designated by a circle, a chance event is expected at this point in the process, that is, one finite number of states of nature is expected to occur.
VI. Decision Under Uncertainty
A. Concepts
Decision making under uncertainty is more difficult than it is for risk or certainty.
B. Criteria of choice
The criterion of equal probabilities, criterion of pessimism (maximin or minimax), criterion of optimism (maximax or minimin), coefficient of optimism, and criterion of regret.
C. Limitations
1. All five criteria presented here have some deficiencies and will usually point to different selections of alternatives.
D. Reminders
1. In management, decision making under uncertainty should be avoided because the results can be disastrous.
2. Enough information should be acquired so that decisions can be made at least under calculated risk, or, at best, under uncertainty.
VII.Utility and Decision Making Theory
A. Concepts
Utility theory has been found to be a useful instrument in analyzing decision making under risk.
B. Characteristics
1. Utility is measured in arbitrary units called ‘utiles’.
2. Money is not an absolute measure as presented in three cases below:
a. The decision maker finds difficult in expressing the values of some of the outcomes of his or her decisions in terms of monetary payoffs.
b. EMV assumes the decision maker is willing to risk losing money in the short run as long as he is better off in the long run. In reality, however, decision makers frequently act to avoid risk in the short run.
c. EMV assumes linear relationship between the amount of money and its value (or utility). In reality, however, it has been observed that with an increase in the amount of wealth accumulated, the value of additional money decreases.
C. Assumptions
1. Utility can be measured on a cardinal scale, e.g.: 1, 2, 3, and so on.
2. Utilities of different objects can be added together, this called the additivity assumption.
D. Utility in Multiple Goals
Concept: It is rare nowadays to have a single goal
Limitations and difficulties:
1. It is usually difficult to obtain an explicit statement of the organization’s goals.
2. Various participants assess the importance (priorities) of the various goals differently.
3. The decision maker may change the importance assigned to specific goals with the passage of time or in different decision situations.
4. Goals and subgroups are viewed differently at various level of the organization and in various departments.
5. The goals themselves are dynamic in response to continuous changes in the organization and its environment.
6. The relationship between alternative and their impact on goals may be difficult to quantify.
Solutions to multiple goals:
1. Expression of goals as requirements (constraints) – applied in linear programming.
2. Conversion of goals to a single scale, e.g.: dollars.
3. Expressing one goal in terms of another (trade-offs).
4. Using a utility or point system.
5. Goal programming – method of treating certain multiple goals involving problem of linear programming.
VIII. Baye’s Theorem
A. Concepts
Baye’s theorem is a procedure that is used when revising the probabilities of the states of nature for evaluating the subdecision regarding the acquisition of additional information needed to revise the prior probabilities.
B. Characteristics
1. The revised probabilities depend on the nature of the additional information, which is found only after the information is acquired.
2. Analyzing the situation prior to the acquisition of the information cannot prescribe the best decision alternative. Instead, it derives decision policy or strategy.
3. A decision policy does recommend several specific alternatives, one for every possible outcome of the additional information.
C. Steps in using revised probabilities
1. The decision situation is evaluated with the prior probabilities (initial evaluation).
2. Assuming that it is impossible to acquire perfect information, the possibility of acquiring partial information is checked (check track record).
3. Revised posterior probabilities are computed, one for each possible outcome of the prediction (compute revised probabilities).
4. The probabilities of each of the research outcomes or indicators are computed (compute the indicator or marginal probabilities).
5. Construct a decision tree.
6. Solve the decision tree.
7. The expected value of the additional information is computed (compute the expected value of imperfect information).
8. A decision on whether or not to acquire the information is made (decide whether or not to acquire the information).
9. An alternative in the original problem is selected (select an alternative).
IX. Analytic Hierarchy Process
A. Concepts
The analytic hierarchy process is a decision model based on structuring the problem elements in terms of how the alternative solutions (the outcome) influence decision criteria. Satisfaction of which help describe how a particular solution contribute to the accomplishment of the decision problem’s main objective (measure of effectiveness).
B. Keywords and characteristics
1. Goals à Criteria à Alternative.
2. Determine which alternative will contribute the mist in accomplishing the goals by comparison.
3. The question: “Which one is more important?” should be used to compute alternatives.
4. The “pairwise comparison scale” developed by Saaty will be used to rate/value importance of each alternative.
5. The use of reciprocals to give value to the other side of the alternative.
C. Steps for a 3-level hierarchy
1. Determine the goal and the alternatives available to accomplish the goal.
2. Determine the criteria in selecting the alternatives. Then draw a structure for the hierarchy process.
3. Compare each criterion according to their importance using the pairwise comparison scale by Saaty. Compute for the ratio, geometric mean, and normalize each to get a resultant.
4. Determine the importance of the sets of courses to each criterion by analyzing the third level of the hierarchy. This is done by constructing judgment matrices, one for each criterion.
5. Organize the results obtained in a decision table.
6. Compute for the composite hierarchical priorities of each alternative based on each criteria.
7. Select the criteria with the highest composite hierarchical priority.
D. Uses
Choosing a job, buying a car, selecting a stock portfolio, choosing a corporate research program, evaluating alternatives for improving health care program, and so on.
X. Waiting Lines (Queuing Theory)
A. Concepts
Waiting line (queuing) theory is a tool used mainly for computing measure of performance of systems providing services. This information is used by management to design service systems and to improve their operations. The queuing methodology is basically a descriptive tool of analysis similar to Markov analysis, which is predicting the behavior of the system.
B. Formation of the queue
The main reason a queue forms when the average service rate is faster than the average arrival rate is that both are fluctuating in an unpredictable manner. As a result, there are short-term variations in both the arrival and service rates.
C. Characteristics of the waiting line situation
1. The demand for service is unstable.
2. Difficulty in needing the demand immediately on request, especially during rush hours.
3. The only way that demand can be immediately supplied, all the time, is to build a high service capacity that can always meet peak demand.
4. Whenever time exceeds capacity, a waiting line or queue is formed.
5. For the management to find appropriate level of service, queuing or waiting line theory is applied.
D. Uses
1. Determining the number of an emergency room in a hospital.
2. Determining the number of runways at an airport.
3. Determining the number of elevators in a building.
4. Determining the number of traffic lights and their frequency of operation.
5. Determining the number of flights between two cities.
6. Determining the number of first-class seats in an airplane.
7. Determining the size of a restaurant.
E. Structure of a queuing system
1. The customers and their source.
2. The arrival process.
3. The service facility and the service process.
4. The queue (waiting line).
F. Managerial application of waiting line theory
This process involves the use of computed measures of performance for selecting an alternative solution to a queuing problem, usually among small number of alternatives. The entire process involves three steps:
1. Establish the measures of performance (or the operating characteristics) of the queuing system.
2. Compute the measures of performance (result variables).
3. Conduct an analysis.
G. Assumptions
Arrival process:
1. An infinite population is assumed.
2. Individual arrivals are assumed in all cases.
3. If the arrival is nonscheduled, frequency distribution is used.
The waiting line:
1. First-in, first-served system in assumed – queue discipline.
2. For the organization of the queue, it is assumed that there is one line for several parallel service facilities.
3. For the behavior in a queue, it is assumed that the customer enters the system, stays in the line (if necessary), receives the service, and leaves. If it is not, simulation can be applied to find out the behavior of the queuing system.
H. Major objective of waiting line theory
Prediction of the behavior of the system as reflected in its operating characteristics or measures of performance.
XI. Markov Analysis
A. Concepts
This was developed by a Russian mathematician, A. Markov, in 1907. It is concerned with the prediction of market shares in a dynamic environment. It is used to determine the behavior of the “system” over time. It is also called a ‘dynamic decision making’. Markov analysis is a descriptive analysis, not normative analysis. Hence, it is similar to the waiting line theory.
B. Features
1. The situation occurs in a chance environment consisting of two or more possible outcomes that occur at the end of a well-defined, usually fixed period. This is called stochastic (or probabilistic) process. Thus, we are now dealing with analysis and prediction under risk.
2. The transition involves a multiperiod case. The probabilities of switching are termed the transition probabilities of the stochastic process.
3. The situation is dynamic in nature and the customers make a sequence of decisions.
4. The process is observed after each transition and is governed by a matrix of transition probabilities.
C. Markov process
1. Consider this situation, if a customer’s brand choice in any given month depends only on his or her choice the month before, the stochastic process is called a Markov process.
2. If the transition probabilities of a customer’s switching from one brand (state) to another remain constant over time, then the Markov process is called a homogenous Markov chain.
D. Characteristics of a Markov analysis
1. As a descriptive tool, the major objective of Markov chain analysis is the prediction of the future behavior of managerial systems.
2. A prediction can be achieved using decision trees or simulation.
E. Advantages
1. Markov analysis can be computed easily and very rapidly.
2. Small problems can be solved manually.
3. For larger problems, a standard computer package can be used.
F. Assumptions of Markov analysis
1. The system has a finite number of discrete (separate) states, none of which is “absorbing” – a state that, once entered, cannot be left.
2. The system’s condition (state) in any given period depends only on its condition in the preceding period and on the transition probabilities.
3. The transition probabilities are constant over time.
4. Change in the system may occur once and only once each period (e.g.: each month).
5. The transition periods occur with regularity.
G. Conditional state probabilities
Management may be interested in finding out the state probabilities in terms of the chance of a particular purchase buying a particular brand, given that he or she previously purchased Brand X. These are called conditional state probabilities.
H. Steady state or Equilibrium
One of the major properties of Markov chain is that, in the long-run, the process usually stabilizes. A stabilized system is said to approach steady state or equilibrium when the system’s state probabilities have become independent of time.
I. Absorbing state
Concepts: A system is said to be in an absorbing state if, once there, it cannot exit to some other state. Example, bankrupt business, a river or lake destroyed by pollution and sediment.
Uses: Markov chains with absorbing states can be applied to business situations dealing with accounts receivable analysis, like extending credits to customers.
J. Difficulties/Limitations of Markov analysis
1. It is difficult to obtain the transition matrix. Although using historical data or subjective data can solve it.
K. Uses of Markov analysis
Replacement, maintenance, brand loyalty, investment evaluation, management of ecology.
XII.Linear Programming
A. Concepts
Linear programming I a powerful tool of management science, designed to solve allocation problems. It is a model that enables an efficient search for the optimal solution.
B. Formulation
Management science models are composed of three component models: the decision (controllable) variables, the environment (uncontrollable) parameters, and the result (dependent) variables. The LP model is composed of the same components but they assume different names: the decision variables (controllable), the objective function (result variables), and the constraints (uncontrollable parameters).
C. Terminology of LP
1. Decision variables (e.g.: X1, X2, and so on).
2. Objective function. This is the mathematical expression.
3. Optimization. LP attempts to either maximize or minimize the values of the objective function.
4. Constraints. The maximization or minimization is subject to a set of constraints.
5. Input-output (technology) coefficient, e.g. 1X1 + 1X2 ≧ 300.
6. Capacities, e.g. 1X1 +1X2 ≧ 300 also called requirements.
7. Nonnegativity. X1 ≧0, X2 ≧0.
D. Advantages of LP
1. LP provides optimal solution in a very efficient manner.
2. LP provides additional information concerning the value of the resources that are allocated.
E. Assumptions (also known as Limiting assumptions)
1. Certainty. It is assumed that all data involved in the linear programming problem are known with certainty.
2. Linear objective function. It is assumed that the objective function is linear – satisfying additivity and homogeneity properties.
3. Linear constraints. The constraints are all assumed to be linear.
4. Nonnegativity. All decision variables take nonnegativity values.
5. Additivity. It is assumed that the total utilization of each resource is determined by adding together that portion of the resource required for the production of each of the various products or activities.
6. Divisibility. It is assumed that the unknown variables X1, X2 ……, are continuous, that is, they can take any fractional value. If the variables are indivisible, a problem in integer programming exists.
7. Independence. Complete independence of coefficient is assumed, both among activities and resources.
8. Proportionality. The requirement that the objective function and constraints must be linear is a proportionality requirement.
XIII. Goal Programming
A. Concepts and advantage
1. GP is an extension of LP but it is more than just an extension. GP enables the decision maker to analyze multiple goal aspiration levels. It also allows deviations from targets, thus introducing flexibility into the decision making process. Decision makers can also change their preferences and allow trade-offs among the goals.
2. For such situation to be treated by GP it is necessary to rank (prioritize) the goals, and, preferably, assign weights that indicate their relative importance.
3. GP approach is currently applied efficiently only to linear situations (linear function and constraints).
4. The “what if” procedures used during the application of GP make it a very attractive tool for the practicing manager.
5. This can be used to support a group of decision makers with diverse interests.
B. Uses (types of analysis)
1. It is used to determine the required resources to achieve a set of desired objectives.
2. It is used to determine the degree of attainment of the goals with the available resources.
3. It is used to provide the best satisfying solution under a varying amount to resources and priorities of the goals.
C. The backbone of GP
1. Deviations, these are the amount by which goals are either overachieved or underachieved.
2. Priorities and weights of the goals, prioritize by ordinal (order of importance, e.g. P1, P2), cardinal (e.g. 1, 2, 3, and so on), or a mixture of both.
3. Dimension of the goals, the objective function of the GP attempts to minimize the sum of the undesirable deviations weighted by their importance.
D. Structure of GP (four elements)
Decision variables, system constraints, goals constraints, objective function.
E. Comparison table between LP and GP
References:
Jang, G.C. (2011). 정책분석론, Lecture Note. South Korea: 전남대학교 행정학과, Chonnam National University.
Turban, E. & Meredith, J. R. ( 1988). Fundamentals of Management Science, 4th Ed. USA: Business Publications, Inc.
I. Policy Analysis
A. Concepts
Policy analysis is determining which of various alternative policies will most achieve a given set of goals in light of the relations between the policies and the goals. Policy analysis can be divided into two major fields:
1. Analytical and descriptive – policy analysis attempts to explain policies and their development.
2. Prescriptive – policy analysis is involved with formulating policies and proposals, like, to social welfare.
B. Policy analysis is closely related to the following concepts: management science, policy evaluation, benefit-cost analysis, quantitative decision-making theory, forecasting.
II. Management Science
A. Concepts
Also called operations research, the application of the scientific approach to the analysis and solution of managerial decision problems.
B. Characteristics
1. A primary focus on managerial decision making.
2. The application of scientific approach to decision making.
3. The examination of the decision situation from a broad perspective, that is, the application of a systems approach.
4. The use of methods and knowledge from several disciplines.
5. A reliance on formal mathematical models (scientific models).
6. The extensive use of electronic computers.
C. Uses
Production, long-range planning, advertisements, sales, marketing, inventory, top management, research, etc.
D. Advantages
1. Systematic and logical approach to decision making.
2. Helps communication within the organization through consultation with experts in various areas.
3. Permits a thorough analysis of a large number of alternative options.
4. Enables evaluation of situations involving uncertainty.
5. Allows decision maker to judge how much information to gather in a given problem.
6. Increases the effectiveness of the decision.
7. Enables quick identification of the best available solution.
E. Limitations
1. Time-consuming.
2. Lack of acceptance by decision makers.
3. Assessments of uncertainties are difficult to obtain.
4. Evaluates the decision in terms of a sometimes oversimplified model of reality.
5. Can be expensive to undertake, relative to the size of the problem.
6. Studies may be shelved for various reasons, resulting in an unproductive expense.
III. Game Theory
A. Concepts
A scientific process of decision making under conflict or competition.
B. Characteristics
1. Two or more decision makers are involved and the consequences (payoff) to each depends on the courses of action taken by all.
2. Objectives do not coincide and may completely opposed.
3. Each party is trying to maximize his or her overall welfare at the expense of the others. The result is either win or loses.
C. Uses
Making strategies, international military conflicts, labor-management negotiations, potential mergers.
D. Assumptions and Formats
1. Two or more players are involved with the same, but opposing, objectives.
2. Simultaneous decisions are assumed in all game situations.
3. Each party is interested in maximizing his or her welfare at the expense of the other.
4. It is generally assumed that most instances involve repetitive situations, series of games.
5. The average payoff per play is termed the value of the game. A game whose value is zero is called a fair game.
6. It is assumed that each player knows all possible courses of action (finite number) open to the opponent as well as all anticipated payoffs.
E. Limitations
1. Concepts such as moves, strategies, complete information, payoff matrix, and simultaneous decisions are theoretical idealizations with intuitive meaning but very little practicability.
2. The two-person, zero-sum game, the only game model completely solved mathematically, is oversimplified.
3. Behavioral problems such as convincing the players of the best strategy may interfere with any analytical solution.
F. Why study game theory? Advantages
1. Game theory stimulates us to think about conflicts in a novel way.
2. Game theory leads us to see why the existing theory is inadequate.
3. The theory is applicable to almost any type of conflict (military, economic, political, and social).
4. The game formulation often helps explain much of the phenomenon being observed.
5. Game theory formulations and solutions may give decision makers a better understanding of the intricacies of life and help explain social behavior.
IV. Decision Analysis
A. Concepts
Decision theory, a quantitative decision analysis procedure applied to decision making, attempts to answer the following questions: what is the degree of risk that is assumed?, how does it relate to the available alternatives?, can the risk be reduced? Decision tables and decision trees are involved in this process.
B. Decision Tables
1. Also known as payoff table.
2. Characteristics of decision tables:
a. Decision making under certainty – complete information is assumed (deterministic).
b. Decision making under risk – partial information is assumed (probabilistic or stochastic decision situations).
c. Decision making under uncertainty – limited information is assumed.
3. The relationship between decision situation and different management science techniques:
Management science techniques
|
Decision situations
| ||
Certainty
|
Risk
|
Uncertainty
|
|
| · Decision tables |
X
|
X
|
X
|
· Decision trees
|
X
|
X
| |
· Game theory
|
X
|
X
| |
· Baye’s theorem
|
X
|
X
| |
· Analytic hierarchy process
|
X
|
X
| |
· Waiting lines (queuing theory)
|
X
| ||
· Markov analysis
|
X
| ||
· Linear programming
|
X
| ||
· Goal programming
|
X
| ||
· Integer programming
|
X
| ||
· Simulation
|
X
|
X
| |
V. Decision Trees
A. Concepts
A graphical presentation of decision tables in the form of a tree in a sequential or multiperiod decision process.
B. Advantages
1. Decision tree shows, at a glance, when decisions are expected to be made, what possible consequences are, and what the resultant payoffs are expected to be.
2. The results of the computations are depicted directly on the tree, simplifying the analysis.
C. Composition of a decision tree
1. Decision points – designated by a square, the decision maker must select one alternative course of action.
2. Chance points – designated by a circle, a chance event is expected at this point in the process, that is, one finite number of states of nature is expected to occur.
VI. Decision Under Uncertainty
A. Concepts
Decision making under uncertainty is more difficult than it is for risk or certainty.
B. Criteria of choice
The criterion of equal probabilities, criterion of pessimism (maximin or minimax), criterion of optimism (maximax or minimin), coefficient of optimism, and criterion of regret.
C. Limitations
1. All five criteria presented here have some deficiencies and will usually point to different selections of alternatives.
D. Reminders
1. In management, decision making under uncertainty should be avoided because the results can be disastrous.
2. Enough information should be acquired so that decisions can be made at least under calculated risk, or, at best, under uncertainty.
VII.Utility and Decision Making Theory
A. Concepts
Utility theory has been found to be a useful instrument in analyzing decision making under risk.
B. Characteristics
1. Utility is measured in arbitrary units called ‘utiles’.
2. Money is not an absolute measure as presented in three cases below:
a. The decision maker finds difficult in expressing the values of some of the outcomes of his or her decisions in terms of monetary payoffs.
b. EMV assumes the decision maker is willing to risk losing money in the short run as long as he is better off in the long run. In reality, however, decision makers frequently act to avoid risk in the short run.
c. EMV assumes linear relationship between the amount of money and its value (or utility). In reality, however, it has been observed that with an increase in the amount of wealth accumulated, the value of additional money decreases.
C. Assumptions
1. Utility can be measured on a cardinal scale, e.g.: 1, 2, 3, and so on.
2. Utilities of different objects can be added together, this called the additivity assumption.
D. Utility in Multiple Goals
Concept: It is rare nowadays to have a single goal
Limitations and difficulties:
1. It is usually difficult to obtain an explicit statement of the organization’s goals.
2. Various participants assess the importance (priorities) of the various goals differently.
3. The decision maker may change the importance assigned to specific goals with the passage of time or in different decision situations.
4. Goals and subgroups are viewed differently at various level of the organization and in various departments.
5. The goals themselves are dynamic in response to continuous changes in the organization and its environment.
6. The relationship between alternative and their impact on goals may be difficult to quantify.
Solutions to multiple goals:
1. Expression of goals as requirements (constraints) – applied in linear programming.
2. Conversion of goals to a single scale, e.g.: dollars.
3. Expressing one goal in terms of another (trade-offs).
4. Using a utility or point system.
5. Goal programming – method of treating certain multiple goals involving problem of linear programming.
VIII. Baye’s Theorem
A. Concepts
Baye’s theorem is a procedure that is used when revising the probabilities of the states of nature for evaluating the subdecision regarding the acquisition of additional information needed to revise the prior probabilities.
B. Characteristics
1. The revised probabilities depend on the nature of the additional information, which is found only after the information is acquired.
2. Analyzing the situation prior to the acquisition of the information cannot prescribe the best decision alternative. Instead, it derives decision policy or strategy.
3. A decision policy does recommend several specific alternatives, one for every possible outcome of the additional information.
C. Steps in using revised probabilities
1. The decision situation is evaluated with the prior probabilities (initial evaluation).
2. Assuming that it is impossible to acquire perfect information, the possibility of acquiring partial information is checked (check track record).
3. Revised posterior probabilities are computed, one for each possible outcome of the prediction (compute revised probabilities).
4. The probabilities of each of the research outcomes or indicators are computed (compute the indicator or marginal probabilities).
5. Construct a decision tree.
6. Solve the decision tree.
7. The expected value of the additional information is computed (compute the expected value of imperfect information).
8. A decision on whether or not to acquire the information is made (decide whether or not to acquire the information).
9. An alternative in the original problem is selected (select an alternative).
IX. Analytic Hierarchy Process
A. Concepts
The analytic hierarchy process is a decision model based on structuring the problem elements in terms of how the alternative solutions (the outcome) influence decision criteria. Satisfaction of which help describe how a particular solution contribute to the accomplishment of the decision problem’s main objective (measure of effectiveness).
B. Keywords and characteristics
1. Goals à Criteria à Alternative.
2. Determine which alternative will contribute the mist in accomplishing the goals by comparison.
3. The question: “Which one is more important?” should be used to compute alternatives.
4. The “pairwise comparison scale” developed by Saaty will be used to rate/value importance of each alternative.
5. The use of reciprocals to give value to the other side of the alternative.
C. Steps for a 3-level hierarchy
1. Determine the goal and the alternatives available to accomplish the goal.
2. Determine the criteria in selecting the alternatives. Then draw a structure for the hierarchy process.
3. Compare each criterion according to their importance using the pairwise comparison scale by Saaty. Compute for the ratio, geometric mean, and normalize each to get a resultant.
4. Determine the importance of the sets of courses to each criterion by analyzing the third level of the hierarchy. This is done by constructing judgment matrices, one for each criterion.
5. Organize the results obtained in a decision table.
6. Compute for the composite hierarchical priorities of each alternative based on each criteria.
7. Select the criteria with the highest composite hierarchical priority.
D. Uses
Choosing a job, buying a car, selecting a stock portfolio, choosing a corporate research program, evaluating alternatives for improving health care program, and so on.
X. Waiting Lines (Queuing Theory)
A. Concepts
Waiting line (queuing) theory is a tool used mainly for computing measure of performance of systems providing services. This information is used by management to design service systems and to improve their operations. The queuing methodology is basically a descriptive tool of analysis similar to Markov analysis, which is predicting the behavior of the system.
B. Formation of the queue
The main reason a queue forms when the average service rate is faster than the average arrival rate is that both are fluctuating in an unpredictable manner. As a result, there are short-term variations in both the arrival and service rates.
C. Characteristics of the waiting line situation
1. The demand for service is unstable.
2. Difficulty in needing the demand immediately on request, especially during rush hours.
3. The only way that demand can be immediately supplied, all the time, is to build a high service capacity that can always meet peak demand.
4. Whenever time exceeds capacity, a waiting line or queue is formed.
5. For the management to find appropriate level of service, queuing or waiting line theory is applied.
D. Uses
1. Determining the number of an emergency room in a hospital.
2. Determining the number of runways at an airport.
3. Determining the number of elevators in a building.
4. Determining the number of traffic lights and their frequency of operation.
5. Determining the number of flights between two cities.
6. Determining the number of first-class seats in an airplane.
7. Determining the size of a restaurant.
E. Structure of a queuing system
1. The customers and their source.
2. The arrival process.
3. The service facility and the service process.
4. The queue (waiting line).
F. Managerial application of waiting line theory
This process involves the use of computed measures of performance for selecting an alternative solution to a queuing problem, usually among small number of alternatives. The entire process involves three steps:
1. Establish the measures of performance (or the operating characteristics) of the queuing system.
2. Compute the measures of performance (result variables).
3. Conduct an analysis.
G. Assumptions
Arrival process:
1. An infinite population is assumed.
2. Individual arrivals are assumed in all cases.
3. If the arrival is nonscheduled, frequency distribution is used.
The waiting line:
1. First-in, first-served system in assumed – queue discipline.
2. For the organization of the queue, it is assumed that there is one line for several parallel service facilities.
3. For the behavior in a queue, it is assumed that the customer enters the system, stays in the line (if necessary), receives the service, and leaves. If it is not, simulation can be applied to find out the behavior of the queuing system.
H. Major objective of waiting line theory
Prediction of the behavior of the system as reflected in its operating characteristics or measures of performance.
XI. Markov Analysis
A. Concepts
This was developed by a Russian mathematician, A. Markov, in 1907. It is concerned with the prediction of market shares in a dynamic environment. It is used to determine the behavior of the “system” over time. It is also called a ‘dynamic decision making’. Markov analysis is a descriptive analysis, not normative analysis. Hence, it is similar to the waiting line theory.
B. Features
1. The situation occurs in a chance environment consisting of two or more possible outcomes that occur at the end of a well-defined, usually fixed period. This is called stochastic (or probabilistic) process. Thus, we are now dealing with analysis and prediction under risk.
2. The transition involves a multiperiod case. The probabilities of switching are termed the transition probabilities of the stochastic process.
3. The situation is dynamic in nature and the customers make a sequence of decisions.
4. The process is observed after each transition and is governed by a matrix of transition probabilities.
C. Markov process
1. Consider this situation, if a customer’s brand choice in any given month depends only on his or her choice the month before, the stochastic process is called a Markov process.
2. If the transition probabilities of a customer’s switching from one brand (state) to another remain constant over time, then the Markov process is called a homogenous Markov chain.
D. Characteristics of a Markov analysis
1. As a descriptive tool, the major objective of Markov chain analysis is the prediction of the future behavior of managerial systems.
2. A prediction can be achieved using decision trees or simulation.
E. Advantages
1. Markov analysis can be computed easily and very rapidly.
2. Small problems can be solved manually.
3. For larger problems, a standard computer package can be used.
F. Assumptions of Markov analysis
1. The system has a finite number of discrete (separate) states, none of which is “absorbing” – a state that, once entered, cannot be left.
2. The system’s condition (state) in any given period depends only on its condition in the preceding period and on the transition probabilities.
3. The transition probabilities are constant over time.
4. Change in the system may occur once and only once each period (e.g.: each month).
5. The transition periods occur with regularity.
G. Conditional state probabilities
Management may be interested in finding out the state probabilities in terms of the chance of a particular purchase buying a particular brand, given that he or she previously purchased Brand X. These are called conditional state probabilities.
H. Steady state or Equilibrium
One of the major properties of Markov chain is that, in the long-run, the process usually stabilizes. A stabilized system is said to approach steady state or equilibrium when the system’s state probabilities have become independent of time.
I. Absorbing state
Concepts: A system is said to be in an absorbing state if, once there, it cannot exit to some other state. Example, bankrupt business, a river or lake destroyed by pollution and sediment.
Uses: Markov chains with absorbing states can be applied to business situations dealing with accounts receivable analysis, like extending credits to customers.
J. Difficulties/Limitations of Markov analysis
1. It is difficult to obtain the transition matrix. Although using historical data or subjective data can solve it.
K. Uses of Markov analysis
Replacement, maintenance, brand loyalty, investment evaluation, management of ecology.
XII.Linear Programming
A. Concepts
Linear programming I a powerful tool of management science, designed to solve allocation problems. It is a model that enables an efficient search for the optimal solution.
B. Formulation
Management science models are composed of three component models: the decision (controllable) variables, the environment (uncontrollable) parameters, and the result (dependent) variables. The LP model is composed of the same components but they assume different names: the decision variables (controllable), the objective function (result variables), and the constraints (uncontrollable parameters).
C. Terminology of LP
1. Decision variables (e.g.: X1, X2, and so on).
2. Objective function. This is the mathematical expression.
3. Optimization. LP attempts to either maximize or minimize the values of the objective function.
4. Constraints. The maximization or minimization is subject to a set of constraints.
5. Input-output (technology) coefficient, e.g. 1X1 + 1X2 ≧ 300.
6. Capacities, e.g. 1X1 +1X2 ≧ 300 also called requirements.
7. Nonnegativity. X1 ≧0, X2 ≧0.
D. Advantages of LP
1. LP provides optimal solution in a very efficient manner.
2. LP provides additional information concerning the value of the resources that are allocated.
E. Assumptions (also known as Limiting assumptions)
1. Certainty. It is assumed that all data involved in the linear programming problem are known with certainty.
2. Linear objective function. It is assumed that the objective function is linear – satisfying additivity and homogeneity properties.
3. Linear constraints. The constraints are all assumed to be linear.
4. Nonnegativity. All decision variables take nonnegativity values.
5. Additivity. It is assumed that the total utilization of each resource is determined by adding together that portion of the resource required for the production of each of the various products or activities.
6. Divisibility. It is assumed that the unknown variables X1, X2 ……, are continuous, that is, they can take any fractional value. If the variables are indivisible, a problem in integer programming exists.
7. Independence. Complete independence of coefficient is assumed, both among activities and resources.
8. Proportionality. The requirement that the objective function and constraints must be linear is a proportionality requirement.
XIII. Goal Programming
A. Concepts and advantage
1. GP is an extension of LP but it is more than just an extension. GP enables the decision maker to analyze multiple goal aspiration levels. It also allows deviations from targets, thus introducing flexibility into the decision making process. Decision makers can also change their preferences and allow trade-offs among the goals.
2. For such situation to be treated by GP it is necessary to rank (prioritize) the goals, and, preferably, assign weights that indicate their relative importance.
3. GP approach is currently applied efficiently only to linear situations (linear function and constraints).
4. The “what if” procedures used during the application of GP make it a very attractive tool for the practicing manager.
5. This can be used to support a group of decision makers with diverse interests.
B. Uses (types of analysis)
1. It is used to determine the required resources to achieve a set of desired objectives.
2. It is used to determine the degree of attainment of the goals with the available resources.
3. It is used to provide the best satisfying solution under a varying amount to resources and priorities of the goals.
C. The backbone of GP
1. Deviations, these are the amount by which goals are either overachieved or underachieved.
2. Priorities and weights of the goals, prioritize by ordinal (order of importance, e.g. P1, P2), cardinal (e.g. 1, 2, 3, and so on), or a mixture of both.
3. Dimension of the goals, the objective function of the GP attempts to minimize the sum of the undesirable deviations weighted by their importance.
D. Structure of GP (four elements)
Decision variables, system constraints, goals constraints, objective function.
E. Comparison table between LP and GP
Item
|
LP
|
GP
|
| Purpose | Optimize | Satisfice |
| Quantitative expressions | Linear | Linear |
| Structure | One objective, many constraints | Multiple objective, many constraints |
| Objective function | Decision variables | Deviational variables |
| Theory | Mature, many extensions | Relatively young |
| Applications | Many, varied | Few but varied |
| Computerized solutions | Generally available | Often not available |
XIV. Integer Programming
A. Concepts
1.
IP is a programming approach
that recognizes the indivisibility of one or more of the decision variables.
2.
A problem which requires that
some or all of the decision variables appearing in the optimal solution must be
nonnegative whole numbers (such as 0, 1, 2, ……) is classified as an IP problem.
This is called the indivisibility requirement.
B. Sensitivity analysis
Concept: An
analysis is made to find out how sensitive the optimal solution is to changes
in the input data. This technique uses two approaches: trial-and-error
approach, and use of an analytical approach.
C. Reminder for IP
1.
Notice that in LP, when more
than one optimal solution exists, there are an infinite number of optimal
solutions. In IP, this case can be found.
XV.Case of divisibility (LP)
vs. indivisibility (IP)
| Divisible | Indivisible |
| e.g.: 9 and 15 are both divisible by 3.
9/3=3, 15/3=5
|
e.g.:
9 and 16 have no common divisible number.
|
References:
Jang, G.C. (2011). 정책분석론, Lecture Note. South Korea: 전남대학교 행정학과, Chonnam National University.
Turban, E. & Meredith, J. R. ( 1988). Fundamentals of Management Science, 4th Ed. USA: Business Publications, Inc.
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