Conversion in Progress

Chapter 5
The Concerns of the Decision Sciences

While it may be difficult to establish a definition which unifies the vast field of the decision sciences, there are some characteristics of the methods commonly practiced in this field upon which most practitioners would agree. These include: a) The methods are principally algorithmic. b) Their purposes are primarily to optimize and secondarily to satisfice objectives. c) The methods are primarily numeric and quantitative.These characteristics are commonly applied to methods within the major area disciplines of; 1) Decision Analysis (DA) and a subset Multiple Criteria Decision Making (MCDM), 2) Statistics, 3) Forecasting, and 4) Mathematical Programming.Other areas contained within the decision sciences but which are emphasized less include Production Quality Control & Scheduling, Markovian Analysis, Project Management, Simulation, Game Theory, Queuing Theory, Inventory Control, Material Requirements Planning, Influence Diagramming, and Financial Modeling. Often the study of these techniques appear within the disciplines of management science and operations research. We will now look at the four major areas outlined above with a particular eye toward demonstrating how the methods in each area contribute to problem solving, decision making, and overcoming cognitive weaknesses. Decision Analysis/MCDM MethodsThere are a number of decision techniques which have been developed to provide a rational model for decision making. The term for the body of these techniques is Decision Analysis (DA). Multiple Criteria Decision Making (MCDM) was a term originally ascribed to the body of techniques known as linear programming, but now MCDM and DA are largely used interchangeably. These techniques may contain some or all the elements of the following general decision model. ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ³ Goal/Problem ³ ³ Alternatives ³ ³ Criteria or Attributes (may include sub-criteria) ³ ³ Preference or Likelihood of Occurrence (Uncertainty) ³ ³ Measurement Scales (e.g. $, yards, horsepower,yes/no) ³ ³ Synthesis Technique ³ ³ ³ ³ Figure 5.1 Elements of The General Decision Model ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙAs an example a goal may be to select a new automobile. Alternatives involved with this goal might include a BMW 325i, an Acura Legend, and a Oldsmobile Cutlass. Criteria would include such common characteristics as cost, performance, obsolescence period, and styling. Preference would relate to a criteria such as styling. Likelihood would relate to a criteria such as maintenance. The comparison scales would differ depending on the criteria. For example $ would apply for costs, an ordinal scale such as great/good/fair/poor for styling, and a scale such as years for obsolescence. Finally, a synthesis technique would dictate how all the above would be "combined" to rank or distance the alternatives. Methods here include additive, multiplicative, geometric mean, and vector processing. See Johnson and Huber[DA2] for a more in depth coverage. Researchers have developed a number of techniques for organizing, controlling and effecting these elements. Some of these follow. DA/MCDM methods are largely utilized for the summary, selection from, and synthesis of a set of alternatives. Eight of these techniques are listed and discussed below.ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿³ Analytical Hierarchy Process ³³ Bayesian Updating ³³ Cost Benefit Analysis ³³ Cost Effectiveness Analysis ³³ Decision Trees ³³ Matrix ³³ Outranking ³³ Subjective Judgement Theory ³³ Utility Assessment ³³ ³³ Figure 5-2. Decision Analysis Techniques ³ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ More detail concerning each of these methods follows: Analytical Hierarchy Process (AHP) is largely a satisficing technique developed by Dr. Thomas Saaty[MC11]. It provides selection and ranking of alternatives using criteria and pairwise relative comparison. Synthesis technique utilizes eigenvectors & eigenvalues processing. It also has a normalized consistency check. Inherent in AHP is a cognitive ST memory 7+2 concept and a 1 to 9 numeric scale for evaluation. This scale was developed using human cognitive experiments. Bayesian Updating is a "a posteriori" technique postulated in the 18th Century by Rev. Thomas Bayes. It combines a users beliefs with evidence and hypotheses. It follows the basic tenets of mathematical probability to help a user evaluate network paths for subsequent action. It was partially developed because humans tend to understate changes in position based upon new information.Cost Benefit Analysis (CBA) is a relatively simple technique where a dollar assignment is made to a list of benefits and costs. Final evaluation is made through an additive or ratio comparison of costs and benefits. A major complaint of this method is the difficulty in determining benefits.Cost Effectiveness Analysis is a technique in the same genre as CBA. An effectiveness measure is created for each criterion. The ratio of cost to effectiveness then provides a ranking of alternatives. Example: Measure of Effectiveness = time to reach 60mph Measure of Cost = dollars time cost ratio Alternative A 5.0 sec $20,000 250Alternative B 15.0 sec $ 5,000 333One criticism of this method is the lack of consumer "preference" inherent in these ratios. For example in the above, cost may be a significant factor to one consumer but not another. This technique assumes cost "indifference." Another problem is the lack of a specific synthesis techniqueto combine the scaled criteria.Decision Trees utilize the application of probabilistic factors and "payoffs" to outcomes (alternatives). A tree is created representing the outcome of all possible states within the stages of a multifaceted decision. One criticism of the tree method is that it uses the "expected value" approach. This approach does not account for the element of risk, which varies from decision maker to decision maker. Matrix is likely the most commonly used technique. It is a satisficing technique which utilizes a simple matrix for the selection of a "best" alternative. It utilizes a subjective weight assignment for applying weights to the criteria, and for applying scores to each alternative's criteria. While simple, it fails two important criticisms of DA techniques - the accounting for interdependence between criteria, and establishing distance measures among alternatives on every criterion.Outranking created by B. Roy at the University of Paris. Outranking is less concerned with a method for applying weights to attributes, and more with a holistic comparison of Alternative A to Alternative B. Roy's utilizes both concordance and discordance measures for accomplishing this. The concordance measure is a ratio computed by summing the weights for those attributes for alternative A which are superior to the attributes for Alternative B divided by the weights for Alternative A as a whole. The closer this ratio is to 1.0, the more superior Alternative A is to Alternative B. The discordance measure looks the largest difference for the attribute sets of A over B compared to the largest difference over all alternatives.Subjective Judgement Theory - a statistically oriented technique which requires the user to evaluate "holistic" hypothetical combinations of criteria. SJT converts these evaluations into weights to be applied to each pre-defined criterion using the least squares method. One criticism is the large number of evaluations which must be performed to elicit these numbers.Utility Assessment encompasses several known techniques for extracting a decision maker's preferences. These include simple ranking, category methods, direct methods, gamble methods and indifference methods. There is considerable value to establishing what is known as a utility curve for each attribute of a decision. This curve establishes a utility score (e.g. a number from 1 to 10) over the range of values a criterion can assume. For example an automobile's acceleration (from 0 to 60 mph) may take a range of 4.0 to 25.0 seconds, being assigned respectively scores of 10 and 0. A linear curve for this attribute would appear as follows.ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿³ ³ ³³ 10 ³ ³³ ³ ³³ ³ ³³ score ³ ³³ ³ ³³ ³ ³³ 0 ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³³ ³³ 4.0 25.0 ³³ ³³ seconds ³³ ³³ Figure 5-3. Example of a Utility Curve ³ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙKeeney and Raiffa [DM4] proposed some characteristics for evaluating the ability of a technique to properly reflect the decision environment. These include; - expression of all dimensions of the problem (DIM), - a meaningful link between the alternatives and the criteria (LNK), - independence of certainty and preference in an attribute (IND), - clear independence in the measures (MEA), and - minimal expression of relationships (REL).It may be somewhat helpful to look at these characteristics in the context of the techniques just covered. An arbitrary scale of high, moderate and low is applied to indicate the degree of attribute presence within a technique. In addition to the stated criteria, two have been added. The first, valuation (VAL), has been created to evaluate the effectiveness within a technique for attaching value to a specific measure. For example how well is a specific $ measure attached to a criterion, or how can a velocity measure be utilized within the context of the technique. A second addition, cognitive assistance (COG), has been added to allow for the inherent ability of a technique to contribute to cognitive weaknesses in decision making.

TECHNIQUE           DIM    LNK    IND     MEA    REL    VAL    COG      

AHP                 mod    hgh    hgh     mod    mod    mod    hgh      

Bayesian            mod    mod    hgh     low    mod    hgh    hgh      

CBA                 mod    mod    low     low    low    mod    low      

CEA                 mod    mod    mod     hgh    mod    hgh    low      

Decision Trees      low    mod    hgh     low    low    mod    low      

Matrix              mod    mod    low     mod    low    hgh    low      

Outranking          mod    mod    low     mod    mod    low    mod      

SJT                 mod    mod    low     mod    mod    low    mod      

Utility             low    mod    hgh     mod    mod    mod    mod

Figure 5-4. Decision Analysis Technique ComparisonStatistical Methods The fundamental purpose of statistical methods, specifically the subclass of inferential statistics, is to utilize available, but limited data to make decisions. Information about the limited data is gathered and summarized in a numeric indicator called a statistic. This process is, in effect, induction. Deduction is then applied via a general technique termed hypothesis testing to fix the limits around which the statistic may be considered valid. The statistic to be used varies depending upon the form of the data, and the decision to be made. Some major statistical tests include; 1) the ttest, 2) the Coefficient of Correlation, 3) Chi Square, 4) Analysis of Variance, and 5) Analysis of Co-varianceSome typical decisions and associated questions which could be answered based upon these techniques follow: The ttest Should we tighten up our grading system? Is our college GPA in line with the mean national college GPA? Coefficient of correlation Should we change the composition of our work groups? Is there a correlation between the effectiveness of a group and the personalities of group members?Chi Square Should we market more aggressively in ourSouthern region? Has the demand for automobiles decreased equivalently across the regions of the country?Analysis of Variance Should we institute new measures to reduce our production error rates? Are the number of errors increasing? Analysis of Co-variance Should we strengthen the personnel in the North District Office? Is the time that it takes to process a form greater for the North District than the Central Office all other factors remaining constant? Hypothesis TestingThe purpose of hypothesis testing is to pose questions concerning the possible conclusions that can be reached through an analysis of the data. This type of testing is only done with data that is representative of the population, not the population itself. For example let's say we want to known the average number of apples eaten daily by American men. To be 100% sure of our answer we would have to poll every man in America. Since this is an impractical task, we instead gather a representative sample of men, ask them how many apples they eat, and then use this data for making inferences about the population as a whole. This is done by constraining the limits within which one can fail to reject those conclusions. We can never fully "accept" these conclusions because we do not have 100% of the data. Typical parts of a hypothesis test include; - a null hypothesis, - an alternative hypothesis, - a specific statistical test, - a rejection region, and - assumptions.A null hypothesis test sets up a statement of fact which the full test will hope to disprove or reject. For example a null hypothesis would be "The average age of apple eaters is greater than or equal to 60". The alternative hypothesis is complementary to the null hypothesis, and is actually the thing you are trying to prove. In this case it would be "The average age of apple eaters is less than 60." The specific statistical test to select would depend upon the data and what you are trying to prove. In this case it happens to be the t-test. The rejection region demarcates how certain you are of the results to be derived from the data you do collect. This again revolves around the fact that we can never be 100% certain of the results indicated by our data unless we have the entire population. Finally, some assumptions need to be made specific. An example is that our sample is representative. If we were to collect our apple data in Miami Beach, where many retirees live, the data may not be representative of the population as a whole. Most of the statistical tests only work under certain assumptions. In summary statistical methods attack those cognitive weaknesses dealing with data in the perception, thinking and memory areas. When exposed to only portions of the population of data, our views cannot always be seen as representative. These methods force the problem into a rigorous structure upon which constrained, yet valid conclusions can be drawn. Forecasting Frequently decision makers are asked to project either the current path of an organization's policies or the effects of alternative decisions on future paths of the organization. For example, what will be the predicted effect on sales if we add two salespersons, or reduce our staff by one? Orwhat are the possible consequences of pursuing a more aggressive operations policy? Forecasting techniques developed for helping to answer questions of both these varieties fall under the headings quantitative and qualitative. QuantitativeQuantitative forecasting techniques utilize past data to help determine relationships between organizational (and/or outside) elements, or to predict what the future will look like. There are two general types - regressive and time series. Regressive methods attempt to point out relationships between or among variables. For example a rise in the overall value in the stock market may be related to a fall in the interest rates charged. Time series methods attempt to model the behavior of variables over time. For example the average cost of new homes rose at a rate of 10% per year for the last ten years. The available methods within each major group vary from simple to complex. Some of these major method types are outlined below with explanations of their use.Regression Linear Regression is a simple regressive model where behavior of a single variable is predicted based upon a values taken on by another variable. For example we could attempt to predict the weight of a college student by asking him his height. We would use past data on other college students to create an equation such as; WEIGHT = 2.5 x HEIGHT. (dependent) (independent)A common method termed least squares is used to compute this relationship. Terms used to label these variables are the dependent and independent variables. The WEIGHT is dependent upon the value of HEIGHT. Multiple Regression (MR) is an extension of linear regression which may use 2 or more variables for predicting the weight. As an example; WEIGHT = 2.5 x HEIGHT + 3.2 x WAIST - 250. The least squares method may also be used in MR as long as the relationships remain 1st order. MR models may also involve equations of greater than 1st order, i.e., powers, roots, and trigonometric functions but require more sophisticated methods for establishing these relationships. Another regressive method is the two stage least squares. This method is used for establishing complex relationships in areas such as sophisticated economic forecasting. The method is called two stage because more than one equation is involved in the process, because there are error terms in the equations, and because the dependent variables in some equations are independent variables in others. Resolution of this process requires a trial and error approach - and thus yields the term two stage.CorrelationCorrelation is a measure to look at how strong two variablesrelate to each other. For example take the following pairs of numbers - (1,2);(2,4);(3,6);(4,8);(5,10). Note that the relationship between the numbers in each pair remains the same - i.e. double. We would say that there is perfect correlation in these numbers - which in the language of forecasting is given a value of 1.0 which is termed the correlation coefficient. Now note the following pairs - (2,.5);(3,.3);(4,.25);(5,.20);(6,.166) Again the pattern in the relationship is consistent. But now the relationship is inverse - as the first number rises, the second one falls. This relationship is given a correlation coefficient of -1.Where there is no discernable relationship a coefficient of 0 is assigned.Time SeriesAs explained earlier, time series methods involve tracking a variable over a time axis. There are two major thrusts in the time series methods - traditional and auto-regressive. The traditional methods are simplistic ones which extrapolate past data into the future. Variations on this theme provide for "smoothing" the predictions, for "decomposing" elements such as seasonal fluctuations, and business cycles, and for "filtering" out noise or random fluctuations in data. The auto-regressive techniques assume that there is dependence between/among the data in the time periods. For example, an increase in the purchase of new cars this month may have been caused, at least in part, by the lack of car sales last month. The traditional methods do not make this assumption, or look for these relationships. Some time series methods are presented in the figure below.ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿³ Moving Average ³³ Exponential Smoothing ³³ Classical Decomposition ³³ Auto Regressive Moving Average (ARIMA) ³³ Box Jenkins ³³ ³³ Figure 5-5. Time Series Analysis Techniques ³ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙQualitative Forecasting MethodsIn addition to the quantitative methods just outlined, a number of qualitative approaches for predicting the results of current and proposed policy exist. Since the focus of this chapter is on algorithmic approaches, these will just be mentioned. The primary focus of these methods is to gather a "gut feel" consensus about the future path of events. This consensus may be gathered from small groups, large groups or by sampling. On a gross basis, these methods include questionnaires and interviews. Questionnaires can be sent anonymously or with attribution. A well regarded method known as the Delphi Technique first polls individuals, compiles the results, distributes the results and then re-polls the participants. Another well regarded approach is the Influence Diagram. This technique requires decision makers to diagram out cause and effect relationships among all the variables in a problem. In this manner the effects of changes made to some variables can be followed through. Qualitative methods generally place more emphasis on the experience, intuition, and wisdom of the method participants. In summary forecasting is available in both quantitative and qualitative varieties. The best approach toward predicting future events is often a combination of both approaches. In absence of a crystal ball, however, any forecasting technique will only be as good as the soundness and quality of the data which goes into it. Mathematical ProgrammingAnother general class of decision science methods, mathematical programming, focuses upon optimizing some objective. The form of this objective may vary substantially. It may be to optimally procure or allocate resources, whether they be material goods, human or financial resources. Or it may be to provide the most efficient scheduling, movement, balancing, or packaging of goods and services. While many sophisticated techniques have been developed in this area, many significant problems remain to be solved. Additionally, many of the techniques already developed are being constantly replaced by even more efficient algorithms. The complexity and mass of elements in this genre of problem make this area particularly challenging. Some major areas of application and research include Linear Programming, Integer Programming, Goal Programming, Network Modeling, and Dynamic Programming. Each of these areas are briefly covered below. Linear Programming (LP) is a technique which optimizes some objective, subject to constraints we impose. It involves the application of criteria constraints to an objective function describing the alternatives. For example we may wish to allocate our research and development funds among the various divisions of our company. Our objective then may be to maximize the allocation such that the highest potential return is realized on our research investment. While the prediction of this return may be subjective in nature, nonetheless we could apply some quantitative measure to predict it. But we also would have constraints surrounding this allocation. For example, to spread our research "risk", we may wish to allocate some minimum amount to each division. And we of course have some overall limit on the amount of funds we can allocate. This example portrays only one of many areas that can be approached using this technique. Typical areas of application for LP include; Mixing Assignments Scheduling SelectionTherefore LP an be used to optimize many things - hours, dollars, pounds of material, or miles travelled. Three algorithmic approaches to solving these kinds of problems are available. In order of increasing sophistication and power, they are the graphical technique, the simplex method, and the Karmarkar method. Integer Programming (IP) is an extension of Linear Programming for problems which require "integer" solutions. While solutions using the LP techniques take a "continuous" form, i.e. real numbers such as 25345.89901, solutions using IP can only take an integer form. This only makes sense for many problems. We cannot purchase 12.365 trucks, or move 16.876 people to Minneapolis. For many problems we cannot simply take the LP solution and round it up or down. This sometimes results in a less than optimal choice. Goal Programming (GP) is another extension of LP. While LP focuses upon a single objective and answer, goal programming focuses upon multiple objectives, or stages of a problem. Frequently problems have multiple, layered, and competing objectives. Goal programming would establish as its central objective the resolution of all the sub-objectives. Each sub-objective then becomes a constraint on the entire problem, and is solved as a unique problem. The unique results are then folded into the larger problem. Network Modeling is a very broad area where the algorithms are concerned with working through optimal paths in networks. These networks can represent physical objects, activities, or events. For example, the network may be a group of computers with wire interconnections. Or a network may be a group of roads in a city, with interspersed retail outlets. In the area of activities, it may be the stages of building a house - foundation, framing, plumbing, electrical, roofing, etc. Or in events, the stages of planning surrounding a major conference. The objectives in establishing a network model vary from minimizing or maximizing distance covered, to evenly spreading the workload, to simply determining that the foundation activities are completed before the finishing touches. Dynamic Programming (DP) is an extension of the general network model. It works by dividing a problem into stages, then working backward from the last stage, analyzing all possible states the network can assume. In this manner a users objective can assume different optimal configurations at each stage. DP is effective in multi-period planning where an organization can work backward from a desired state through periods, analyzing what decision paths need to be modified at the various stages of development. SummaryThe objective of development in the decision sciences has been to improve the ability of the human decision maker to make more timely and quality decisions. Toward this end, extensive algorithmic techniques have been developed for discovering information about current operations, for optimally using resources, for looking ahead, and for properly framing the decision itself. Practicing decision science departments have been vastly successful in planting these techniques in daily private and public sector operations. But they are also aware of limitations and shortfalls in their usage. Development continues in the DS arena, and should be enhanced significantly by parallel developments in the AI arena. At the same time education in this area needs to be expanded. Many decision makers continue to rely upon faulty, personal, inductive methods and are unaware of the efficacy of decision science methods.