Averages mask nonlinearity and lead to prediction errors. For example, suppose a firm did a sustainability survey among two of its target segments. The average level of concern is the same for the two segments, but people in the second segment are overall much more likely to buy green products.
A large-scale survey in the Netherlands, for example, revealed little difference in the number of loyalty-program cards carried by consumers who said they were quite concerned versus only weakly concerned about privacy. How is it possible that people said they were worried about privacy but then agreed to sign up for loyalty programs that require the disclosure of sensitive personal information?
Awareness of nonlinear relationships is also important when choosing performance metrics. For instance, to assess the effectiveness of their inventory management, some firms track days of supply, or the number of days that products are held in inventory, while other firms track the number of times their inventory turns over annually.
But the choice may have unintended consequences—for instance, on employee motivation. Assume a firm was able to reduce days of supply from 12 to six and that with additional research, it could further reduce days of supply to four. This is the same as saying that the inventory turn rate could increase from 30 times a year to 60 times a year and that it could be raised again to 90 times a year.
Other areas where companies can choose different metrics include warehousing picking time versus picking rate , production production time versus production rate , and quality control time between failures versus failure rate. If anything, most people find doubling the weaker retention rate more appealing than increasing the stronger one by, say, a third. Managers underestimate the benefits of small increases to high retention rates.
As retention rates rise, customer lifetime value increases gradually at first and then suddenly shoots up. Most companies focus on identifying customers who are most likely to defect and then target them with marketing programs. Linear thinking leads managers to underestimate the benefits of small increases to high retention rates.
The classic example of this can be seen in mortgages. Property owners are often surprised by how slowly they chip away at their debt during the early years of their loan terms. But in a mortgage with a fixed interest rate and fixed term, less of each payment goes toward the principal at the beginning. Executives use this formula to calculate per unit profit:. The firm can increase per unit profit by producing and selling more widgets, because it will spread fixed costs over more units.
That attractive increase might tempt you into thinking per unit profit will skyrocket if you increase sales from , to , units. Not so. If the firm doubles widget sales from , to , which is much harder to do than going from , to , , the per unit profit increases only by about 6 cents.
Managers focus a great deal on the benefits of economies of scale and growth. However, linear thinking may lead them to overestimate volume as a driver of profit and thus underestimate other more impactful drivers, like price.
Firms often base evaluations of investments on the payback period, the amount of time required to recover the costs. Obviously, shorter paybacks are more favorable. Say you have two projects slated for funding. Both teams believe they can cut their payback period in half.
Company leadership, however, may ultimately care more about return on investment than time to breakeven. So as the payback period increases, ARR drops steeply at first and then more slowly. If your focus is achieving a higher ARR, halving the payback period of project A is a better choice. Managers comparing portfolios of similar-sized projects may also be surprised to learn that the return on investment is higher on one containing a project with a one-year payback and another with a four-year payback than on a portfolio containing two projects expected to pay back in two years.
They should be careful not to underestimate the effect that decreases in relatively short payback periods will have on ARR. As long as people are employed as managers, biases that are hardwired into the human brain will affect the quality of business decisions.
Nevertheless, it is possible to minimize the pitfalls of linear thinking. MBA programs should explicitly warn future managers about this phenomenon and teach them ways to deal with it.
Companies can also undertake initiatives to educate employees by, for instance, presenting them with puzzles that involve nonlinear relationships. In our experience, people find such exercises engaging and eye-opening. Take this quiz to see if you can make the best decisions. You eat one inch pizza. You eat two 8-inch pizzas. Suppose your analysts segmented your customer base by deciles for lifetime value where decile 1 is the most valuable. Deciles 1 and 2. Deciles 3 and 8.
Increase the productivity of the first factory from to products per hour. Increase the productivity of the second factory from to products per hour. Limitations of Decision Making under Pure Uncertainty Decision analysis in general assumes that the decision-maker faces a decision problem where he or she must choose at least and at most one option from a set of options.
In some cases this limitation can be overcome by formulating the decision making under uncertainty as a zero-sum two-person game. In decision making under pure uncertainty, the decision-maker has no knowledge regarding which state of nature is "most likely" to happen. He or she is probabilistically ignorant concerning the state of nature therefore he or she cannot be optimistic or pessimistic. In such a case, the decision-maker invokes consideration of security.
Notice that any technique used in decision making under pure uncertainties, is appropriate only for the private life decisions. Moreover, the public person i. Otherwise, the decision-maker is not capable of making a reasonable and defensible decision.
You might try to use Decision Making Under Uncertainty JavaScript E-lab for checking your computation, performing numerical experimentation for a deeper understanding, and stability analysis of your decision by altering the problem's parameters.
Further Readings: Biswas T. Martin's Press, Driver M. Brousseau, and Ph. Eiser J. Flin R. Ghemawat P. Decision Making Under Risk Risk implies a degree of uncertainty and an inability to fully control the outcomes or consequences of such an action. Risk or the elimination of risk is an effort that managers employ. However, in some instances the elimination of one risk may increase some other risks.
Effective handling of a risk requires its assessment and its subsequent impact on the decision process. The decision process allows the decision-maker to evaluate alternative strategies prior to making any decision. The process is as follows: The problem is defined and all feasible alternatives are considered.
The possible outcomes for each alternative are evaluated. Outcomes are discussed based on their monetary payoffs or net gain in reference to assets or time. Various uncertainties are quantified in terms of probabilities. The quality of the optimal strategy depends upon the quality of the judgments.
The decision-maker should identify and examine the sensitivity of the optimal strategy with respect to the crucial factors. In such cases, the problem is classified as decision making under risk. The decision-maker is able to assign probabilities based on the occurrence of the states of nature. Expected Payoff: The actual outcome will not equal the expected value.
What you get is not what you expect, i. Value B 0. Expected Opportunity Loss EOL : a Setup a loss payoff matrix by taking largest number in each state of nature column say L , and subtract all numbers in that column from it, L - Xij, b For each action, multiply the probability and loss then add up for each action, c Choose the action with smallest EOL. Loss Payoff Matrix G 0. Since I don't know anything about the nature, every state of nature is equally likely to occur: a For each state of nature, use an equal probability i.
Payoff Bonds 0. One important factor is the emotion of regret. This occurs when a decision outcome is compared to the outcome that would have taken place had a different decision been made.
This is in contrast to disappointment, which results from comparing one outcome to another as a result of the same decision. Accordingly, large contrasts with counterfactual results have a disproportionate influence on decision making. Regret results compare a decision outcome with what might have been. Therefore, it depends upon the feedback available to decision makers as to which outcome the alternative option would have yielded. Altering the potential for regret by manipulating uncertainty resolution reveals that the decision-making behavior that appears to be risk averse can actually be attributed to regret aversion.
There is some indication that regret may be related to the distinction between acts and omissions. Some studies have found that regret is more intense following an action, than an omission. For example, in one study, participants concluded that a decision maker who switched stock funds from one company to another and lost money, would feel more regret than another decision maker who decided against switching the stock funds but also lost money.
People usually assigned a higher value to an inferior outcome when it resulted from an act rather than from an omission. Presumably, this is as a way of counteracting the regret that could have resulted from the act.
You might like to use Making Risky Decisions JavaScript E-lab for checking your computation, performing numerical experimentation for a deeper understanding, and stability analysis of your decision by altering the problem's parameters. Further Readings: Beroggi G. George Ch.
Rowe W. Krieger Pub. Suijs J. For example, consider the following decision problem a company is facing concerning the development of a new product: States of Nature High Sales Med. Sales Low Sales A 0. We will refer to these subjective probability assessments as 'prior' probabilities. However, the manager is hesitant about this decision.
Based on "nothing ventured, nothing gained" the company is thinking about seeking help from a marketing research firm. The marketing research firm will assess the size of the product's market by means of a survey.
The manager has to make a decision as to how 'reliable' the consulting firm is. By sampling and then reviewing the past performance of the consultant, we can develop the following reliability matrix : 1.
What the Ap 0. These records are available to their clients free of charge. To construct a reliability matrix, you must consider the marketing research firm's performance records for similar products with high sales. Then, find the percentage of which products the marketing research firm correctly predicted would have high sales A , medium sales B , and little C or almost no sales.
Similar analysis should be conducted to construct the remaining columns of the reliability matrix. Note that for consistency, the entries in each column of the above reliability matrix should add up to one. In this example, what is the numerical value of P A A p? That is, what is the chance that the marketing firm predicts A is going to happen, and A actually will happen?
This important information can be obtained by applying the Bayes Law from your probability and statistics course as follows: a Take probabilities and multiply them "down" in the above matrix, b Add the rows across to get the sum, c Normalize the values i.
Many managerial problems, such as this example, involve a sequence of decisions. When a decision situation requires a series of decisions, the payoff table cannot accommodate the multiple layers of decision-making. Thus, a decision tree is needed. Do not gather useless information that cannot change a decision: A question for you: In a game a player is presented two envelopes containing money.
He is told that one envelope contains twice as much money as the other envelope, but he does not know which one contains the larger amount. The player then may pick one envelope at will, and after he has made a decision, he is offered to exchange his envelope with the other envelope.
If the player is allowed to see what's inside the envelope he has selected at first, should the player swap, that is, exchange the envelopes?
The outcome of a good decision may not be good, therefor one must not confuse the quality of the outcome with the quality of the decision. As Seneca put it "When the words are clear, then the thought will be also". It utilizes a network of two types of nodes: decision choice nodes represented by square shapes , and states of nature chance nodes represented by circles.
Construct a decision tree utilizing the logic of the problem. For the chance nodes, ensure that the probabilities along any outgoing branch sum to one. Calculate the expected payoffs by rolling the tree backward i. You may imagine driving your car; starting at the foot of the decision tree and moving to the right along the branches.
At each square you have control, to make a decision and then turn the wheel of your car. At each circle , Lady Fortuna takes over the wheel and you are powerless. Here is a step-by-step description of how to build a decision tree: Draw the decision tree using squares to represent decisions and circles to represent uncertainty, Evaluate the decision tree to make sure all possible outcomes are included, Calculate the tree values working from the right side back to the left, Calculate the values of uncertain outcome nodes by multiplying the value of the outcomes by their probability i.
On the tree, the value of a node can be calculated when we have the values for all the nodes following it. The value for a choice node is the largest value of all nodes immediately following it. The value of a chance node is the expected value of the nodes following that node, using the probability of the arcs.
By rolling the tree backward, from its branches toward its root, you can compute the value of all nodes including the root of the tree. Putting these numerical results on the decision tree results in the following graph: A Typical Decision Tree Click on the image to enlarge it Determine the best decision for the tree by starting at its root and going forward.
Based on proceeding decision tree, our decision is as follows: Hire the consultant, and then wait for the consultant's report. If the report predicts either high or medium sales, then go ahead and manufacture the product. Otherwise, do not manufacture the product. Clearly the manufacturer is concerned with measuring the risk of the above decision, based on decision tree.
Coefficient of Variation as Risk Measuring Tool and Decision Procedure: Based on the above decision, and its decision-tree, one might develop a coefficient of variation C.
V risk-tree, as depicted below: Coefficient of Variation as a Risk Measuring Tool and Decision Procedure Click on the image to enlarge it Notice that the above risk-tree is extracted from the decision tree, with C. For example the consultant fee is already subtracted from the payoffs. From the above risk-tree, we notice that this consulting firm is likely with probability 0.
Clearly one must not consider only one consulting firm, rather one must consider several potential consulting during decision-making planning stage.
The risk decision tree then is a necessary tool to construct for each consulting firm in order to measure and compare to arrive at the final decision for implementation. You may start with the following extreme and interesting cases by using this JavaScript for the needed computation: Consider a flat prior, without changing the reliability matrix.
Consider a perfect reliability matrix i. Consider a perfect prior, without changing the reliability matrix. Consider a flat reliability matrix i. Consider the consultant prediction probabilities as your own prior, without changing the reliability matrix. Influence diagrams: As can be seen in the decision tree examples, the branch and node description of sequential decision problems often become very complicated. At times it is downright difficult to draw the tree in such a manner that preserves the relationships that actually drive the decision.
The need to maintain validation, and the rapid increase in complexity that often arises from the liberal use of recursive structures, have rendered the decision process difficult to describe to others.
The reason for this complexity is that the actual computational mechanism used to analyze the tree, is embodied directly within the trees and branches. The probabilities and values required to calculate the expected value of the following branch are explicitly defined at each node. Influence diagrams are also used for the development of decision models and as an alternate graphical representations of decision trees. The following figure depicts an influence diagram for our numerical example.
In the influence diagram above, the decision nodes and chance nodes are similarly illustrated with squares and circles. Arcs arrows imply relationships, including probabilistic ones.
Finally, decision tree and influence diagram provide effective methods of decision-making because they: Clearly lay out the problem so that all options can be challenged Allow us to analyze fully the possible consequences of a decision Provide a framework to quantify the values of outcomes and the probabilities of achieving them Help us to make the best decisions on the basis of existing information and best guesses Visit also: Decision Theory and Decision Trees Further Readings Bazerman M.
Connolly T. Arkes, and K. Cooke R. Describes much of the history of the expert judgment problem. It also includes many of the methods that have been suggested to do numerical combination of expert uncertainties. Furthermore, it promotes a method that has been used extensively by us and many others, in which experts are given a weighting that judge their performance on calibration questions.
This is a good way of getting around the problem of assessing the "quality" of an expert, and lends a degree of objectivity to the results that is not obtained by other methods. Bouyssou D. Daellenbach H. Klein D. Thierauf R. Work they do not want to do themselves.
Work they do not have time to do themselves. All such work falls under the broad umbrella of consulting service. Regardless of why managers pay others to advise them, they typically have high expectations concerning the quality of the recommendations, measured in terms of reliability and cost. The following figure depicts the process of the optimal information determination. The Determination of the Optimal Information Deciding about the Consulting Firm: Each time you are thinking of hiring a consultant you may face the danger of looking foolish, not to mention losing thousands or even millions of dollars.
To make matters worse, most of the consulting industry's tried-and-true firms have recently merged, split, disappeared, reappeared, or reconfigured at least once. How can you be sure to choose the right consultants? Test the consultant's knowledge of your product. It is imperative to find out the depth of a prospective consultant's knowledge about your particular product and its potential market. Ask the consultant to provide a generic project plan, task list, or other documentation about your product.
Is there an approved budget and duration? What potential customers' involvement is expected? Who is expected to provide the final advice and provide sign-off? Even the best consultants are likely to have some less-than-successful moments in their work history. Conducting the reliability analysis process is essential. Ask specific questions about the consultants' past projects, proud moments, and failed efforts.
Of course it's important to check a potential consultant's references. Open in a separate window. Overview of Dataset An empirical study is carried out to assess the efficiency of the proposed methodology to forecast the COVID pandemic.
Qualitative Performance Measures The performance of the proposed NAR-NNTS model has been analyzed with three different training algorithms using the following measures [ 53 — 56 ]: Root mean square error is a polynomial counting rule. Date Confirmed Recovered Death 1-Sep 3,, 2,, 66, Time series response plots for the confirmed cases using LM training algorithm.
Time series response plots for the recovered cases using LM training algorithm. Time series response plots for the death cases using LM training algorithm.
Autocorrelation of error for the confirmed cases using LM training algorithm. Autocorrelation of error for the recovered cases using LM training algorithm. Autocorrelation of error for the death cases using LM training algorithm.
Conclusion and Future works The epidemiological data forecasting model always plays an important role in planning preventive measures for infectious diseases, such as SARS, dengue, Ebola virus and many more. Footnotes Publisher's note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Contributor Information Suyel Namasudra, Email: moc. References 1. Accessed on 06 Aug Remuzzi A, Remuzzi G. Health Policy. Severe acute respiratory syndrome coronavirus 2. Accessed on 31 July Accessed on 01 Aug Front Public Health. Forecasting dengue epidemics using a hybrid methodology. Physica A Stat Mech Appl. Benvenuto D, et al. Data Brief. Fong SJ, et al. Finding an accurate early forecasting model from small dataset: a case of NCoV novel coronavirus outbreak.
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Concurr Comput Pract Exer. The fact is, decisions are made in a context of other decisions. The typical metaphor used to explain this is that of a stream. There is a stream of decisions surrounding a given decision, many decisions made earlier have led up to this decision and made it both possible and limited.
Many other decisions will follow from it. Another way to describe this situation is to say that most decisions involve a choice from a group of preselected alternatives, made available to us from the universe of alternatives by the previous decisions we have made. For example, when you decide to go to the park, your decision has been enabled by many previous decisions. You had to decide to live near the park; you had to decide to buy a car or learn about bus routes, and so on.
By deciding to live where you do, you have both enabled and disabled a whole series of other decisions. As another example, when you enter a store to buy a DVD player or TV, you are faced with the preselected alternatives stocked by the store. There may be models available in the universe of models, but you will be choosing from, say, only a dozen. In this case, your decision has been constrained by the decisions made by others about which models to carry.
We might say, then, that every decision 1 follows from previous decisions, 2 enables many future decisions, and 3 prevents other future decisions.
People who have trouble making decisions are sometimes trapped by the constraining nature of decision making. Every decision you make precludes other decisions, and therefore might be said to cause a loss of freedom.
If you decide to marry Terry, you no longer can decide to marry Shawn. However, just as making a decision causes a loss of freedom, it also creates new freedom, new choices and new possibilities. So making a decision is liberating as well as constraining. And a decision left unmade will often result in a decision by default or a decision being made for you. It is important to realize that every decision you make affects the decision stream and the collections of alternatives available to you both immediately and in the future.
In other words, decisions have far reaching consequences. Sign in. Log into your account. Forgot your password? Password recovery. Recover your password.
Get help. Tools for the Age of Knowledge. Introduction to Decision Making. By Robert Harris. July 2, Previous article Introduction to Problem Solving.
Next article Decision Making Techniques. Related articles. Creative Thinking Techniques October 21, You'll remember the five creative methods we discussed in the Introduction to Creative Thinking: evolution, synthesis, revolution, reapplication, changing direction. Many classic creative thinking techniques make Criteria for Evaluating a Creative Solution July 20, Some idea of the value or merit of an idea or a solution to a problem can be discovered by the degree to which Problem Solving Techniques January 5, As with creative thinking, flexibility is a crucially important feature in problem solving.
Many of these techniques you will begin to use regularly for Here is a list of several very useful ideas developed over the years to advance our understanding of problem solving and to explain some Critical Thinking Materials January 4,
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