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Decision Tables - a brief overview Dr. Rogelio Dávila Pérez ITESM, Campus Guadalajara

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Index Definition Structure Steps to build a decision table Example Solution to the example Exercises

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Decision Tables In the 50's General Electric, the Sutherland Corporation, and the United States Air Force worked on a complex file maintenance project, using flowcharts and traditional narratives, they spend six labor-years of effort but failed to define the problem. It was not until 1958, when four analysts using decision tables, successfully defined the problem in less than four weeks 1. _____________________________________ 1 Taken from A History of Decision Tables located at

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Definition Tables represent an easy way for humans to read, understand and execute complex procedures, particular policies, etc. A decision table is a useful tool that allows us: -To present decision procedures in a clear tabular form. -To understand complex logic expressed in traditional narrative form. -To check for inconsistencies verifying that every possibility was considered in the solution.

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Structure A decision table is typically divided in four areas: The conditions are decisions that depending on their values, define different states of affairs in the problem. Actions (effects, results, etc.) are operations or values that will be determined by particular circumstances. Conditions Condition Alternatives Actions Action Entries

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FTFTFTFT…T FFTTFFTT…T FFFFTTTT…T …… FFFFFFFF…T XX X X X XX X XX X X …… X X X Actions Conditions All possible combinations Actions per combination (each column represents a different state of affairs)

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Steps to create a decision table 1.List all the conditions which determine which action to take. 2.Calculate the space of combinations. 3.Fill all combinations in the table. 4.Analyze column by column to determine which actions are appropriate for each combination. 5.Reduce the table by eliminating redundant columns.

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Example Policy for charging charter flight costumers for certain in-flight services: 2 If the flight is more than half-full and costs more than $350 per seat, we serve free cocktails unless it is a domestic flight. We charge for cocktails on all domestic flights; that is, for all the ones where we serve cocktails. (Cocktails are only served on flights that are more than half-full.) _____________________________________ 2 Example taken form: Structured Analysis and System Specification, Tom de Marco, Yourdon inc., New York, 1979.

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List all the conditions that determine which action to take. ConditionsValues The flight more than half- full? Yes (Y), No (N) Cost is more than $350?Y, N Is it a domestic flight?Y, N

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Calculate the space of combinations ConditionsNumber of Combinations Possible Combinations 12YN 24YYYY NYNY YNYN NNNN 38YYYYYY NYYNYY YNYYNY NNYNNY YYNYYN NYNNYN YNNYNN NNNNNN …… n 2 n

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Calculate the space of combinations 1 Number of Values to the power of the number of conditions with these values If all conditions are simply Y/N values: 2 number of conditions If 1 condition with 3 values and 3 with 2: 3 1 * 2 3 = 24 Or, use the values per condition and multiply each value down the column, e.g. 3*2*2*2=24 _____________________________________ 1 Taken from Mariel de Wildes Decision Table Training Session

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Calculate the space of combinations Conditions in the example are 3 and all are two-valued ones, hence we have: All combinations are 2 3 = 8

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Fill all combinations in the table. POSSIBLE COMBINATIONS CONDITONS more than half- full NNNNYYYY more than $350 per seat NNYYNNYY domestic flightNYNYNYNY ACTIONS

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Analyze column by column to determine which actions are appropriate for each combination POSSIBLE COMBINATIONS CONDITONS more than half- full NNNNYYYY more than $350 per seat NNYYNNYY domestic flightNYNYNYNY ACTIONS serve cocktails XXXX free X

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Reduce the table by eliminating redundant columns. POSSIBLE COMBINATIONS CONDITONS more than half- full NNNNYYYY more than $350 per seat NNYYNNYY domestic flightNYNYNYNY ACTIONS serve cocktails XXXX free X Note that some columns are identical but by one condition.

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Reduce the table by eliminating redundant columns. POSSIBLE COMBINATIONS CONDITONS more than half- full NNNNYYYY more than $350 per seat NNYYNNYY domestic flightNYNYNYNY ACTIONS serve cocktails XXXX free X Note that some columns are identical but by one condition. Which means that actions are independent from the value of that particular condition.

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Reduce the table by eliminating redundant columns. POSSIBLE COMBINATIONS CONDITONS more than half- full NNNNYYYY more than $350 per seat NNYYNNYY domestic flightNYNYNYNY ACTIONS serve cocktails XXXX free X Note that some columns are identical but by one condition. Which means that actions are independent from the value of that particular condition. Hence, the table can be simplified.

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Reduce the table by eliminating redundant columns. POSSIBLE COMBINATIONS CONDITONS more than half- full NNNYYYY more than $350 per seat NYYNNYY domestic flight-NYNYNY ACTIONS serve cocktails XXXX free X First we combine the yellow ones nullifying the condition.

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Reduce the table by eliminating redundant columns. POSSIBLE COMBINATIONS CONDITONS more than half- full NNYYYY more than $350 per seat NYNNYY domestic flight--NYNY ACTIONS serve cocktails XXXX free X First we combine the yellow ones nullifying the condition. Then the red ones.

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Reduce the table by eliminating redundant columns. POSSIBLE COMBINATIONS CONDITONS more than half- full NNYYYY more than $350 per seat NYNNYY domestic flight--NYNY ACTIONS serve cocktails XXXX free X First we combine the yellow ones nullifying the condition. Then the red ones. Notice that yellow and red columns are identical but by one condition.

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Reduce the table by eliminating redundant columns. POSSIBLE COMBINATIONS CONDITONS more than half- full NYYYY more than $350 per seat -NNYY domestic flight-NYNY ACTIONS serve cocktails XXXX free X First we combine the yellow ones nullifying the condition. Then the red ones. Notice that yellow and red columns are identical but by one condition. So, we combine them.

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Reduce the table by eliminating redundant columns. POSSIBLE COMBINATIONS CONDITONS more than half- full NYYY more than $350 per seat -NYY domestic flight--NY ACTIONS serve cocktails XXX free X First we combine the yellow ones nullifying the condition. Then the red ones. Notice that yellow and red columns are identical but by one condition. So, we combine them. Then we combine the violet colored ones.

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Reduce the table by eliminating redundant columns. POSSIBLE COMBINATIONS CONDITONS more than half- full NYYY more than $350 per seat -NYY domestic flight--NY ACTIONS serve cocktails XXX free X Notice that even when we observe that the green columns seem to be identical but by one condition.

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Reduce the table by eliminating redundant columns. POSSIBLE COMBINATIONS CONDITONS more than half- full NYYY more than $350 per seat -NYY domestic flight--NY ACTIONS serve cocktails XXX free X Notice that even when we observe that the green columns are identical but by one condition. It is not the same a NULIFYIED condition than a valued one.

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Reduce the table by eliminating redundant columns. POSSIBLE COMBINATIONS CONDITONS more than half- full NYYY more than $350 per seat -NYY domestic flight--NY ACTIONS serve cocktails XXX free X Notice that even when we observe that the green columns are identical but by one condition. It is not the same a NULIFYIED condition than a valued one. BE CAREFUL, DO NOT OVERSIMPLIFY THE TABLE OR IT WILL GET REDUNDANT.

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Final solution 4 Combinations CONDITONS more than half-fullNYYY more than $350 per seat -NYY domestic flight--NY ACTIONS serve cocktails XXX free X _____________________________________ 4 In previous steps, other combinations were possible that if followed would have led to different but equivalent solution tables.

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Exercises Subsidy policy for the cub scout pack 3 : The subsidy to the cub scout pack is based on number of scouts, rank, and length of membership. The subsidy for each scout is $25 for first-year members, $35 for second-year members, and $50 for scouts who have been members longer than two years. In addition to this base, each scout gets an extra subsidy of $10 if he has attained the rank of Wolf, $15 if he has attained the rank of Bear, and $20 if he has attained the rank of Lion – unless he does it in his first year, in which case he receives $70. _____________________________________ 3 Example taken form: Structured Analysis and System Specification, Tom de Marco, Yourdon inc., New York, 1979.

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Exercises Specify the following policy using a decision table: 1 A mailing is to be sent out to customers. The content of the mailing is about the current level of discounting and potential levels of discounting. The content is different for different types of customers. Customer Types A, B and C get a normal letter except Customer Type C, who get a special letter. Any customer with 2 or more current lines or with a credit rating of X get a special paragraph added with an offer to subscribe to another level of discounting. _____________________________________ 1 Taken from Mariel de Wildes Decision Table Training Session

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