Table below is an illustration of a decision table developed using the steps previously outlined. In this example a company is trying to maintain a meaningful mailing list of customers. The objective is to send out only the catalogs from which customers will buy merchandise.
The managers realize that certain loyal customers order from every catalog and that some people on the mailing list never order. These ordering patterns are easy to observe, but deciding which catalogs to send customers who order only from selected catalogs is more difficult. Once these decisions are made, a decision table is constructed for three conditions (C1: customer ordered from Fall catalog; C2: customer ordered from Christmas catalog; and C3: customer ordered from specialty catalog), each having two alternatives (Y or N). Three actions can be taken (A1: send out this year’s Christmas catalog; A2: send out the new specialty catalog; and A3: send out both catalogs). The resulting decision table has six rows (three conditions and three actions) and eight columns (two alternatives two alternatives two alternatives).
|Conditions and Actions||1||2||3||4||5||6||7||8|
|Customer ordered from Fall catalog.||Y||Y||Y||Y||N||N||N||N|
|Customer ordered from Christmas catalog.||Y||Y||N||N||Y||Y||N||N|
|Customer ordered from specialty catalog.||Y||N||Y||N||Y||N||Y||N|
|Send out this year’s Christmas catalog.||X||X||X||X|
|Send out specialty catalog.||X||X|
|Send out both catalogs.||X||X|
The decision table is now examined to see if it can be reduced. There are no mutually exclusive conditions, so it is not possible to get by with fewer than three condition rows. No rules allow the combination of actions. It is possible, however, to combine some of the rules as shown in the figure below. For instance, Rules 2, 4, 6, and 8 can be combined because they all have two things in common:
- They instruct us to send out this year’s Christmas catalog.
- The alternative for Condition 3 is always N.
It doesn’t matter what the alternatives are for the first two conditions, so it is possible to insert dashes [—] in place of the Y or N.
The remaining rules—Rules 1, 3, 5, and 7—cannot be reduced to a single rule because two different actions remain. Instead, Rules 1 and 5 can be combined; likewise, Rules 3 and 7 can be combined.
Checking for Completeness and Accuracy
Checking over your decision tables for completeness and accuracy is essential. Four main problems can occur in developing decision tables: incompleteness, impossible situations, contradictions, and redundancy.
Ensuring that all conditions, condition alternatives, actions, and action rules are complete is of utmost importance. Suppose an important condition—if a customer ordered less than $50—had been left out of the catalog store problem discussed earlier. The whole decision table would change because a new condition, new set of alternatives, new action, and one or more new action rules would have to be added. Suppose the rule is: IF the customer did not order more than $50, THEN do not send any catalogs.Anew Rule 4 would be added to the decision table, as shown below.
|Conditions and Actions||1'||2'||3'||4'|
|Customer ordered from Fall catalog.||_||_||_||_|
|Customer ordered from Christmas catalog.||Y||_||N||_|
|Customer ordered from specialty catalog.||Y||N||Y||_|
|Customer ordered $50 or more.||T||Y||Y||N|
|Send out this year’s Christmas catalog.||X|
|Send out specialty catalog.||X|
|Send out both catalogs.||X|
|Do not send out any catalog.||X|
When building decision tables as outlined in the foregoing steps, it is sometimes possible to set up impossible situations. An example is illustrated in the figure below. Rule 1 is not feasible, because a person cannot earn greater than $50,000 per year and less than $2,000 per month at the same time. The other three rules are valid. The problem went unnoticed because the first condition was measured in years and the second condition in months.
Contradictions occur when rules suggest different actions but satisfy the same conditions. The fault could lie with the way the analyst constructed the table or with the information the analyst received. Contradictions often occur if dashes [—] are incorrectly inserted into the table. Redundancy occurs when identical sets of alternatives require the exact same action. Figure below illustrates a contradiction and a redundancy. The analyst has to determine what is correct and then resolve the contradiction or redundancy.
Decision tables are an important tool in the analysis of structured decisions. One major advantage of using decision tables over other methods is that tables help the analyst ensure completeness. When using decision tables, it is also easy to check for possible errors, such as impossible situations, contradictions, and redundancy. Decision table processors, which take the table as input and provide computer program code as output, are also available.