Decision tables are an excellent means to visualize and manage large sets of rules in consolidated fashion.  Scaling up to large rule sets just about demands it.  Even carefully-designed decision tables, however, are prone to anomalies and other problems -- especially if multi-dimensional.  So they must be scrutinized closely, preferably using automated assistance.

Completeness is an example.  Last month's column^[1] presented the following rule along with Decision Table C to illustrate multi-dimensional decision tables.

Decision Table C 

Decision Criteria	Delivery Method for an Order
	Picked Up by Customer	Shipped by Normal Service	Shipped by Premium Service
Rush order	No	Yes	Yes
Order includes fragile item	No	Yes	--
Order includes specialty item	No	No	--
Order includes high-priced item	No	No	--
Order includes item involving hazardous materials	No	Yes	Yes
Category of customer	Silver	Gold	Platinum
Destination of order	--	Local	Remote

How complete is this decision table?  Not very!  Here is a step-by step analysis, preceded by a brief explanation of the table's layout.

Layout.  Decision Table C establishes the basis for determining the delivery method for an order.  Three possible delivery methods (the outcomes) are indicated along the top.  Seven decision criteria appear at left as labels for the rows.  (This table therefore involves seven dimensions.)  Six of these decision criteria are binary (yes, no or local, remote), whereas one, category of customer, involves three possibilities (silver, gold, platinum).  The choice of delivery method for an order depends on what appears in the cells of a column.  A dash ( -- ) in a cell indicates that the associated decision criteria does not matter in determining the outcome; that is, any alternative for that decision criteria will produce the same outcome.

Completeness Analysis.  How complete is Decision Table C?  Here is a step-by-step analysis.

1. The total number of possible combinations for the instances of the seven decision criteria can be calculated as:  2⁶ x 3 = 192.  This calculation reflects the fact that six of the decision criteria apparently have two alternatives each (yes and no for five of them, and local and remote for the other), whereas the seventh, category of customer, apparently has three (silver, gold, and platinum).
   
   
2. The total number of combinations actually represented in the table can be determined as follows.  Column 2 represents one combination -- each cell has something in it.  Columns 1 and 3 are a bit more complicated because they both have dashes in one or more cells, indicating acceptance of any alternative -- for example, either yes or no.  Column 1 includes one such cell, so that column actually provides the basis for establishing the outcome for two combinations -- one if the cell had had local and one if it had had remote.  Column 3 includes three such cells, so that column actually establishes the basis for 2³ or 8 outcomes.  Altogether, the decision table actually establishes the basis for establishing 11 outcomes (2 + 1 + 8 = 11).
   
   
3. Having determined how many combinations the decision table actually addresses (11), we can now determine how many it does not:  192 - 11 = 181.  So some 181 possible combinations have not been addressed at all!  We must therefore conclude this decision table is not very complete.

References

[1]  Ronald G. Ross, "Decision Tables, Part 1 ~ The Route to Consolidated Business Logic," Business Rules Journal, Vol. 6, No. 7 (July 2005), URL:  http://www.BRCommunity.com/a2005/b240.html 

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