Efficient is a synonym of Effective. Effective is similar to Actual. Actual is the opposite of Virtual. 
Productivity is derived from Produce. Productivity is a type of Ratio. Ratio is related to Scale. 
Efficient <--Synonym--> Effective <--SimilarTo--> Actual <--Antonym--> Virtual 
Produce <--DerivedFrom-- Productivity --IsA--> Ratio <--RelatedTo--> Scale 