Please. I need the answer to understanding the evolution of mechanisms of cross-pollination in crops. 

The only reason I can really think of is to prevent self pollination. With a spectrum in the timing of flowering you would get cross-pollination between earlier and later flowering phenotypes. 

in general plant breeding depends on variation and selection, without variation there is no selection.  Variation comes only through out crossing between plants, in case of protoandrous (anthers matures first) and protogynous (gynoceium matures first), i.e. it favours cross pollination.  

Are yo talking about sex changer or protogynous/protandrous hermaphrodites? In hermaphrodites, protandry often occurs when mating opportunities are limited, e.g. when making more and more pollen does not increase reproductive success. Protogyny evolves under opposite conditions. See also Charnov (1982): Sex allocation.

I will guess that the preference comes from the different parental investment in offspring. Theoretically, it is reasonable to assume that if nutrients are scarce, there will be a preference for being male first, thus not to be the one investing, and to turn female once nutrient levels increase. Also, factors like the required body size, aging etc. will affect the preference for the difference in life cycles. For example, if maternal investment is significant, a preference for being a mother first will be advantageous.