Hi Anjalee,
Maybe it would be good to share a bit more information on your scenario and the chosen solution design. I am currently missing the point of triggering a Process Chain using Web Application Designer.
Anyway, I recommend to be careful with using OLAP variables in DTP filters. For sure not all functionality is present, e.g. because the variable pop-up is absent. Your constellation of an input ready variable and a customer-exit variable will only work in the context of a BEx Query and probably not if used in a DTP filter.
Best regards,
Sander