Can we write a case study by referring our previous work instead of re-writing?
Yes you can publish a case study as a (conference) paper and your proposed structure looks reasonable, albeit I have a few comments.


  I don't want to re-phrase the introduction, related work, the algorithms and our proposed methods etc. 


You'll clearly need a new introduction. You'll possibly also need a new related work section too (which is missing from your proposed flow). The algorithms and proposed methods can be copy-and-pasted, as long as they are attributed to your previous work, but you might need to revise some of the introductory material to those algorithms and methods.

Since you're in computer science, you have another option: Publish the complete work as a journal paper, rather than a conference paper.