This paper considers a redundancy optimization problem in which multiple-choice and resource constraints are incorporated. The problem is expressed as a nonlinear integer programming problem and is characterized as an NP-hard problem. The purpose of the paper is to develop a SSRP (solution space reduction procedure). Therefore, the problem is analyzed first to characterize some solution properties. An iterative SSRP is then derived using those solution properties. Finally, the iterative SSRP is used to define an efficient B&BP (branch-and-bound procedure) algorithm. Experimental tests show how: dramatically the SSRP can work on removing any intermediately-found unnecessary decision variables from further consideration in solution search, efficient this B&BP is.