This paper proposes a solution approach to linear problems with many constraints of variable upper bound (VUB) type. This type of constraints are commonly found in various scheduling type problems for which tighter bounds are essential to achieve an efficiency in enumeration. An analytical framework based on factorization is adopted to devise a solution approach to the problem and extend it for more generalized VUB problem (GVUB). This research shows why the VUB type constraints are amenable to the factorization and gives a unified approach to generalized upper bound(GUB) problems, VUB problems and GVUB problems. Implementation issues are also included.