An elevator system includes a cab supported for movement within a hoistway. A tension device, which remains close to one end of the hoistway, maintains a desired tension on a load bearing member that supports the cab and moves to achieve a desired placement of the cab. The load bearing member extends from a first end of the hoistway toward the cab, wraps around a first sheave supported on the cab, extends toward the first end of the hoistway, wraps around a second sheave supported near the first end of the hoistway, extends toward a second end of the hoistway, wraps about a third sheave supported near the second end of the hoistway, extends toward the cab, wraps around a fourth sheave supported on the cab, and extends toward the second end of the hoistway where it is secured to the tension device.