Diagnosis is the reasoning leading to the identification of the cause of a problem. Given a system instrumented with a set of sensors, diagnosis can be performed thanks to diagnosis tests that are designed from the system model. The tests only involve measured variables and can be checked with the measured values. The configuration of tests that pass and tests that do not pass provides a way to isolate the faults. However the fact that all faults are discriminable, i.e. the system is fully diagnosable, depends on the set of tests and hence of the sensors that are placed on the system. The number of tests that can be designed is generally huge and more than sufficient to achieve full or maximal diagnosability. This paper addresses several variants of the problem of selecting the set of tests/sensors so that diagnosability is maximal and a cost criterion is minimized. The variant problems are formalized in the integer programming framework.