We consider two kinds of software testing-resource allocation problems. The first problem is to minimize the number of remaining faults given a fixed amount of testing-effort, and a reliability objective. The second problem is to minimize the amount of testing-effort given the number of remaining faults, and a reliability objective. We have proposed several strategies for module testing to help software project managers solve these problems, and make the best decisions. We provide several systematic solutions based on a nonhomogeneous Poisson process model, allowing systematic allocation of a specified amount of testing-resource expenditures for each software module under some constraints. We describe several numerical examples on the optimal testing-resource allocation problems to show applications & impacts of the proposed strategies during module testing. Experimental results indicate the advantages of the approaches we proposed in guiding software engineers & project managers toward best testing resource allocation in practice. Finally, an extensive sensitivity analysis is presented to investigate the effects of various principal parameters on the optimization problem of testing-resource allocation. The results can help us know which parameters have the most significant influence, and the changes of optimal testing-effort expenditures affected by the variations of fault detection rate & expected initial faults.