Bank's manual underwriting involves a group of underwriting inspectors, which perform a known set of procedures with the loan applications submitted by the borrowers, in order to determine the risk of providing a loan and eventually approve or disapprove it. Due to the fact that the evaluation process of applications must satisfy quality of service requirements usually set at legislator level and the bank resources are limited, one has to define such dispatching rules, that specify which application must be sent to which inspector and when in such a way that the requirements are met. This paper presents a case study of the application of "computer-aided scheduling" to the new problem of optimal management of applications, which is seen in the bank manual underwriting process. Here it is shown that the problem of optimal distribution of applications between the inspectors in the bank's manual underwriting can be represented as an optimal dispatching problem, commonly encountered in the distributed processing environment. We build the simulation model of the corresponding dispatching system and find best decision rule with the help of computational simulations. The realization of best decision-making is done by finding in a given set of dispatching rules the best one (either static or adaptive) for a given criterion and by estimating its parameters (if needed). By virtue of numerical examples it is shown how the quality of service requirements are met using different dispatching rules.