Emptiable minimal siphons (EMSs) play a key role in the development of many deadlock control policies for resource allocation systems modeled with Petri nets. Recent research results show that siphon-based deadlock prevention methods can avoid complete siphon enumeration by using mixed-integer programming (MIP). This brief proposes a novel MIP approach, called MIP $'$ for short, to compute EMSs for deadlock control in a class of Petri nets, i.e., a system of simple sequential processes with resources (S3PR). Compared with classical MIP, since MIP $'$ utilizes the structural characteristics of S3PR nets to compute EMSs and more constraints are included in it, its solution space is drastically narrowed. As a result, the number of iterations to solve the MIP $'$ problem is significantly reduced, and the computational efficiency is considerably improved. Comparisons are provided on several S3PR nets to show its superior efficiency.