## 6 Higher Education Student Enrollment Capacity Planning Methods & Techniques
### Methods Based on Decision Support Systems
#### 6.2.2 Proposed Bottom-Up Procedure  
Following the proposed bottom-up framework demonstrated in Figure 2 and proceeding from the collected data in Table 1, the exercise to collect data for a sample faculty was conducted on the instructor, curriculum, and student data dimensions. Then, by fixing (maintaining) the student to faculty ratio, Equation (4) develops the model of the proposed formulation to plan the program-level capacity planning in a bottom-up approach. It converts the program input data acquired from the different data centers into one number, i.e., the student planned capacity for faculty 'F'. This equation is then repeated for each faculty or program, all mounting up to a total student planned capacity for the university that is then compared to the top-down methodology for better tolerance management. The hierarchy of the cascading and summation of in each program '\(p\)' for every department '\(d\)' in college '\(c\)' will provide the student planned capacity in the university for all colleges '\(C\)' using all their departments '\(D\)' for all their programs '\(P\)'. For better illustration, this hierarchical process is shown in Figure 4.  
\[\text{SPC}=\sum_{c=1}^{\text{C}}\sum_{d=1}^{D}\sum_{p=1}^{\text{P}}\frac{ \left(\sum_{t=1}^{\text{F}}\mathbf{\Psi}_{t}(p)\ \right)\ *\ \mathbf{\mu}_{\text{S}}(p)}{\overline{\mathbf{\pi}_{\text{cs}}^{ \text{s}}}(p)*\overline{\mathbf{\pi}_{\text{cn}}^{\text{cr}}}(p)*\overline{ \mathbf{\pi}_{\text{cr}}^{\text{cs}}}(p)} \tag{4}\]  
where SPC is the student planned capacity for all programs in the university measured in students (st) for a pre-determined set of operational hours; \(\mathbf{\Psi}_{t}(p)\) represents the available contact hours for faculty '\(t\)' in program '\(p\)' measured in hours per person (faculty), i.e., \(\text{hr}/\hat{t}\); \(\mathbf{\text{M}_{\text{s}}^{\text{c}}}(p)\) is the number of students registered in a course in program '\(p\)'; \(\overline{\mathbf{\pi}_{\text{sc}}^{\text{sc}}}(p)\) is the average number of sections, 'courses', each student is registered per semester in program '\(p\)'; \(\overline{\mathbf{\pi}_{\text{cn}}^{\text{cr}}}(p)\) represents the average rate to convert student credit hours to required faculty contact hours in program '\(p\)'; and \(\overline{\mathbf{\pi}_{\text{cr}}^{\text{cs}}}(p)\) is the average credit hours for each section 'course' in program '\(p\)'. Given the extensive and expansive task of data acquisition required to perform the bottom-up procedure for KAU, a sample college has been chosen to provide conceptual validity and illustrate the significance of the proposed method. The college under study is the College of Engineering in KAU, which includes 8 different departments offering 14 undergraduate programs and 22 graduate programs. Following the bottom-up model using Equation (4), the results are presented in Table 3. Figure 5 provides a visual summary of the results and demonstrates the optimal student capacity for the faculty of engineering. The horizontal axis represents the average number of students per section in the faculty charted versus the primary and secondary vertical  
Figure 4: Bottom-up framework for KAU student capacity planning. axes representing the total number of students/faculty members and the consequential percentages of over/under capacity in contact hours on faculty members' teaching load, respectively. Figure 5 shows that for the faculty of engineering to maintain a 1:10 faculty to student ratio and run on 100% teaching load capacity in terms of available contact hours (i.e., 0% over/underload in contact hours), the average number of students per section should be 17.1 students. This implies having a capacity of 3482 students and 353 faculty members with a teaching load of 3608 contact hours. The Faculty of Engineering currently has 3515 students and 350 faculty members, with an available teaching load of 3574 contact hours.