On the Sizing of Security Personnel Staff While Accounting for Overtime Pay

Abstract

At many universities today, especially those in developing countries, budget cuts are leading to the reduction of staff for various campus services. One such service is campus security. However, a more holistic view may in fact reveal that, at least when it comes to security, workload reductions may actually increase the overall cost to the University since such reductions result in increased criminal activity which could be detrimental to the university either through direct financial losses, harm to students and staff or through a loss of reputation. For a given workload (i.e., the number of personnel assigned to each post for each shift) one must determine the appropriate staff size to satisfy this workload while minimizing overall cost. The desired workload may vary monthly (e.g., additional staff needed during special events) and, in addition, the number of available staff may vary monthly (e.g., because of increased vacation leave requests during the summer break). Staff must be provided at least 40 h per week so too many staff is not cost effective while insufficient staff requires excessive overtime in order to satisfy the required workload which is also not cost effective. We investigate the optimal trade-off so as to minimize the total financial cost for varying workloads and staff availability. We also take into account the various agreements between management and the employees’ Union. We use standard Integer Programming techniques to solve the resulting problem. The additional constraints increase the complexity of the problem but we use a lower bound on the optimal solution to show that the solution obtained is close to optimal.