The research aims to look at the under utilization and over utilization costs associated to appointment scheduling times. One of the main variables in relation to appointment times within different industries, such as healthcare wait times and production lines, is the processing time for each individual job process. Costs associated to the job process times, either underage or overage costs, are extremely important to decision making processes. Effectively, this is a mixed integer linear programming problem. It aims to minimize the total cost associated with the worst case scenario of processing duration times. Important implications include the reduction of costs in worst case scenarios dealing with waiting lines, by finding an optimal solution to this linear programming problem. Further implications into effective management of waiting lines to minimize overage and underage usage costs can be obtained.