Option 1 displays the analysis performed on 1 hour time periods, shift patterns to include work hours of 4 to 12 hours. This yielded a recommendation of 2 Junior, 2 Intermediate, and 25 Senior workers to meet the demand requirement. The minimum payroll total cost of this analysis is $16,412. Option 2 displays the analysis performed on 1 hour time periods, shift patterns to include work hours of 4, 8, or 12 hours. This yielded a recommendation of 2 Junior, 2 Intermediate, and 25 Senior workers to meet the demand requirement. The minimum payroll total cost of this analysis is $16,412. Option 3 displays the analysis performed on 4-hour time periods, shift patterns to include work hours of 4, 8, or 12 hours. This yielded a recommendation of 2 Junior, 2 Intermediate, and 25 Senior workers to meet the demand requirement. The minimum payroll total cost of this analysis is $16,412. As seen from the initial test, the total costs and workforce required to meet demand are the same across the three scenarios. Since Option 3 only had 26 possible shift patterns for 1 day compared to Option 1 and 2 that had with 224 possible shift patterns for 1 day, the team concluded to design the model around 4-hour time periods, with employees working 4, 8, or 12-hour time periods. Model Architecture The mathematical model was created in three major parts, which build upon each other, and utilizes a combination of python coding, integer programming, and the FFD Heuristic. Calculate average alert arrival rates and feasible shift patterns Minimize payroll costs Optimize: Assign: Minimize staff and create staff schedules Part 1: Input Identifying hourly demand based on average alerts is the initial step of the optimization model. Determining all feasible shift patterns for 14 days, with four-hour time periods, has possibilities, while shift patterns for 1 day has possibilities. Therefore, the model begins with the creation of alert demand for 1 day and repeats seven times to generate demand values for 1 week. Each of the seven days follows the varying alert pattern described in section 3.1 Primary Problem Requirements and corresponds to a day of the week shown in Figure 4: Poisson vs Average Alert Distribution. The varying alert generation rates and seven day patterns are developed by a Poisson distribution,
Option 1 displays the analysis performed on 1 hour time periods, shift patterns to include work hours of 4 to 12 hours. This yielded a recommendation of 2 Junior, 2 Intermediate, and 25 Senior workers to meet the demand requirement. The minimum payroll total cost of this analysis is $16,412. Option 2 displays the analysis performed on 1 hour time periods, shift patterns to include work hours of 4, 8, or 12 hours. This yielded a recommendation of 2 Junior, 2 Intermediate, and 25 Senior workers to meet the demand requirement. The minimum payroll total cost of this analysis is $16,412. Option 3 displays the analysis performed on 4-hour time periods, shift patterns to include work hours of 4, 8, or 12 hours. This yielded a recommendation of 2 Junior, 2 Intermediate, and 25 Senior workers to meet the demand requirement. The minimum payroll total cost of this analysis is $16,412. As seen from the initial test, the total costs and workforce required to meet demand are the same across the three scenarios. Since Option 3 only had 26 possible shift patterns for 1 day compared to Option 1 and 2 that had with 224 possible shift patterns for 1 day, the team concluded to design the model around 4-hour time periods, with employees working 4, 8, or 12-hour time periods. Model Architecture The mathematical model was created in three major parts, which build upon each other, and utilizes a combination of python coding, integer programming, and the FFD Heuristic. Calculate average alert arrival rates and feasible shift patterns Optimize: Minimize payroll costs Assign: Minimize staff and create staff schedules Part 1: Input Identifying hourly demand based on average alerts is the initial step of the optimization model. Determining all feasible shift patterns for 14 days, with four-hour time periods, has possibilities, while shift patterns for 1 day has possibilities. Therefore, the model begins with the creation of alert demand for 1 day and repeats seven times to generate demand values for 1 week. Each of the seven days follows the varying alert pattern described in section 3.1 Primary Problem Requirements and corresponds to a day of the week shown in Figure 4: Poisson vs Average Alert Distribution. The varying alert generation rates and seven day patterns are developed by a Poisson distribution,
CSOC-Report.docx