Reference no: EM132944407
Big Town Fire Department would like to schedule their human resource requirements in fire and safety operations. The town runs two schedules per day, 12 hours each. Employees are compensated hourly at $30 per hour plus 33% for benefits. Employees who work the night shift received $5 more per hour and have a commensurate increase in benefits.
The weekly firefighter personnel requirements are:
The normal shift for a fire-fighter is 4 days 12 hours a day followed 3 consecutive days off, working on either the day or the night shift. Big Town managers would like to schedule the fire fighters in the least cost way, but must make sure the requirements are met?
-a. What if the total number of firefighters are limited due to turnover or other challenges in hiring? Starting from the benchmark solution, limit the total number of firefighters by 1, 2, 3, ..., 10. To enable finding an answer, allow the firefighters to work "double" shifts (day and night), and pay the double-shift employees "time and a half" for their work on all hours over 48 hours per week. Report the implications in terms of cost. Note 1: If the benchmark solution had 22 firefighters in total (not the actual answer), then, the goal here would be to find the best schedule with 21 firefighters, with some overtime involved. Then repeat for 20, 19, etc. Note 2: To include shifts that allow for overtime, you may need to make some assumptions about how much overtime is permitted for a firefighter per week. How safe is it if firefighters are working too much?