The River City Fire Department (RCFD) fights fires and provides a variety of rescue operations in the River City metropolitan area. The RCFD staffs 13 ladder companies, 26 pumper companies, and several rescue units and ambulances. Normal staffing requires186 firefighters to be on duty every day. RCFD is organized with three fire fighting units. Each unit works a full 24-hour day and then has two days (48 hours) off. For example, Unit 1 covers Monday, Unit 2 covers Tuesday, and Unit 3 covers Wednesday. Then Unit 1 returns on Thursday, and so on. Over a three-week (21-day) scheduling period, each unit will be scheduled for seven days. On a rotational basis, fire fighters within each unit are given one of the seven regularly scheduled days off. This day off is referred to as a Kelley day. Thus, over a three-week scheduling period, each fire fighter in a unit works six of the seven scheduled unit days and gets one Kelley day off. Determining the number of fire fighters to be assigned to each unit includes the 186 fire fighters
Who must be on duty plus the number of fire fighters in the unit who are off for a Kelley day. Furthermore, each unit needs additional staffing to cover fire fighter absences due to injury, sick leave, vacations, or personal time. This additional staffing involves finding the best mix of adding full-time fire fighters to each unit and the selective use of overtime. If the number of absences on a particular day brings the number of available fire fighters below
The required 186, fire fighters who are currently off (e.g., on a Kelley day) must be scheduled to work overtime. Overtime is compensated at 1.55 times the regular pay rate. Analysis of the records maintained over the last several years concerning the number of daily absences shows a normal probability distribution. A mean of 20 and a standard deviation of 5 provide a good approximation of the probability distribution for the number of daily absences.
Develop a report that will enable Fire Chief O. E. Smith to determine the necessary numbers for the Fire Department. Include, at a minimum, the following items in your report:
1. Assuming no daily absences and taking into account the need to staff Kelley days, determine the base number of fire fighters needed by each unit
2. Using a minimum cost criterion, how many additional fire fighters should be added to each unit in order to cover the daily absences? These extra daily needs will be filled by the additional fire fighters and, when necessary, the more expensive use of overtime by off-duty fire fighters.
3. On a given day, what is the probability that Kelley-day fire fighters will be called in to work overtime?
4. Based on the three-unit organization, how many fire fighters should be assigned to each unit? What is the total number of full-time fire fighters required for the River City Fire Department?