Metropolitan Fire Brigade (MFB) delivers a variety of emergency services in Melbourne and its surrounding suburbs. It staffs 14 ladder companies, 27 pumper companies, and several rescue units and ambulances. Normal staffing in each firefighting unit requires 192 firefighters to be on duty every day. MFB is organised with three firefighting 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, firefighters within each unit are given one of the seven regularly scheduled days off. This day off is referred to as a Kelly day. Thus, over a threeweek scheduling period, each firefighter in a unit works six of the seven scheduled unit days and gets one Kelly day off. Page 2 of 5 Determining the number of firefighters to be assigned to each unit includes the 192 firefighters who must be on duty plus the number of firefighters in the unit who are off for a Kelly day. Furthermore, each unit needs additional staffing to cover firefighter absences due to injury, sick leave, vacations, or personal time. This additional staffing involves finding the best mix of adding full-time firefighters to each unit and the selective use of overtime. If the number of absences on a particular day brings the number of available firefighters below the required 192, firefighters who are currently off (i.e. on a Kelly day) must be scheduled to work overtime. Over time is compensated approximately 1.94 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 21 and a standard deviation of 5 provides a good approximation of the probability distribution for the number of daily absences. Using a single-period inventory model with probabilistic demand, develop a report with recommendations that will inform MFB of the followings:
1. Assuming no daily absences and taking into account the need to staff Kelly days, determine the base number of firefighters needed by each unit.
2. Using a minimum cost criterion, how many aditional firefighters should be added to each unit in order to cover the daily absences? These extra daily needs will be filled by the additional firefighters and, when necessary, the more expensive use of overtime by off-duty firefighters.
3. On a given day, what is the probability that Kelly-day firefighters will be called in to work overtime?
4. Based on the three-unit organisation, how many firefighters should be assigned to each unit? What is the total number of full-time firefighters required for MFB?