# Case Problem 2 River City Fire Department

This is a case problem from my Applied Decision Methods course taken from Chapter 10 on Inventory Models, of the textbook, 12th edition “An Introduction to ManagementScience, Quantitative Approaches To Decision Making, Need to develop a Managerial Report. Case Problem 2 River City Fire Department 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, andseveral rescue units and ambulances. Normal staffing requires 186 fire-fighters to be on duty every day. RCFD is organized with three firefighting units. Each unitworks, 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 1returns 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 withineach unit are given one of the seven regularly scheduled days off. This day of is referred to as a Kelley day. Thus, over a three-week scheduling period. Eachfirefighter in a unit works six of the seven scheduled unit days and gets one Kelly day off. Determining the number of firefighters to be assigned to each unitincludes the 186 firefighters who must be on duty plus the number of firefighters in the unit who are off for a Kelley day. Furthermore, each unit needs additionalstaffing to cover firefighter absences due to injury, sick leave, vacations, or personal time. This additional staffing involves finding the best mix of addingfull-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 belowthe required 186, firefighters who are currently off (e.g., on a Kelly day) must be scheduled to work overtime. Overtime is compensated at 1.55 ties the regular payrate. 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 anda standard deviation of 5 provide a good approximation of the probability distribution for the number of daily absences. Managerial Report Develop a report that willenable Fire Chief O. E. Smith to determine the necessary numbers for the Fire Department, Include, a minimum, the following items in your report. 1. Assuming no dailyabsences and taking into account the need to staff Kelley days, determine the base number of firefighters needed by each unit. 2. Using a minimum cost criterion, howmany additional firefighters should be added to each unit in order to cover the daily absences? These extra daily need will be filled by the additional firefightersand, 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 calledin to work overtime? 4. Base don the three-unit organization, how many firefighters should be assigned to each unit? What is the total number of full-time firefightersrequired for the River City Fire Department?