Hello someone, everyone...

need some help with this question.. not sure if I should use a "single-period inventory model' to solve it or use a deterministic approach. Pleas help. Thanks.


The River City Fire Department (RCFD) fights fire 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 requires 186 fire fighters to be on duty everyday.
RCFD is organized 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 unt 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 three week scheduling period, each firefighter 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 unit includes the 186 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 a vailable firefighters below the required 186, firefighters who are currently off (eg on a Kelly 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