Problem:
Personnel Scheduling- Palm Beach General Hospital is concerned with the staffing of its emergency department. A recent analysis indicated that a typical day may be divided into six periods. In each period a different demand level, measured by "cases," is experienced.
Average Number
Time Period of Cases
7 A.M - 11 A.M 80
11 A.M. - 3 P.M. 60
3 P.M.- 7 P.M. 120
7 P.M.- 11 P.M 60
11P.M. - 3 A.M. 40
3 A.M. - 7 A.M. 20
Past experience indicated that one emergency room (ER) nurse, is required to handle 2.5 cases each hour. Thus, for example, between 7 A.M. and 8 A.M. there is a need for 8 nurses to handle the 20 cases (80 cases per 4 hours).
ER nurses work in shifts of 8 hours. The normal shifts are:
7 A.M. to 3 P.M.
3 P.M. to 11 P.M.
11 P.M. to 7 A.M.
However, three nurses said that they are willing to start an eight hour shift at 11 A.M. if necessary and two said they will start at 7 P.M. if asked
Required:
Question 1) Clearly state your decision variables and construct a linear program that minimizes the total number of ER nurses to report to duty to cover load requirements.
Solve the given numerical problem and illustrate step by step calculation.