Dr. Paula Smith is the chief medical staff at Davidson Critical Care Unit. She needs to determine the schedule for nurses to make sure that there are enough of them on duty throughout the day. Paula has broken down the day into twelve 2-hour periods. The slowest time of the day encompasses the three periods from 12:00 a.m. to 6:00 AM., which, beginning at midnight, requires a minimum of 30, 20, and 40 nurses, respectively. The demand for nurses steadily increases during the next four daytime periods. Beginning with the 6:00 AM - 8:00 AM period, a minimum of 50, 60, 80, and 80 nurses are required for these four periods, respectively. After 2:00 PM, the demand for nurses decreases during the afternoon and evening hours. For the five 2-hour periods beginning at 2:00 PM and ending at midnight, 70, 70, 60, 50, and 50 nurses are required, respectively. A nurse reports for duty at the beginning of one of the 2-hour periods and works 8 consecutive hours (which is required in the nurses’ contract). Dr. Smith wants to determine a nursing schedule that will meet the hospital’s minimum requirements throughout the day while using the minimum number of nurses. Develop a linear programming model to determine the optimal schedule for Davidson Critical Care Unit. Examine your LP solution and recommend a workable strategy for Dr. Smith.
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
Dr. Paula Smith is the chief medical staff at Davidson Critical Care Unit. She needs to determine the schedule for nurses to make sure that there are enough of them on duty throughout the day. Paula has broken down the day into twelve 2-hour periods. The slowest time of the day encompasses the three periods from 12:00 a.m. to 6:00 AM., which, beginning at midnight, requires a minimum of 30, 20, and 40 nurses, respectively. The demand for nurses steadily increases during the next four daytime periods. Beginning with the 6:00 AM - 8:00 AM period, a minimum of 50, 60, 80, and 80 nurses are required for these four periods, respectively. After 2:00 PM, the demand for nurses decreases during the afternoon and evening hours. For the five 2-hour periods beginning at 2:00 PM and ending at midnight, 70, 70, 60, 50, and 50 nurses are required, respectively. A nurse reports for duty at the beginning of one of the 2-hour periods and works 8 consecutive hours (which is required in the nurses’ contract). Dr. Smith wants to determine a nursing schedule that will meet the hospital’s minimum requirements throughout the day while using the minimum number of nurses.
Develop a linear programming model to determine the optimal schedule for Davidson Critical Care Unit. Examine your LP solution and recommend a workable strategy for Dr. Smith.
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