A regional hospital wishes to solve the following nurse scheduling problem. The average nightly demand for ICU nurse is given below. Any ICU nurse in this hospital will work five consecutive days before taking two days off and repeats this 5-day on and 2-day off cycle. The management goal is to hire as few nurses as possible while meeting the demand on a weekly basis.

Su	M	T	W	Th	F	Sat
9	15	8	5	11	19	22

An operations research analyst comes up with the following linear program and she claims the optimal solution will provides the management a weekly shift schedule.

 

X1, X2,…, X7 ≥ 0

Based on the above LP formulation, what do the decision variables X1, X2, …, X7 represent? Give clear definition for each.

Minimize x1 + x2 + x3 + x4 + x5 + x6 + x7 Subject To x1 + x1 + x2 + x1 + x2 + x3 + x1 + x2 + x3 + x4 + x1 + x4 + x5 + x6 + x7 >= 15 x5 + x6 + x7 >= 8 x6 + x7 >= 5 x7 >= 11 x2 + x3 + x4 + x5 x2 + x3 + >= 19 >= 22 x3 + x4 + x5 + x6 +x7 >= 9 x4 + x5 + x6