The manager of a local hospital is facing a financial problem and needs to reduce the nursing cost in the emergency department. Currently there is N nurses working in the department. Each nurse receives his basic salary and the cost of overtime shifts, by the end of each month. In fact, an overtime will be considered if the number of assigned shifts per week to any nurse is larger than the number of required shifts per nurse per week (D). Each day covers 3 different shifts (Morning, Afternoon and Night) and the nurse can work at most one shift per day. Moreover, each nurse is not allowed to work two consecutive shifts. On the other hand, there is a required number of nurses per shift. The manger wants to prepare a feasible schedule for the next month for the nurses in the department while minimizing the overtime cost ( we assume that one month is 4 weeks). The manager is not allowed to lay off any nurse. We give the following parameter: N: number of nurses. M: number of working days per month. S: number of shifts. W: number of weeks. D: number of required shifts per nurse per week. (Over time will be considered if the number of assigned shifts per week to any nurse is larger than D). Re number of required nurses per shift.; Vr: 1, ...,S. Tw: set of days of week w; V W: 1, ....,W. We suggest the following decision variables: Xpriflif nurse () Works en shitet (r) of day (O ) vj : 1...,N; Vi:1,.,M; vr : 1...,S. 0 other wise Ojw : nunber of overtime shifts of nurse (j) in week (w) Vj: 1, ....,N; Vw: 1, ....,W C/ Consider the preferences: Assume that each nurse has two days off per week and that she is allowed to select tow preferred days among all the days of the week. Instead of minimizing the total number of overtime shifts the manger is aiming to optimize the number of preference respected of all the nurses. Add the required parameters and update the model to fit with the new requirements. (2 pts) The manager of a local hospital is facing a financial problem and needs to reduce the nursing cost in the emergency department. Currently there is N nurses working in the department. Each nurse receives his basic salary and the cost of overtime shifts, by the end of each month. In fact, an overtime will be considered if the number of assigned shifts per week to any nurse is larger than the number of required shifts per nurse per week (D). Each day covers 3 different shifts (Morning, Afternoon and Night) and the nurse can work at most one shift per day. Moreover, each nurse is not allowed to work two consecutive shifts. On the other hand, there is a required number of nurses per shift. The manger wants to prepare a feasible schedule for the next month for the nurses in the department while minimizing the overtime cost ( we assume that one month is 4 weeks). The manager is not allowed to lay off any nurse. We give the following parameter: N: number of nurses. M: number of working days per month. S: number of shifts. W: number of weeks. D: number of required shifts per nurse per week. (Over time will be considered if the number of assigned shifts per week to any nurse is larger than D). Re number of required nurses per shift.; Vr: 1, ...,S. Tw: set of days of week w; V W: 1, ....,W. We suggest the following decision variables: Xpriflif nurse () Works en shitet (r) of day (O ) vj : 1...,N; Vi:1,.,M; vr : 1...,S. 0 other wise Ojw : nunber of overtime shifts of nurse (j) in week (w) Vj: 1, ....,N; Vw: 1, ....,W C/ Consider the preferences: Assume that each nurse has two days off per week and that she is allowed to select tow preferred days among all the days of the week. Instead of minimizing the total number of overtime shifts the manger is aiming to optimize the number of preference respected of all the nurses. Add the required parameters and update the model to fit with the new requirements. (2 pts)