After evaluating the arrivals of patients to an emergency department of the Dublin Hospital, the medical

director identified the number of doctors needed per each time period. Now, she needs to develop an

optimal schedule of doctors assigned to the emergency department.

Each time period may be covered by staff attendants $($full$-$time doctors$)$ and medical interns $($residents$)$

that just finished their medical programs. The attendants have three shifts of $8$ hours each, starting from

$8$ am$,4$ pm and $12$ am$.$ The interns$$ schedule includes two $12-$hour shifts starting from $8$ am and $8$ pm$.$

The hourly cost is $$130$ per attendant and $$44$ per intern. Help the medical director to identify the optimal

schedule of doctors and interns in the emergency department.

Questions.

$1.$ Formulate an integer programming model that can be used to develop a schedule that will satisfy

customer service needs at a minimum total daily cost.

$2.$ Create a spreadsheet model using the formulation from question $1.$ Solve the model using Excel

Solver for the optimal schedule of doctors and interns. Present the optimal schedule and

comment on the solution. Will this optimal solution be appropriate for the emergency

department? Explain.

$3.$ After reviewing the solution in question $2,$ the medical director has realized that some additional

requirements must be incorporated into the schedule. Specifically, she wants to ensure that at

least two attendants are working at any time period. She also wants to hire no more than $7$ interns

that will be working daily. Provide the mathematical formulation of the additional constraints and

incorporate these constraints into the spreadsheet model from question $2.$ Solve the revised

model, present and explain the new optimal schedule, and compare it with the optimal schedule

in question $2.$

$4.$ For the optimal model in question $3,$ use SolverTable to analyze the effect of changing the daily

number of interns from $0$ to $20($with an increment of $1)$ on the minimum total cost, and number

of doctors and interns in respective time periods. Present and briefly explain the results of your

sensitivity analysis.

$5.$ For the optimal model in question $3,$ provide a two$-$way sensitivity analysis using SolverTable for

parameters of your choice. Present and briefly explain the results of your sensitivity analy