代写MSDS 490: Healthcare Analytics and Decision Making Homework Assignment 2帮做Python语言程序

MSDS 490: Healthcare Analytics and Decision Making

Homework Assignment 2

Due Date: 10/23/2024 (Wednesday Midnight)

Submission Instructions: zip all your solution files (AMPL code, data, Word document, figures, etc.) into one, following the file naming convention Last Name First Name HW#.zip Use online submission tools in Canvas to submit this homework. Use AMLP (with gurobi solver) to model and solve problems in this homework.

Total Score: 100. Each Problem has an Equal Weight.

1. Modify the data used in the 24-hour model in “ClassOneDayShift.dat” so that in the revised model a time-break is not provided to a nurse. How does your solution change from the one that allows lunch break. Now, modify the model in “ClassOneDayShift.mod” to allow up to 2 nurse shortfall during an hour of service. What is the difference in the total surplus in this solution compared to the solution from the original model that ensures no shortfall (model with inequality constraints).

2. Consider the above question. However, change the objective function to minimizes the total of shortfall and surplus nurses available to care for patients at each hour; i.e. we only plan for meeting the demand as close to the estimate, while ignoring cost. What can you say about the solution obtained in this way compared to the solution from the model designed to minimize the total cost (with different costs for part time and full-time workers). How does your shortfall and surplus change if you further constrain the total part time workers at any given time by 3.

3. Developing a MAD-AR(3) Model with Seasonality using Optimization. We will continue to use data from DailyPa-tientVolumeInSample.xlsx. We will ignore the issue of coefficient significance and confidence intervals. (i) Estimate the coefficients of an AR(3) model with day of the week seasonality by minimizing the mean absolute deviation of the error in the fitted line. In addition to the equations in the lecture notes, you need to ensure that the sum of the residual in the fitted line is zero. (ii) Modify the model in (i) to ensure that the sum of the absolute value of each coefficient in the AR(3) model is less than 1. Implement and solve both (i) and (ii) using AMPL mod and dat files.

4. We have m patients and n providers to care for these patients. In the in-class work we considered the following model for nearly equalizing the patient-to-provider assignment. Let xij be a binary variable which takes a value 1, if provider i is assigned to patient j, and bij is the benefit of assigning provider i to patient j, while ensuring that that each provider has nearly equal workload. Patient j generates wij workload for provider i. Weights w1, w2 are used to balance the benefits with nearly equal workload requirement. A basic provider-patient assignment model is as follows:

The Patient-Provider.csv provides benefit and workload information on 52 patients and 8 providers. Your goal is to implement the above model in AMPL, and solve it for the following combinations (w1, w2) = (0, 1); (0.1, 0.9); (0.2, 0.8); (0.3, 0.7); (0.4, 0.6); (0.5, 0.5); (0.6, 0.4); (0.7, 0.3); (0.8, 0.2); (0.9, 0.1); (1, 0). Plot the total benefit and equal work load values for the solutions obtained for these combination of weights. Add a new constraint to the above model that ensures that the number of patients assigned to a provider do not exceed a fixed number δ. Solve the modified model for (w1, w2) = (0.5, 0.5) for δ = 6, 7, 8. Note that your revised model should be infeasible for δ = 6.