initial model formulation
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Lewis Woolfson
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import pandas as pd
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import pyomo.environ as pe
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import pyomo.gdp as pyogdp
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import os
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import matplotlib.pyplot as plt
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import matplotlib.cm as cm
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from itertools import product
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# check with Taha if code is too similar to Alstom?
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class TheatreScheduler:
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def __init__(self, case_file_path, session_file_path):
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"""
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Read case and session data into Pandas DataFrames
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Args:
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case_file_path (str): path to case data in CSV format
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session_file_path (str): path to theatre session data in CSV format
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"""
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try:
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self.df_cases = pd.read_csv(case_file_path)
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except FileNotFoundError:
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print("Case data not found.")
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try:
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self.df_sessions = pd.read_csv(session_file_path)
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except FileNotFoundError:
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print("Session data not found")
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self.model = self.create_model()
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def _generate_case_durations(self):
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"""
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Generate mapping of cases IDs to median case time for the procedure
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Returns:
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(dict): dictionary with CaseID as key and median case time (mins) for procedure as value
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"""
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return pd.Series(self.df_cases["Median Duration"].values, index=self.df_cases["CaseID"]).to_dict()
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def _generate_session_durations(self):
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"""
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Generate mapping of all theatre sessions IDs to session duration in minutes
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Returns:
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(dict): dictionary with SessionID as key and session duration as value
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"""
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return pd.Series(self.df_sessions["Duration"].values, index=self.df_sessions["SessionID"]).to_dict()
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def _generate_session_start_times(self):
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"""
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Generate mapping from SessionID to session start time
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Returns:
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(dict): dictionary with SessionID as key and start time in minutes since midnight as value
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"""
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# Convert session start time from HH:MM:SS format into seconds elapsed since midnight
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self.df_sessions.loc[:, "Start"] = pd.to_timedelta(self.df_sessions["Start"])
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self.df_sessions.loc[:, "Start"] = self.df_sessions["Start"].dt.total_seconds() / 60
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return pd.Series(self.df_sessions["Start"].values, index=self.df_sessions["SessionID"]).to_dict()
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def _get_ordinal_case_deadlines(self):
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"""
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#TODO
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Returns:
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"""
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self.df_cases.loc[:, "TargetDeadline"] = pd.to_datetime(self.df_cases["TargetDeadline"], format="%d/%m/%Y")
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self.df_cases.loc[:, "TargetDeadline"] = self.df_cases["TargetDeadline"].apply(lambda date: date.toordinal())
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return pd.Series(self.df_cases["TargetDeadline"].values, index=self.df_cases["CaseID"]).to_dict()
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def _get_ordinal_session_dates(self):
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"""
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#TODO
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Returns:
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"""
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self.df_sessions.loc[:, "Date"] = pd.to_datetime(self.df_sessions["Date"], format="%d/%m/%Y")
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self.df_sessions.loc[:, "Date"] = self.df_sessions["Date"].apply(lambda date: date.toordinal())
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return pd.Series(self.df_sessions["Date"].values, index=self.df_sessions["SessionID"]).to_dict()
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def _generate_disjunctions(self):
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"""
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#TODO
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Returns:
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disjunctions (list): list of tuples containing disjunctions
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"""
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cases = self.df_cases["CaseID"].to_list()
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sessions = self.df_sessions["SessionID"].to_list()
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disjunctions = []
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for (case1, case2, session) in product(cases, cases, sessions):
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if (case1 != case2) and (case2, case1, session) not in disjunctions:
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disjunctions.append((case1, case2, session))
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return disjunctions
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def create_model(self):
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model = pe.ConcreteModel()
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# Model Data
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# List of case IDs in surgical waiting list
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model.CASES = pe.Set(initialize=self.df_cases["CaseID"].tolist())
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# List of sessions IDs
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model.SESSIONS = pe.Set(initialize=self.df_sessions["SessionID"].tolist())
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# List of tasks - all possible (caseID, sessionID) combination
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model.TASKS = pe.Set(initialize=model.CASES * model.SESSIONS, dimen=2)
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# The duration (median case time) for each operation
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model.CASE_DURATION = pe.Param(model.CASES, initialize=self._generate_case_durations())
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# The duration of each theatre session
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model.SESSION_DURATION = pe.Param(model.SESSIONS, initialize=self._generate_session_durations())
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# The start time of each theatre session
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model.SESSION_START_TIME = pe.Param(model.SESSIONS, initialize=self._generate_session_start_times())
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# The deadline of each case
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model.CASE_DEADLINES = pe.Param(model.CASES, initialize=self._get_ordinal_case_deadlines())
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# The date of each theatre session
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model.SESSION_DATES = pe.Param(model.SESSIONS, initialize=self._get_ordinal_session_dates())
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model.DISJUNCTIONS = pe.Set(initialize=self._generate_disjunctions(), dimen=3)
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ub = 1440 # seconds in a day
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model.M = pe.Param(initialize=1e3*ub) # big M
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max_util = 0.85
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num_cases = self.df_cases.shape[0]
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# Decision Variables
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model.SESSION_ASSIGNED = pe.Var(model.TASKS, domain=pe.Binary)
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model.CASE_START_TIME = pe.Var(model.TASKS, bounds=(0, ub), within=pe.PositiveReals)
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model.CASES_IN_SESSION = pe.Var(model.SESSIONS, bounds=(0, num_cases), within=pe.PositiveReals)
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# Objective
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def objective_function(model):
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return pe.summation(model.CASES_IN_SESSION)
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#return sum([model.SESSION_ASSIGNED[case, session] for case in model.CASES for session in model.SESSIONS])
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model.OBJECTIVE = pe.Objective(rule=objective_function, sense=pe.maximize)
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# Constraints
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# Case start time must be after start time of assigned theatre session
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def case_start_time(model, case, session):
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return model.CASE_START_TIME[case, session] >= model.SESSION_START_TIME[session] - \
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((1 - model.SESSION_ASSIGNED[(case, session)])*model.M)
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model.CASE_START = pe.Constraint(model.TASKS, rule=case_start_time)
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# Case end time must be before end time of assigned theatre session
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def case_end_time(model, case, session):
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return model.CASE_START_TIME[case, session] + model.CASE_DURATION[case] <= model.SESSION_START_TIME[session] + \
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model.SESSION_DURATION[session]*max_util + ((1 - model.SESSION_ASSIGNED[(case, session)]) * model.M)
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model.CASE_END_TIME = pe.Constraint(model.TASKS, rule=case_end_time)
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# Cases can be assigned to a maximum of one session
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def session_assignment(model, case):
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return sum([model.SESSION_ASSIGNED[(case, session)] for session in model.SESSIONS]) <= 1
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model.SESSION_ASSIGNMENT = pe.Constraint(model.CASES, rule=session_assignment)
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def set_deadline_condition(model, case, session):
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return model.SESSION_DATES[session] <= model.CASE_DEADLINES[case] + ((1 - model.SESSION_ASSIGNED[case, session])*model.M)
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model.APPLY_DEADLINE = pe.Constraint(model.TASKS, rule=set_deadline_condition)
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def no_case_overlap(model, case1, case2, session):
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return [model.CASE_START_TIME[case1, session] + model.CASE_DURATION[case1] <= model.CASE_START_TIME[case2, session] + \
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((2 - model.SESSION_ASSIGNED[case1, session] - model.SESSION_ASSIGNED[case2, session])*model.M),
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model.CASE_START_TIME[case2, session] + model.CASE_DURATION[case2] <= model.CASE_START_TIME[case1, session] + \
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((2 - model.SESSION_ASSIGNED[case1, session] - model.SESSION_ASSIGNED[case2, session])*model.M)]
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model.DISJUNCTIONS_RULE = pyogdp.Disjunction(model.DISJUNCTIONS, rule=no_case_overlap)
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def theatre_util(model, session):
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return model.CASES_IN_SESSION[session] == \
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sum([model.SESSION_ASSIGNED[case, session] for case in model.CASES])
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model.THEATRE_UTIL = pe.Constraint(model.SESSIONS, rule=theatre_util)
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pe.TransformationFactory("gdp.bigm").apply_to(model)
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return model
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def solve(self, solver_name, options=None, solver_path=None, local=True):
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if solver_path is not None:
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solver = pe.SolverFactory(solver_name, executable=solver_path)
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else:
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solver = pe.SolverFactory(solver_name)
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# TODO remove - too similar to alstom
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if options is not None:
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for key, value in options.items():
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solver.options[key] = value
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if local:
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solver_results = solver.solve(self.model, tee=True)
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else:
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solver_manager = pe.SolverManagerFactory("neos")
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solver_results = solver_manager.solve(self.model, opt=solver)
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results = [{"Case": case,
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"Session": session,
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"Session Date": self.model.SESSION_DATES[session],
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"Case Deadline": self.model.CASE_DEADLINES[case],
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"Days before deadline": self.model.CASE_DEADLINES[case] - self.model.SESSION_DATES[session],
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"Start": self.model.CASE_START_TIME[case, session](),
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"Assignment": self.model.SESSION_ASSIGNED[case, session]()}
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for (case, session) in self.model.TASKS]
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self.df_times = pd.DataFrame(results)
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all_cases = self.model.CASES.value_list
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cases_assigned = []
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for (case, session) in self.model.SESSION_ASSIGNED:
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if self.model.SESSION_ASSIGNED[case, session] == 1:
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cases_assigned.append(case)
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cases_missed = list(set(all_cases).difference(cases_assigned))
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print("Number of cases assigned = {} out of {}:".format(len(cases_assigned), len(all_cases)))
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print("Cases assigned: ", cases_assigned)
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print("Number of cases missed = {} out of {}:".format(len(cases_missed), len(all_cases)))
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print("Cases missed: ", cases_missed)
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self.model.CASES_IN_SESSION.pprint()
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print("Total Objective = {}".format(sum(self.model.CASES_IN_SESSION.get_values().values())))
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print("Number of constraints = {}".format(solver_results["Problem"].__getitem__(0)["Number of constraints"]))
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#self.model.SESSION_ASSIGNED.pprint()
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print(self.df_times[self.df_times["Assignment"] == 1].to_string())
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self.draw_gantt()
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def draw_gantt(self):
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df = self.df_times[self.df_times["Assignment"] == 1]
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cases = sorted(list(df['Case'].unique()))
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sessions = sorted(list(df['Session'].unique()))
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bar_style = {'alpha': 1.0, 'lw': 25, 'solid_capstyle': 'butt'}
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text_style = {'color': 'white', 'weight': 'bold', 'ha': 'center', 'va': 'center'}
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colors = cm.Dark2.colors
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df.sort_values(by=['Case', 'Session'])
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df.set_index(['Case', 'Session'], inplace=True)
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fig, ax = plt.subplots(1, 1)
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for c_ix, c in enumerate(cases, 1):
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for s_ix, s in enumerate(sessions, 1):
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if (c, s) in df.index:
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xs = df.loc[(c, s), 'Start']
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xf = df.loc[(c, s), 'Start'] + \
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self.df_cases[self.df_cases["CaseID"] == c]["Median Duration"]
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ax.plot([xs, xf], [s] * 2, c=colors[c_ix % 7], **bar_style)
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ax.text((xs + xf) / 2, s, c, **text_style)
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ax.set_title('Assigning Ophthalmology Cases to Theatre Sessions')
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ax.set_xlabel('Time')
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ax.set_ylabel('Sessions')
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ax.grid(True)
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fig.tight_layout()
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plt.show()
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if __name__ == "__main__":
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case_path = os.path.join(os.path.dirname(os.getcwd()), "data", "cases.csv")
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session_path = os.path.join(os.path.dirname(os.getcwd()), "data", "sessions.csv")
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cbc_path = "C:\\Users\\LONLW15\\Documents\\Linear Programming\\Solvers\\cbc.exe"
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options = {"seconds": 300}
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scheduler = TheatreScheduler(case_file_path=case_path, session_file_path=session_path)
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scheduler.solve(solver_name="cbc", solver_path=cbc_path, options=options)
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#scheduler.solve(solver_name="cbc", local=False, options=None)
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