# Complete PYOMO implementation

import pyomo.environ as pyo
from pyomo.opt import SolverFactory

def conference_scheduling_optimization():
    """Optimize conference paper scheduling using Pyomo"""

    # 1. MODEL CREATION
    model = pyo.ConcreteModel()

    # 2. DATA SETUP
    papers = [1, 2, 3]  # Paper IDs
    authors = [1, 2, 3]  # Author IDs
    max_papers_per_session = 2  # Maximum papers per session

    # Author-paper associations
    author_paper_map = {
        1: [1],
        2: [2],
        3: [3]
    }

    # 3. SETS
    model.P = pyo.Set(initialize=papers)  # Papers
    model.A = pyo.Set(initialize=authors)  # Authors
    model.S = pyo.RangeSet(1, len(papers))  # Sessions (at most one session per paper)

    # 4. VARIABLES
    model.x = pyo.Var(model.P, model.S, within=pyo.Binary)  # Paper-session assignment
    model.y = pyo.Var(model.S, within=pyo.Binary)  # Session usage

    # 5. OBJECTIVE FUNCTION
    def obj_rule(model):
        return sum(model.y[j] for j in model.S)
    model.objective = pyo.Objective(rule=obj_rule, sense=pyo.minimize)

    # 6. CONSTRAINTS

    # Each paper must be scheduled in exactly one session
    def paper_scheduling_rule(model, i):
        return sum(model.x[i, j] for j in model.S) == 1
    model.paper_scheduling_constraint = pyo.Constraint(model.P, rule=paper_scheduling_rule)

    # The number of papers in any session cannot exceed the maximum allowed
    def session_capacity_rule(model, j):
        return sum(model.x[i, j] for i in model.P) <= max_papers_per_session * model.y[j]
    model.session_capacity_constraint = pyo.Constraint(model.S, rule=session_capacity_rule)

    # An author cannot present more than one paper in the same session
    def author_conflict_rule(model, j, k):
        return sum(model.x[i, j] for i in author_paper_map[k]) <= 1
    model.author_conflict_constraint = pyo.Constraint(model.S, model.A, rule=author_conflict_rule)

    # Linking sessions to papers
    def linking_rule(model, i, j):
        return model.x[i, j] <= model.y[j]
    model.linking_constraint = pyo.Constraint(model.P, model.S, rule=linking_rule)

    # 7. SOLVING WITH GUROBI
    solver = SolverFactory('gurobi')

    # Solve the model
    results = solver.solve(model, tee=True)

    # 8. RESULT PROCESSING
    if results.solver.termination_condition == pyo.TerminationCondition.optimal:
        print("Optimal solution found!")
        print(f"Optimal value: {pyo.value(model.objective)}")

        # Extract variable values
        print("\nPaper-session assignments:")
        for i in model.P:
            for j in model.S:
                if pyo.value(model.x[i, j]) > 0.5:  # Binary variable check
                    print(f"Paper {i} is scheduled in session {j}")

    elif results.solver.termination_condition == pyo.TerminationCondition.infeasible:
        print("Problem is infeasible")
    elif results.solver.termination_condition == pyo.TerminationCondition.unbounded:
        print("Problem is unbounded")
    else:
        print(f"Solver terminated with condition: {results.solver.termination_condition}")

    return model

# Run the optimization
conference_scheduling_optimization()