# Complete GUROBIPY implementation

import gurobipy as gp
from gurobipy import GRB

def optimize_conference_schedule():
    """Optimize the scheduling of conference papers into sessions."""
    
    # 1. MODEL & DATA SETUP
    model = gp.Model("conference_schedule")
    
    # Data: Example setup based on the provided schema and data
    papers = [1, 2, 3]  # Paper IDs
    authors = [1, 2, 3]  # Author IDs
    max_papers_per_session = 2  # Business configuration parameter
    
    # Author-paper associations
    author_paper_map = {
        1: [1],  # Author 1 has Paper 1
        2: [2],  # Author 2 has Paper 2
        3: [3]   # Author 3 has Paper 3
    }
    
    # Sessions (initially empty, to be determined by the optimization)
    sessions = range(1, len(papers) + 1)  # Assume at most one session per paper initially
    
    # 2. VARIABLES
    # Decision variables: x[i, j] = 1 if paper i is scheduled in session j
    x = model.addVars(papers, sessions, vtype=GRB.BINARY, name="x")
    
    # Session usage variables: y[j] = 1 if session j is used
    y = model.addVars(sessions, vtype=GRB.BINARY, name="y")
    
    # 3. OBJECTIVE FUNCTION
    # Minimize the total number of sessions used
    model.setObjective(gp.quicksum(y[j] for j in sessions), GRB.MINIMIZE)
    
    # 4. CONSTRAINTS
    
    # Each paper must be scheduled in exactly one session
    model.addConstrs((gp.quicksum(x[i, j] for j in sessions) == 1 for i in papers), name="one_session_per_paper")
    
    # The number of papers in any session cannot exceed the maximum allowed
    model.addConstrs((gp.quicksum(x[i, j] for i in papers) <= max_papers_per_session * y[j] for j in sessions), name="session_capacity")
    
    # An author cannot present more than one paper in the same session
    for k in authors:
        papers_by_author = author_paper_map.get(k, [])
        model.addConstrs((gp.quicksum(x[i, j] for i in papers_by_author) <= 1 for j in sessions), name=f"author_{k}_conflict")
    
    # Linking sessions to papers
    model.addConstrs((x[i, j] <= y[j] for i in papers for j in sessions), name="link_sessions")
    
    # 5. SOLVING & RESULTS
    model.optimize()
    
    if model.status == GRB.OPTIMAL:
        print(f"Optimal value: {model.objVal}")
        for j in sessions:
            if y[j].x > 0.5:  # Session is used
                scheduled_papers = [i for i in papers if x[i, j].x > 0.5]
                print(f"Session {j} includes papers: {scheduled_papers}")
    elif model.status == GRB.INFEASIBLE:
        print("Problem is infeasible")
    elif model.status == GRB.UNBOUNDED:
        print("Problem is unbounded")
    
    return model

# Run the optimization
optimize_conference_schedule()