Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-27 21:46:24

Prompt:
You are an Operations Research (OR) expert focused ONLY on optimization modeling. Your role is to analyze the business domain and design LINEAR optimization problems without involving database design decisions.

CRITICAL MATHEMATICAL CONSTRAINTS FOR LINEAR/MIXED-INTEGER PROGRAMMING:
- The optimization problem MUST be either Linear Programming (LP) or Mixed-Integer Programming (MIP)
- Objective function MUST be linear: minimize/maximize ∑(coefficient × variable)
- All constraints MUST be linear: ∑(coefficient × variable) ≤/≥/= constant
- Decision variables can be continuous (LP) or mixed continuous/integer (MIP)
- NO variable products, divisions, or other nonlinear relationships
- Design business scenarios that naturally lead to linear mathematical formulations
- Generate between 2 and 20 constraints for optimization feasibility

YOUR SCOPE: Focus exclusively on optimization modeling and understanding current schema-to-optimization mapping. Do NOT propose database changes.
ROW COUNT AWARENESS: Be aware that data engineer will apply 3-row minimum rule - tables unable to generate sufficient meaningful rows will be moved to business_configuration_logic.json.

CRITICAL: Respond with ONLY a valid JSON object. No explanations, no markdown, no extra text.

Database: icfp_1

```sql
CREATE TABLE Inst (
  instID NUMBER,
  name TEXT,
  country TEXT
);
```

```sql
CREATE TABLE Authors (
  authID NUMBER,
  lname TEXT,
  fname TEXT
);
```

```sql
CREATE TABLE Papers (
  paperID NUMBER,
  title TEXT
);
```

```sql
CREATE TABLE Authorship (
  authID NUMBER,
  instID NUMBER,
  paperID NUMBER,
  authOrder NUMBER
);
```



Current Business Configuration Logic: {} (initially empty)

TASK: Design a realistic LINEAR optimization problem and analyze how it maps to the current schema.

JSON STRUCTURE REQUIRED:

{
  "database_id": "icfp_1",
  "iteration": 0,
  "business_context": "Describe the realistic business scenario that leads to linear optimization (avoid scenarios requiring nonlinear relationships)",
  "optimization_problem_description": "Detailed description of what needs to be optimized using linear objective functions and constraints",
  "optimization_formulation": {
    "objective": "minimize/maximize specific_linear_metric with clear definition (sum of weighted variables only)",
    "decision_variables": "What linear variables can be controlled/decided (continuous or integer)",
    "constraints": "What linear limitations must be respected (no variable products or divisions) - design 2 to 20 constraints"
  },
  
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "coefficient_name[indices]": {
        "currently_mapped_to": "table.column OR business_configuration_logic.key OR missing",
        "mapping_adequacy": "good/missing/redundant/partial/inaccurate",
        "description": "what this coefficient represents in the optimization model"
      }
    },
    "constraint_bounds": {
      "constraint_name[indices]": {
        "currently_mapped_to": "table.column OR business_configuration_logic.key OR missing", 
        "mapping_adequacy": "good/missing/redundant/partial/inaccurate",
        "description": "what this constraint bound represents"
      }
    },
    "decision_variables": {
      "variable_name[indices]": {
        "currently_mapped_to": "table.column OR business_configuration_logic.key OR missing",
        "mapping_adequacy": "good/missing/redundant/partial/inaccurate", 
        "description": "what this decision variable represents",
        "variable_type": "continuous/integer/binary"
      }
    }
  },
  
  "missing_optimization_requirements": [
    "List what data/parameters are needed for complete linear optimization model"
  ],
  
  "iteration_status": {
    "complete": false,
    "confidence": "low/medium/high",
    "next_focus": "What optimization aspects need refinement"
  }
}

Response:
{
  "database_id": "icfp_1",
  "iteration": 0,
  "business_context": "A conference is organizing a series of paper presentations and wants to optimize the scheduling of papers to minimize the total number of sessions required, while ensuring that no author is scheduled to present more than one paper in the same session.",
  "optimization_problem_description": "The goal is to minimize the number of sessions required to present all papers, ensuring that each author presents only one paper per session. Each session can accommodate a limited number of papers.",
  "optimization_formulation": {
    "objective": "minimize total_sessions",
    "decision_variables": "x[p, s] = 1 if paper p is scheduled in session s, 0 otherwise (binary)",
    "constraints": [
      "sum(x[p, s] for s) = 1 for all papers p (each paper is scheduled in exactly one session)",
      "sum(x[p, s] for p) <= max_papers_per_session for all sessions s (session capacity)",
      "sum(x[p, s] for p if author a is an author of paper p) <= 1 for all authors a and sessions s (author presents at most one paper per session)"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "total_sessions": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "represents the total number of sessions used"
      }
    },
    "constraint_bounds": {
      "max_papers_per_session": {
        "currently_mapped_to": "business_configuration_logic.key",
        "mapping_adequacy": "missing",
        "description": "maximum number of papers that can be scheduled in a single session"
      }
    },
    "decision_variables": {
      "x[p, s]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "binary variable indicating if paper p is scheduled in session s",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "Data on maximum number of papers per session",
    "Data on which authors are associated with which papers"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Refine mapping of decision variables and constraints to existing schema"
  }
}
