Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-27 23:33:23

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: voter_1

```sql
CREATE TABLE AREA_CODE_STATE (
  area_code NUMBER,
  state TEXT
);
```

```sql
CREATE TABLE CONTESTANTS (
  contestant_number NUMBER,
  contestant_name TEXT
);
```

```sql
CREATE TABLE VOTES (
  vote_id NUMBER,
  phone_number NUMBER,
  state TEXT,
  contestant_number NUMBER,
  created TIME
);
```



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": "voter_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": "voter_1",
  "iteration": 0,
  "business_context": "A voting competition where contestants receive votes from different states. The goal is to maximize the total number of votes received by contestants while ensuring that each contestant receives a minimum number of votes from each state.",
  "optimization_problem_description": "Maximize the total number of votes received by all contestants, subject to constraints ensuring that each contestant receives at least a minimum number of votes from each state.",
  "optimization_formulation": {
    "objective": "maximize total_votes = \u2211(votes[c,s] for all contestants c and states s)",
    "decision_variables": "votes[c,s]: the number of votes received by contestant c from state s (integer)",
    "constraints": [
      "\u2211(votes[c,s] for all s) \u2264 total_votes_c for each contestant c",
      "votes[c,s] \u2265 min_votes_per_state for each contestant c and state s"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "votes[c,s]": {
        "currently_mapped_to": "VOTES.contestant_number",
        "mapping_adequacy": "partial",
        "description": "The number of votes received by contestant c from state s"
      }
    },
    "constraint_bounds": {
      "total_votes_c": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "The total number of votes a contestant can receive"
      },
      "min_votes_per_state": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "The minimum number of votes each contestant must receive from each state"
      }
    },
    "decision_variables": {
      "votes[c,s]": {
        "currently_mapped_to": "VOTES.contestant_number",
        "mapping_adequacy": "partial",
        "description": "The number of votes received by contestant c from state s",
        "variable_type": "integer"
      }
    }
  },
  "missing_optimization_requirements": [
    "Total votes a contestant can receive (total_votes_c)",
    "Minimum votes per state for each contestant (min_votes_per_state)"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Refine mapping of decision variables and constraints to existing schema or business configuration logic"
  }
}
