Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-25 22:43:58

Prompt:
You are an Operations Research (OR) expert in iteration 1 of an alternating optimization process. The algorithm alternates between OR expert analysis and data engineering implementation until convergence.

CRITICAL MATHEMATICAL CONSTRAINTS FOR LINEAR/MIXED-INTEGER PROGRAMMING:
- The optimization problem MUST remain 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
- If previous iteration introduced nonlinear elements, redesign as linear formulation
- Maintain between 2 and 20 constraints for optimization feasibility

YOUR SCOPE: Focus exclusively on optimization modeling and mapping analysis. Do NOT propose database changes.
ROW COUNT AWARENESS: Understand that data engineer applies 3-row minimum rule - insufficient table data gets moved to business_configuration_logic.json.


DATA AVAILABILITY CHECK: 
Before listing missing requirements, verify:
- Check current schema for required data columns
- Check business configuration logic for required parameters  
- Only list as "missing" if data is truly unavailable
- If all mappings are "good", missing_requirements should be []

CONSISTENCY RULES:
- IF all mapping_adequacy == "good" THEN missing_optimization_requirements = []
- IF missing_optimization_requirements = [] THEN complete CAN be true
- IF complete == true THEN confidence should be "high"

SELF-CHECK: Before responding, verify:
1. Does current schema contain the data I claim is missing?
2. Are my mapping assessments consistent with missing requirements?
3. Is my complete status consistent with missing requirements?

MAPPING COMPLETENESS CHECK: Ensure logical consistency between:
- All objective coefficients mapped with adequacy evaluation
- All constraint bounds mapped with adequacy evaluation  
- All decision variables mapped with adequacy evaluation
- Missing requirements list matches inadequate mappings only


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



CURRENT STATE (iteration 0):
{
  "iteration": 1,
  "converged": false,
  "business_context": "A voting competition where contestants aim to maximize their votes across different states. The goal is to allocate a limited budget for promotional activities to maximize the total number of votes received.",
  "optimization_problem": "Maximize the total number of votes received by contestants by allocating a promotional budget across states. The budget allocation must respect state-specific constraints and ensure fairness in promotional spending.",
  "objective": "maximize \u2211(votes_received[contestant_number, state])",
  "table_count": 2,
  "key_changes": [
    "Schema changes include creating new tables for decision variables and constraints, moving scalar parameters to business_configuration_logic.json, and updating the data dictionary to reflect optimization mappings."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Refine the mapping of decision variables and constraints, and gather missing data for complete optimization model",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating new tables for decision variables and constraints, moving scalar parameters to business_configuration_logic.json, and updating the data dictionary to reflect optimization mappings.

CREATE TABLE PROMOTIONAL_BUDGET (
  contestant_number INTEGER,
  state STRING,
  budget FLOAT
);

CREATE TABLE VOTES_RECEIVED (
  contestant_number INTEGER,
  state STRING,
  votes INTEGER
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "PROMOTIONAL_BUDGET": {
      "business_purpose": "Promotional budget allocated to each contestant in each state",
      "optimization_role": "decision_variables",
      "columns": {
        "contestant_number": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each contestant",
          "optimization_purpose": "Index for decision variable",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "state": {
          "data_type": "STRING",
          "business_meaning": "State where promotional budget is allocated",
          "optimization_purpose": "Index for decision variable",
          "sample_values": [
            "CA",
            "TX",
            "NY"
          ]
        },
        "budget": {
          "data_type": "FLOAT",
          "business_meaning": "Amount of promotional budget allocated",
          "optimization_purpose": "Decision variable value",
          "sample_values": [
            5000.0,
            10000.0,
            15000.0
          ]
        }
      }
    },
    "VOTES_RECEIVED": {
      "business_purpose": "Number of votes received by each contestant in each state",
      "optimization_role": "objective_coefficients",
      "columns": {
        "contestant_number": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each contestant",
          "optimization_purpose": "Index for objective coefficient",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "state": {
          "data_type": "STRING",
          "business_meaning": "State where votes were received",
          "optimization_purpose": "Index for objective coefficient",
          "sample_values": [
            "CA",
            "TX",
            "NY"
          ]
        },
        "votes": {
          "data_type": "INTEGER",
          "business_meaning": "Number of votes received",
          "optimization_purpose": "Objective coefficient value",
          "sample_values": [
            2500,
            5000,
            7500
          ]
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "total_budget": {
    "sample_value": 100000,
    "data_type": "INTEGER",
    "business_meaning": "Total available budget for promotional activities",
    "optimization_role": "Constraint bound for total promotional spending",
    "configuration_type": "scalar_parameter"
  },
  "conversion_rate": {
    "sample_value": 0.5,
    "data_type": "FLOAT",
    "business_meaning": "Conversion rate of promotional budget to votes per state",
    "optimization_role": "Used in calculating votes received",
    "configuration_type": "scalar_parameter"
  },
  "max_budget_per_state": {
    "sample_value": 20000,
    "data_type": "INTEGER",
    "business_meaning": "Maximum promotional budget allowed per state",
    "optimization_role": "Constraint bound for state-level promotional spending",
    "configuration_type": "scalar_parameter"
  },
  "votes_received_formula": {
    "formula_expression": "conversion_rate * promotional_budget",
    "data_type": "STRING",
    "business_meaning": "Formula to calculate votes received based on promotional budget",
    "optimization_role": "Used in objective function to calculate votes received",
    "configuration_type": "business_logic_formula"
  }
}


TASK: Refine the optimization problem formulation by analyzing current data schema mapping and identifying requirements while maintaining LINEAR structure.

JSON STRUCTURE REQUIRED:

{
  "database_id": "voter_1",
  "iteration": 1,
  "business_context": "Updated realistic business scenario description that supports linear optimization",
  "optimization_problem_description": "Refined description of LINEAR optimization problem", 
  "optimization_formulation": {
    "objective": "refined linear minimize/maximize with mathematical precision (sum of weighted variables only)",
    "decision_variables": "clearly defined controllable linear variables (continuous or integer)",
    "constraints": "mathematically precise LINEAR constraint definitions (no variable products or divisions) - maintain 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 still needed for linear formulation (should be [] if all mappings are good)"
  ],
  
  "iteration_status": {
    "complete": true/false based on linear formulation completeness,
    "confidence": "updated confidence level",
    "next_focus": "What needs refinement for linear optimization OR 'Ready for convergence'"
  }
}

Response:
{
  "database_id": "voter_1",
  "iteration": 1,
  "business_context": "A voting competition where contestants aim to maximize their votes across different states by allocating a limited promotional budget. The optimization ensures fair and efficient budget allocation while respecting state-specific constraints.",
  "optimization_problem_description": "Maximize the total number of votes received by contestants across states by allocating a promotional budget, subject to total budget and state-level spending limits.",
  "optimization_formulation": {
    "objective": "maximize \u2211(votes_received[contestant_number, state])",
    "decision_variables": "budget[contestant_number, state] (continuous)",
    "constraints": [
      "\u2211(budget[contestant_number, state]) \u2264 total_budget",
      "budget[contestant_number, state] \u2264 max_budget_per_state for all contestant_number, state"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "votes_received[contestant_number, state]": {
        "currently_mapped_to": "VOTES_RECEIVED.votes",
        "mapping_adequacy": "good",
        "description": "Number of votes received by each contestant in each state"
      }
    },
    "constraint_bounds": {
      "total_budget": {
        "currently_mapped_to": "business_configuration_logic.total_budget",
        "mapping_adequacy": "good",
        "description": "Total available budget for promotional activities"
      },
      "max_budget_per_state": {
        "currently_mapped_to": "business_configuration_logic.max_budget_per_state",
        "mapping_adequacy": "good",
        "description": "Maximum promotional budget allowed per state"
      }
    },
    "decision_variables": {
      "budget[contestant_number, state]": {
        "currently_mapped_to": "PROMOTIONAL_BUDGET.budget",
        "mapping_adequacy": "good",
        "description": "Promotional budget allocated to each contestant in each state",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
