Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-27 21:45:57

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": "Optimize the allocation of campaign resources across counties to maximize the number of votes for a political party in an upcoming election.",
  "optimization_problem": "The goal is to determine the optimal allocation of campaign resources (e.g., funds, personnel) to different counties to maximize the expected number of votes for a specific political party, considering constraints such as budget limits and minimum resource allocation requirements.",
  "objective": "maximize sum(votes_coefficient[i] * resource_allocation[i])",
  "table_count": 2,
  "key_changes": [
    "Schema changes include creating new tables for objective coefficients, constraint bounds, and decision variables. Business configuration logic is updated to include scalar parameters and formulas for optimization constraints and objectives."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Identify and integrate missing data for coefficients and constraints",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating new tables for objective coefficients, constraint bounds, and decision variables. Business configuration logic is updated to include scalar parameters and formulas for optimization constraints and objectives.

CREATE TABLE ObjectiveCoefficients (
  county_id INTEGER,
  votes_coefficient FLOAT
);

CREATE TABLE DecisionVariables (
  county_id INTEGER,
  resource_allocation FLOAT
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "ObjectiveCoefficients": {
      "business_purpose": "Stores coefficients for the objective function related to votes gained per resource unit",
      "optimization_role": "objective_coefficients",
      "columns": {
        "county_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each county",
          "optimization_purpose": "Links coefficients to specific counties",
          "sample_values": "1, 2, 3"
        },
        "votes_coefficient": {
          "data_type": "FLOAT",
          "business_meaning": "Expected votes gained per unit of resource",
          "optimization_purpose": "Coefficient in the objective function",
          "sample_values": "0.5, 1.2, 0.8"
        }
      }
    },
    "DecisionVariables": {
      "business_purpose": "Stores decision variables for resource allocation to counties",
      "optimization_role": "decision_variables",
      "columns": {
        "county_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each county",
          "optimization_purpose": "Links decision variables to specific counties",
          "sample_values": "1, 2, 3"
        },
        "resource_allocation": {
          "data_type": "FLOAT",
          "business_meaning": "Amount of resources allocated to the county",
          "optimization_purpose": "Decision variable in the optimization model",
          "sample_values": "500, 1000, 750"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "total_budget": {
    "sample_value": "1000000",
    "data_type": "FLOAT",
    "business_meaning": "Total budget available for resource allocation",
    "optimization_role": "Used as an upper bound constraint in the optimization model",
    "configuration_type": "scalar_parameter"
  },
  "min_allocation": {
    "sample_value": "100",
    "data_type": "FLOAT",
    "business_meaning": "Minimum amount of resources that must be allocated to each county",
    "optimization_role": "Used as a lower bound constraint in the optimization model",
    "configuration_type": "scalar_parameter"
  },
  "max_allocation": {
    "sample_value": "10000",
    "data_type": "FLOAT",
    "business_meaning": "Maximum amount of resources that can be allocated to each county",
    "optimization_role": "Used as an upper bound constraint in the optimization model",
    "configuration_type": "scalar_parameter"
  }
}


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

JSON STRUCTURE REQUIRED:

{
  "database_id": "election",
  "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": "election",
  "iteration": 1,
  "business_context": "Optimize the allocation of campaign resources across counties to maximize the number of votes for a political party in an upcoming election, considering budget constraints and minimum/maximum resource allocation per county.",
  "optimization_problem_description": "Determine the optimal allocation of campaign resources to different counties to maximize the expected number of votes, subject to budget limits and resource allocation constraints.",
  "optimization_formulation": {
    "objective": "maximize sum(ObjectiveCoefficients.votes_coefficient[i] * DecisionVariables.resource_allocation[i])",
    "decision_variables": "resource_allocation[i] for each county i, continuous",
    "constraints": [
      "sum(DecisionVariables.resource_allocation[i]) <= business_configuration_logic.total_budget",
      "DecisionVariables.resource_allocation[i] >= business_configuration_logic.min_allocation for each county i",
      "DecisionVariables.resource_allocation[i] <= business_configuration_logic.max_allocation for each county i"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "votes_coefficient[i]": {
        "currently_mapped_to": "ObjectiveCoefficients.votes_coefficient",
        "mapping_adequacy": "good",
        "description": "Expected votes gained per unit of resource for county i"
      }
    },
    "constraint_bounds": {
      "total_budget": {
        "currently_mapped_to": "business_configuration_logic.total_budget",
        "mapping_adequacy": "good",
        "description": "Total budget available for resource allocation"
      },
      "min_allocation[i]": {
        "currently_mapped_to": "business_configuration_logic.min_allocation",
        "mapping_adequacy": "good",
        "description": "Minimum amount of resources that must be allocated to each county i"
      },
      "max_allocation[i]": {
        "currently_mapped_to": "business_configuration_logic.max_allocation",
        "mapping_adequacy": "good",
        "description": "Maximum amount of resources that can be allocated to each county i"
      }
    },
    "decision_variables": {
      "resource_allocation[i]": {
        "currently_mapped_to": "DecisionVariables.resource_allocation",
        "mapping_adequacy": "good",
        "description": "Amount of resources allocated to county i",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
