Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-25 22:27:13

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 political party aims to maximize the total number of seats won across multiple elections by strategically allocating campaign resources to representatives in different states.",
  "optimization_problem": "The objective is to maximize the total seats won by the party across all elections. The decision variables represent the amount of campaign resources allocated to each representative. Constraints include budget limits, minimum resource allocations per representative, and maximum resource allocations per state.",
  "objective": "maximize \u2211(Seats_i \u00d7 Resource_i)",
  "table_count": 2,
  "key_changes": [
    "Schema changes include creating tables for decision variables and constraint bounds, moving scalar parameters to business configuration logic, and updating the data dictionary to reflect optimization mappings."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Identify and map missing data/parameters for constraints and decision variables",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating tables for decision variables and constraint bounds, moving scalar parameters to business configuration logic, and updating the data dictionary to reflect optimization mappings.

CREATE TABLE election (
  Seats INTEGER
);

CREATE TABLE resource_allocation (
  Resource_Amount FLOAT
);

CREATE TABLE state_resource_limits (
  Maximum_Resource_Allocation INTEGER
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "election": {
      "business_purpose": "Stores election results for each representative",
      "optimization_role": "objective_coefficients",
      "columns": {
        "Seats": {
          "data_type": "INTEGER",
          "business_meaning": "Number of seats won by representative i",
          "optimization_purpose": "Coefficient in the objective function",
          "sample_values": [
            1,
            2,
            3
          ]
        }
      }
    },
    "resource_allocation": {
      "business_purpose": "Stores campaign resource allocations for each representative",
      "optimization_role": "decision_variables",
      "columns": {
        "Resource_Amount": {
          "data_type": "FLOAT",
          "business_meaning": "Amount of campaign resources allocated to representative i",
          "optimization_purpose": "Decision variable in the optimization model",
          "sample_values": [
            1000.0,
            2000.0,
            3000.0
          ]
        }
      }
    },
    "state_resource_limits": {
      "business_purpose": "Stores maximum resource allocation limits for each state",
      "optimization_role": "constraint_bounds",
      "columns": {
        "Maximum_Resource_Allocation": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum amount of resources that can be allocated to representatives in a state",
          "optimization_purpose": "Constraint bound in the optimization model",
          "sample_values": [
            50000,
            60000,
            70000
          ]
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "Total_Budget": {
    "sample_value": 1000000,
    "data_type": "INTEGER",
    "business_meaning": "Total budget available for campaign resources",
    "optimization_role": "Constraint bound for total resource allocation",
    "configuration_type": "scalar_parameter"
  },
  "Minimum_Resource_Allocation": {
    "sample_value": 1000,
    "data_type": "INTEGER",
    "business_meaning": "Minimum amount of resources that must be allocated to each representative",
    "optimization_role": "Constraint bound for minimum resource allocation",
    "configuration_type": "scalar_parameter"
  },
  "Maximum_Resource_Allocation_State_j": {
    "sample_value": 50000,
    "data_type": "INTEGER",
    "business_meaning": "Maximum amount of resources that can be allocated to representatives in a state",
    "optimization_role": "Constraint bound for state-level resource allocation",
    "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_representative",
  "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_representative",
  "iteration": 1,
  "business_context": "A political party aims to maximize the total number of seats won across multiple elections by strategically allocating campaign resources to representatives in different states, while adhering to budget constraints and state-specific resource limits.",
  "optimization_problem_description": "The objective is to maximize the total seats won by the party across all elections. The decision variables represent the amount of campaign resources allocated to each representative. Constraints include a total budget limit, minimum resource allocations per representative, and maximum resource allocations per state.",
  "optimization_formulation": {
    "objective": "maximize \u2211(Seats_i \u00d7 Resource_i)",
    "decision_variables": "Resource_i: continuous, representing the amount of campaign resources allocated to representative i",
    "constraints": [
      "\u2211(Resource_i) \u2264 Total_Budget",
      "Resource_i \u2265 Minimum_Resource_Allocation for all i",
      "\u2211(Resource_i for all i in state j) \u2264 Maximum_Resource_Allocation_State_j for all j"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Seats_i": {
        "currently_mapped_to": "election.Seats",
        "mapping_adequacy": "good",
        "description": "Number of seats won by representative i"
      }
    },
    "constraint_bounds": {
      "Total_Budget": {
        "currently_mapped_to": "business_configuration_logic.Total_Budget",
        "mapping_adequacy": "good",
        "description": "Total budget available for campaign resources"
      },
      "Minimum_Resource_Allocation": {
        "currently_mapped_to": "business_configuration_logic.Minimum_Resource_Allocation",
        "mapping_adequacy": "good",
        "description": "Minimum amount of resources that must be allocated to each representative"
      },
      "Maximum_Resource_Allocation_State_j": {
        "currently_mapped_to": "state_resource_limits.Maximum_Resource_Allocation",
        "mapping_adequacy": "good",
        "description": "Maximum amount of resources that can be allocated to representatives in a state"
      }
    },
    "decision_variables": {
      "Resource_i": {
        "currently_mapped_to": "resource_allocation.Resource_Amount",
        "mapping_adequacy": "good",
        "description": "Amount of campaign resources allocated to representative i",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
