Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-28 00:11:08

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 wants to optimize the allocation of campaign resources to maximize the number of seats won in upcoming elections. The party can decide how much effort to allocate to each representative's campaign, considering the historical performance and current political landscape.",
  "optimization_problem": "The goal is to maximize the total number of seats won by allocating campaign resources efficiently across different representatives. The decision variables represent the level of campaign effort allocated to each representative, subject to constraints on total available resources and minimum effort required for each campaign.",
  "objective": "maximize sum(Seats[i] * Effort[i])",
  "table_count": 1,
  "key_changes": [
    "Schema changes include creating new tables for missing optimization data and updating configuration logic for scalar parameters and formulas."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Identify and integrate missing data for resource constraints and effort levels",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating new tables for missing optimization data and updating configuration logic for scalar parameters and formulas.

CREATE TABLE election (
  Seats INTEGER,
  Minimum_Effort FLOAT,
  Maximum_Effort FLOAT
);

CREATE TABLE representative_effort (
  Effort FLOAT
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "election": {
      "business_purpose": "Stores election-related data for representatives",
      "optimization_role": "objective_coefficients/constraint_bounds",
      "columns": {
        "Seats": {
          "data_type": "INTEGER",
          "business_meaning": "Number of seats associated with each representative",
          "optimization_purpose": "Objective coefficient for optimization",
          "sample_values": "1, 2, 3"
        },
        "Minimum_Effort": {
          "data_type": "FLOAT",
          "business_meaning": "Minimum effort required for each representative",
          "optimization_purpose": "Constraint lower bound",
          "sample_values": "10.0, 15.0, 20.0"
        },
        "Maximum_Effort": {
          "data_type": "FLOAT",
          "business_meaning": "Maximum effort allowed for each representative",
          "optimization_purpose": "Constraint upper bound",
          "sample_values": "50.0, 60.0, 70.0"
        }
      }
    },
    "representative_effort": {
      "business_purpose": "Stores the level of campaign effort allocated to each representative",
      "optimization_role": "decision_variables",
      "columns": {
        "Effort": {
          "data_type": "FLOAT",
          "business_meaning": "Level of campaign effort allocated",
          "optimization_purpose": "Decision variable for optimization",
          "sample_values": "20.0, 30.0, 40.0"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "Total_Resources": {
    "sample_value": "100000",
    "data_type": "INTEGER",
    "business_meaning": "Total campaign resources available for allocation",
    "optimization_role": "Constraint on total resources",
    "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 is optimizing the allocation of campaign resources to maximize the number of seats won in upcoming elections. The party allocates effort to each representative's campaign, considering historical performance and current political landscape, while adhering to resource constraints.",
  "optimization_problem_description": "The goal is to maximize the total number of seats won by efficiently allocating campaign resources across different representatives. The decision variables represent the level of campaign effort allocated to each representative, subject to constraints on total available resources and minimum and maximum effort required for each campaign.",
  "optimization_formulation": {
    "objective": "maximize sum(Seats[i] * Effort[i])",
    "decision_variables": "Effort[i] for each representative, where Effort[i] is continuous",
    "constraints": [
      "sum(Effort[i]) <= Total_Resources",
      "Minimum_Effort[i] <= Effort[i] <= Maximum_Effort[i] for each representative"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Seats[i]": {
        "currently_mapped_to": "election.Seats",
        "mapping_adequacy": "good",
        "description": "Number of seats associated with each representative"
      }
    },
    "constraint_bounds": {
      "Total_Resources": {
        "currently_mapped_to": "business_configuration_logic.Total_Resources",
        "mapping_adequacy": "good",
        "description": "Total campaign resources available for allocation"
      },
      "Minimum_Effort[i]": {
        "currently_mapped_to": "election.Minimum_Effort",
        "mapping_adequacy": "good",
        "description": "Minimum effort required for each representative"
      },
      "Maximum_Effort[i]": {
        "currently_mapped_to": "election.Maximum_Effort",
        "mapping_adequacy": "good",
        "description": "Maximum effort allowed for each representative"
      }
    },
    "decision_variables": {
      "Effort[i]": {
        "currently_mapped_to": "representative_effort.Effort",
        "mapping_adequacy": "good",
        "description": "Level of campaign effort allocated to each representative",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
