Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-25 22:30:30

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 gas company aims to optimize the allocation of its gas stations to different companies to maximize overall profits while respecting company ranks and station capacities.",
  "optimization_problem": "The company wants to maximize the total profits from gas stations by assigning each station to a company, considering the company's rank and the station's potential profit contribution. The assignment must respect the company's rank and ensure that no station is assigned to more than one company.",
  "objective": "maximize \u2211(Profit_ij * X_ij) where Profit_ij is the profit from station i assigned to company j, and X_ij is a binary decision variable indicating the assignment.",
  "table_count": 2,
  "key_changes": [
    "Schema changes and configuration logic updates implemented to address missing profit and rank data, ensuring complete optimization model mapping."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Identify and map the missing profit and rank data to complete the optimization model.",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes and configuration logic updates implemented to address missing profit and rank data, ensuring complete optimization model mapping.

CREATE TABLE station_profit (
  station_id INTEGER,
  company_id INTEGER,
  profit FLOAT,
  assignment BOOLEAN
);

CREATE TABLE company_rank (
  company_id INTEGER,
  max_rank INTEGER
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "station_profit": {
      "business_purpose": "Profit from each gas station when assigned to a specific company.",
      "optimization_role": "objective_coefficients",
      "columns": {
        "station_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for a gas station.",
          "optimization_purpose": "Index for station i.",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "company_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for a company.",
          "optimization_purpose": "Index for company j.",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "profit": {
          "data_type": "FLOAT",
          "business_meaning": "Profit from station i assigned to company j.",
          "optimization_purpose": "Coefficient in the objective function.",
          "sample_values": [
            5000.0,
            7500.0,
            10000.0
          ]
        },
        "assignment": {
          "data_type": "BOOLEAN",
          "business_meaning": "Binary decision variable indicating assignment of station i to company j.",
          "optimization_purpose": "Decision variable X_ij.",
          "sample_values": [
            true,
            false,
            true
          ]
        }
      }
    },
    "company_rank": {
      "business_purpose": "Maximum rank allowed for each company.",
      "optimization_role": "constraint_bounds",
      "columns": {
        "company_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for a company.",
          "optimization_purpose": "Index for company j.",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "max_rank": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum rank allowed for the company.",
          "optimization_purpose": "Constraint bound for company rank.",
          "sample_values": [
            100,
            150,
            200
          ]
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "Max_Rank": {
    "sample_value": 100,
    "data_type": "INTEGER",
    "business_meaning": "Maximum rank allowed for a company.",
    "optimization_role": "Constraint bound for company rank.",
    "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": "gas_company",
  "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": "gas_company",
  "iteration": 1,
  "business_context": "A gas company aims to optimize the allocation of its gas stations to different companies to maximize overall profits while respecting company ranks and station capacities.",
  "optimization_problem_description": "Maximize the total profits from gas stations by assigning each station to a company, considering the company's rank and the station's potential profit contribution. The assignment must respect the company's rank and ensure that no station is assigned to more than one company.",
  "optimization_formulation": {
    "objective": "maximize \u2211(Profit_ij * X_ij) where Profit_ij is the profit from station i assigned to company j, and X_ij is a binary decision variable indicating the assignment.",
    "decision_variables": "X_ij: binary decision variable indicating the assignment of station i to company j.",
    "constraints": "1. \u2211(X_ij) \u2264 1 for all i (each station is assigned to at most one company), 2. \u2211(X_ij) \u2264 max_rank_j for all j (total assignments to company j do not exceed its maximum rank)."
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Profit_ij[i,j]": {
        "currently_mapped_to": "station_profit.profit",
        "mapping_adequacy": "good",
        "description": "Profit from station i assigned to company j."
      }
    },
    "constraint_bounds": {
      "max_rank_j[j]": {
        "currently_mapped_to": "company_rank.max_rank",
        "mapping_adequacy": "good",
        "description": "Maximum rank allowed for company j."
      }
    },
    "decision_variables": {
      "X_ij[i,j]": {
        "currently_mapped_to": "station_profit.assignment",
        "mapping_adequacy": "good",
        "description": "Binary decision variable indicating the assignment of station i to company j.",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
