Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-25 22:30:48

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 farm competition organizer wants to maximize the overall quality of the competition by selecting the best farms to participate, considering the number of animals each farm has and the city's capacity to host the event.",
  "optimization_problem": "The organizer needs to decide which farms to invite to the competition to maximize the total number of high-quality animals (horses, cattle, pigs, sheep, and goats) while respecting the hosting city's capacity constraints.",
  "objective": "maximize \u2211(Quality_Score_Farm_i \u00d7 Invite_Farm_i) where Quality_Score_Farm_i is a weighted sum of the animals on the farm.",
  "table_count": 3,
  "key_changes": [
    "Schema changes include creating tables for farms, animals, and city capacities, and updating business configuration logic to handle scalar parameters and formulas for optimization."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Define the quality score for each farm and the city's capacity constraints.",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating tables for farms, animals, and city capacities, and updating business configuration logic to handle scalar parameters and formulas for optimization.

CREATE TABLE farms (
  farm_id INTEGER,
  invite_status BOOLEAN
);

CREATE TABLE animals (
  farm_id INTEGER,
  horses INTEGER,
  cattle INTEGER,
  pigs INTEGER,
  sheep_and_goats INTEGER
);

CREATE TABLE city_capacities (
  max_farms INTEGER,
  max_horses INTEGER,
  max_cattle INTEGER,
  max_pigs INTEGER,
  max_sheep_goats INTEGER
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "farms": {
      "business_purpose": "Represents farms eligible for the competition.",
      "optimization_role": "business_data",
      "columns": {
        "farm_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each farm.",
          "optimization_purpose": "Identifier for decision variables.",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "invite_status": {
          "data_type": "BOOLEAN",
          "business_meaning": "Whether the farm is invited to the competition.",
          "optimization_purpose": "Decision variable for inviting the farm.",
          "sample_values": [
            true,
            false,
            true
          ]
        }
      }
    },
    "animals": {
      "business_purpose": "Represents the number of each type of animal on each farm.",
      "optimization_role": "business_data",
      "columns": {
        "farm_id": {
          "data_type": "INTEGER",
          "business_meaning": "Foreign key linking to the farms table.",
          "optimization_purpose": "Identifier for decision variables.",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "horses": {
          "data_type": "INTEGER",
          "business_meaning": "Number of horses on the farm.",
          "optimization_purpose": "Used in quality score calculation and constraints.",
          "sample_values": [
            5,
            10,
            15
          ]
        },
        "cattle": {
          "data_type": "INTEGER",
          "business_meaning": "Number of cattle on the farm.",
          "optimization_purpose": "Used in quality score calculation and constraints.",
          "sample_values": [
            20,
            30,
            40
          ]
        },
        "pigs": {
          "data_type": "INTEGER",
          "business_meaning": "Number of pigs on the farm.",
          "optimization_purpose": "Used in quality score calculation and constraints.",
          "sample_values": [
            50,
            60,
            70
          ]
        },
        "sheep_and_goats": {
          "data_type": "INTEGER",
          "business_meaning": "Number of sheep and goats on the farm.",
          "optimization_purpose": "Used in quality score calculation and constraints.",
          "sample_values": [
            30,
            40,
            50
          ]
        }
      }
    },
    "city_capacities": {
      "business_purpose": "Represents the city's capacity constraints for hosting the competition.",
      "optimization_role": "constraint_bounds",
      "columns": {
        "max_farms": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum number of farms the city can host.",
          "optimization_purpose": "Constraint bound for the total number of invited farms.",
          "sample_values": [
            10
          ]
        },
        "max_horses": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum number of horses the city can accommodate.",
          "optimization_purpose": "Constraint bound for the total number of horses from invited farms.",
          "sample_values": [
            50
          ]
        },
        "max_cattle": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum number of cattle the city can accommodate.",
          "optimization_purpose": "Constraint bound for the total number of cattle from invited farms.",
          "sample_values": [
            100
          ]
        },
        "max_pigs": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum number of pigs the city can accommodate.",
          "optimization_purpose": "Constraint bound for the total number of pigs from invited farms.",
          "sample_values": [
            200
          ]
        },
        "max_sheep_goats": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum number of sheep and goats the city can accommodate.",
          "optimization_purpose": "Constraint bound for the total number of sheep and goats from invited farms.",
          "sample_values": [
            150
          ]
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "Max_Farms": {
    "sample_value": 10,
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of farms the city can host.",
    "optimization_role": "Constraint bound for the total number of invited farms.",
    "configuration_type": "scalar_parameter"
  },
  "Max_Horses": {
    "sample_value": 50,
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of horses the city can accommodate.",
    "optimization_role": "Constraint bound for the total number of horses from invited farms.",
    "configuration_type": "scalar_parameter"
  },
  "Max_Cattle": {
    "sample_value": 100,
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of cattle the city can accommodate.",
    "optimization_role": "Constraint bound for the total number of cattle from invited farms.",
    "configuration_type": "scalar_parameter"
  },
  "Max_Pigs": {
    "sample_value": 200,
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of pigs the city can accommodate.",
    "optimization_role": "Constraint bound for the total number of pigs from invited farms.",
    "configuration_type": "scalar_parameter"
  },
  "Max_Sheep_Goats": {
    "sample_value": 150,
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of sheep and goats the city can accommodate.",
    "optimization_role": "Constraint bound for the total number of sheep and goats from invited farms.",
    "configuration_type": "scalar_parameter"
  },
  "Quality_Score_Farm_i": {
    "formula_expression": "(horses * 0.3) + (cattle * 0.25) + (pigs * 0.2) + (sheep_and_goats * 0.25)",
    "data_type": "STRING",
    "business_meaning": "Weighted sum of animals on each farm to represent its quality.",
    "optimization_role": "Objective coefficient for the quality score of each farm.",
    "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": "farm",
  "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": "farm",
  "iteration": 1,
  "business_context": "A farm competition organizer aims to maximize the overall quality of the competition by selecting the best farms to participate, considering the number of animals each farm has and the city's capacity to host the event. The quality of each farm is determined by a weighted sum of the animals it possesses.",
  "optimization_problem_description": "The organizer needs to decide which farms to invite to the competition to maximize the total quality score of the invited farms, while respecting the hosting city's capacity constraints on the number of farms and animals.",
  "optimization_formulation": {
    "objective": "maximize \u2211(Quality_Score_Farm_i \u00d7 Invite_Farm_i)",
    "decision_variables": "Invite_Farm_i: binary variable indicating whether farm i is invited (1) or not (0)",
    "constraints": [
      "\u2211(Invite_Farm_i) \u2264 Max_Farms",
      "\u2211(horses_i \u00d7 Invite_Farm_i) \u2264 Max_Horses",
      "\u2211(cattle_i \u00d7 Invite_Farm_i) \u2264 Max_Cattle",
      "\u2211(pigs_i \u00d7 Invite_Farm_i) \u2264 Max_Pigs",
      "\u2211(sheep_and_goats_i \u00d7 Invite_Farm_i) \u2264 Max_Sheep_Goats"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Quality_Score_Farm_i": {
        "currently_mapped_to": "business_configuration_logic.Quality_Score_Farm_i",
        "mapping_adequacy": "good",
        "description": "Weighted sum of animals on each farm to represent its quality."
      }
    },
    "constraint_bounds": {
      "Max_Farms": {
        "currently_mapped_to": "business_configuration_logic.Max_Farms",
        "mapping_adequacy": "good",
        "description": "Maximum number of farms the city can host."
      },
      "Max_Horses": {
        "currently_mapped_to": "business_configuration_logic.Max_Horses",
        "mapping_adequacy": "good",
        "description": "Maximum number of horses the city can accommodate."
      },
      "Max_Cattle": {
        "currently_mapped_to": "business_configuration_logic.Max_Cattle",
        "mapping_adequacy": "good",
        "description": "Maximum number of cattle the city can accommodate."
      },
      "Max_Pigs": {
        "currently_mapped_to": "business_configuration_logic.Max_Pigs",
        "mapping_adequacy": "good",
        "description": "Maximum number of pigs the city can accommodate."
      },
      "Max_Sheep_Goats": {
        "currently_mapped_to": "business_configuration_logic.Max_Sheep_Goats",
        "mapping_adequacy": "good",
        "description": "Maximum number of sheep and goats the city can accommodate."
      }
    },
    "decision_variables": {
      "Invite_Farm_i": {
        "currently_mapped_to": "farms.invite_status",
        "mapping_adequacy": "good",
        "description": "Decision variable for inviting the farm.",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
