Iteration 2 - OR_EXPERT_REFINEMENT
Sequence: 5
Timestamp: 2025-07-27 22:54:53

Prompt:
You are an Operations Research (OR) expert in iteration 2 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 1):
{
  "iteration": 2,
  "converged": false,
  "business_context": "Optimize the allocation of ships to battles to minimize the total number of deaths caused by ships, considering the constraints on ship availability and battle requirements.",
  "optimization_problem": "Allocate ships to battles to minimize total deaths, ensuring each ship is assigned to at most one battle and each battle receives the required number of ships.",
  "objective": "minimize total_deaths = sum(deaths_caused_by_ship_in_battle[i,j] * x[i,j])",
  "table_count": 1,
  "key_changes": [
    "Incorporated missing data for deaths caused by ships in battles, adjusted schema to include objective coefficients, and updated business configuration logic for scalar parameters and formulas."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Incorporate deaths_caused_by_ship_in_battle data into schema for complete linear formulation",
  "mapping_adequacy_summary": "partially_adequate"
}

CURRENT SCHEMA:
```sql
-- Iteration 2 Database Schema
-- Objective: Incorporated missing data for deaths caused by ships in battles, adjusted schema to include objective coefficients, and updated business configuration logic for scalar parameters and formulas.

CREATE TABLE ship_battle_assignment (
  ship_id INTEGER,
  battle_id INTEGER,
  assignment BOOLEAN
);

CREATE TABLE battle_requirements (
  battle_id INTEGER,
  min_ships INTEGER
);

CREATE TABLE deaths_by_ship_battle (
  ship_id INTEGER,
  battle_id INTEGER,
  deaths INTEGER
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "ship_battle_assignment": {
      "business_purpose": "Tracks ship assignments to battles",
      "optimization_role": "decision_variables",
      "columns": {
        "ship_id": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for each ship",
          "optimization_purpose": "Used to identify ships in assignments",
          "sample_values": "1, 2, 3"
        },
        "battle_id": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for each battle",
          "optimization_purpose": "Used to identify battles in assignments",
          "sample_values": "101, 102, 103"
        },
        "assignment": {
          "data_type": "BOOLEAN",
          "business_meaning": "Indicates if a ship is assigned to a battle",
          "optimization_purpose": "Binary decision variable",
          "sample_values": "true, false"
        }
      }
    },
    "battle_requirements": {
      "business_purpose": "Stores minimum ship requirements for battles",
      "optimization_role": "constraint_bounds",
      "columns": {
        "battle_id": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for each battle",
          "optimization_purpose": "Links to battles for requirement checks",
          "sample_values": "101, 102, 103"
        },
        "min_ships": {
          "data_type": "INTEGER",
          "business_meaning": "Minimum number of ships required for a battle",
          "optimization_purpose": "Constraint bound for ship assignments",
          "sample_values": "3, 5, 7"
        }
      }
    },
    "deaths_by_ship_battle": {
      "business_purpose": "Stores the number of deaths caused by each ship in each battle",
      "optimization_role": "objective_coefficients",
      "columns": {
        "ship_id": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for each ship",
          "optimization_purpose": "Used to identify ships in death calculations",
          "sample_values": "1, 2, 3"
        },
        "battle_id": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for each battle",
          "optimization_purpose": "Used to identify battles in death calculations",
          "sample_values": "101, 102, 103"
        },
        "deaths": {
          "data_type": "INTEGER",
          "business_meaning": "Number of deaths caused by a ship in a battle",
          "optimization_purpose": "Coefficient in the objective function",
          "sample_values": "10, 20, 30"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "ship_availability_limit": {
    "sample_value": "10",
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of ships available for assignment",
    "optimization_role": "Limits the number of ships that can be assigned",
    "configuration_type": "scalar_parameter"
  },
  "total_deaths_formula": {
    "formula_expression": "sum(deaths_caused_by_ship_in_battle[i,j] * x[i,j])",
    "data_type": "STRING",
    "business_meaning": "Calculates the total deaths caused by ship assignments",
    "optimization_role": "Objective function to minimize",
    "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": "battle_death",
  "iteration": 2,
  "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": "battle_death",
  "iteration": 2,
  "business_context": "Optimize the allocation of ships to battles to minimize the total number of deaths caused by ships, considering the constraints on ship availability and battle requirements.",
  "optimization_problem_description": "Allocate ships to battles to minimize total deaths, ensuring each ship is assigned to at most one battle and each battle receives the required number of ships.",
  "optimization_formulation": {
    "objective": "minimize total_deaths = sum(deaths_by_ship_battle.deaths * ship_battle_assignment.assignment)",
    "decision_variables": "x[i,j] where x[i,j] is a binary variable indicating if ship i is assigned to battle j",
    "constraints": [
      "sum(x[i,j] for all j) <= 1 for each ship i",
      "sum(x[i,j] for all i) >= battle_requirements.min_ships for each battle j",
      "sum(x[i,j] for all i) <= ship_availability_limit"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "deaths[i,j]": {
        "currently_mapped_to": "deaths_by_ship_battle.deaths",
        "mapping_adequacy": "good",
        "description": "Number of deaths caused by ship i in battle j"
      }
    },
    "constraint_bounds": {
      "min_ships[j]": {
        "currently_mapped_to": "battle_requirements.min_ships",
        "mapping_adequacy": "good",
        "description": "Minimum number of ships required for battle j"
      },
      "ship_availability_limit": {
        "currently_mapped_to": "business_configuration_logic.ship_availability_limit",
        "mapping_adequacy": "good",
        "description": "Maximum number of ships available for assignment"
      }
    },
    "decision_variables": {
      "x[i,j]": {
        "currently_mapped_to": "ship_battle_assignment.assignment",
        "mapping_adequacy": "good",
        "description": "Binary variable indicating if ship i is assigned to battle j",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
