Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-25 22:38:12

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 shipping company aims to minimize the total operational cost of its fleet while ensuring that each ship meets specific mission requirements. The company needs to allocate ships to missions based on their tonnage, speed, and nationality constraints.",
  "optimization_problem": "The objective is to minimize the total operational cost of the fleet, which is a linear combination of the cost associated with each ship's tonnage and speed. The constraints ensure that each mission is assigned to exactly one ship, each ship is assigned to at most one mission, and the ship's tonnage and speed meet the mission requirements.",
  "objective": "minimize \u2211(c_tonnage * Tonnage_i + c_speed * Speed_knots_i) * x_ij",
  "table_count": 2,
  "key_changes": [
    "Schema changes include creating tables for mission requirements and ship attributes, and updating business configuration logic to include cost coefficients and mission constraints."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Identify and map missing cost coefficients and mission requirements to complete the optimization model.",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating tables for mission requirements and ship attributes, and updating business configuration logic to include cost coefficients and mission constraints.

CREATE TABLE missions (
  mission_id INTEGER,
  min_tonnage INTEGER,
  min_speed INTEGER,
  required_nationality STRING
);

CREATE TABLE ships (
  ship_id INTEGER,
  tonnage INTEGER,
  speed_knots INTEGER,
  nationality STRING
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "missions": {
      "business_purpose": "Details of each mission including minimum tonnage, speed, and nationality requirements.",
      "optimization_role": "constraint_bounds",
      "columns": {
        "mission_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each mission",
          "optimization_purpose": "Used to link missions to ships",
          "sample_values": "1, 2, 3"
        },
        "min_tonnage": {
          "data_type": "INTEGER",
          "business_meaning": "Minimum tonnage required for the mission",
          "optimization_purpose": "Used in the tonnage constraint",
          "sample_values": "5000, 6000, 7000"
        },
        "min_speed": {
          "data_type": "INTEGER",
          "business_meaning": "Minimum speed required for the mission",
          "optimization_purpose": "Used in the speed constraint",
          "sample_values": "20, 25, 30"
        },
        "required_nationality": {
          "data_type": "STRING",
          "business_meaning": "Required nationality for the mission",
          "optimization_purpose": "Used in the nationality constraint",
          "sample_values": "USA, UK, Canada"
        }
      }
    },
    "ships": {
      "business_purpose": "Details of each ship including tonnage, speed, and nationality.",
      "optimization_role": "business_data",
      "columns": {
        "ship_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each ship",
          "optimization_purpose": "Used to link ships to missions",
          "sample_values": "1, 2, 3"
        },
        "tonnage": {
          "data_type": "INTEGER",
          "business_meaning": "Tonnage of the ship",
          "optimization_purpose": "Used in the tonnage constraint",
          "sample_values": "5000, 6000, 7000"
        },
        "speed_knots": {
          "data_type": "INTEGER",
          "business_meaning": "Speed of the ship in knots",
          "optimization_purpose": "Used in the speed constraint",
          "sample_values": "20, 25, 30"
        },
        "nationality": {
          "data_type": "STRING",
          "business_meaning": "Nationality of the ship",
          "optimization_purpose": "Used in the nationality constraint",
          "sample_values": "USA, UK, Canada"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "c_tonnage": {
    "sample_value": 0.5,
    "data_type": "FLOAT",
    "business_meaning": "Cost coefficient associated with ship tonnage",
    "optimization_role": "Used in the objective function to calculate operational cost",
    "configuration_type": "scalar_parameter"
  },
  "c_speed": {
    "sample_value": 0.3,
    "data_type": "FLOAT",
    "business_meaning": "Cost coefficient associated with ship speed",
    "optimization_role": "Used in the objective function to calculate operational cost",
    "configuration_type": "scalar_parameter"
  },
  "Min_Tonnage_j": {
    "sample_value": 5000,
    "data_type": "INTEGER",
    "business_meaning": "Minimum tonnage required for mission j",
    "optimization_role": "Used in the tonnage constraint",
    "configuration_type": "scalar_parameter"
  },
  "Min_Speed_j": {
    "sample_value": 20,
    "data_type": "INTEGER",
    "business_meaning": "Minimum speed required for mission j",
    "optimization_role": "Used in the speed constraint",
    "configuration_type": "scalar_parameter"
  },
  "Required_Nationality_j": {
    "sample_value": "USA",
    "data_type": "STRING",
    "business_meaning": "Required nationality for mission j",
    "optimization_role": "Used in the nationality constraint",
    "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": "ship_mission",
  "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": "ship_mission",
  "iteration": 1,
  "business_context": "A shipping company aims to minimize the total operational cost of its fleet while ensuring that each ship meets specific mission requirements. The company needs to allocate ships to missions based on their tonnage, speed, and nationality constraints.",
  "optimization_problem_description": "The objective is to minimize the total operational cost of the fleet, which is a linear combination of the cost associated with each ship's tonnage and speed. The constraints ensure that each mission is assigned to exactly one ship, each ship is assigned to at most one mission, and the ship's tonnage and speed meet the mission requirements.",
  "optimization_formulation": {
    "objective": "minimize \u2211(c_tonnage * Tonnage_i + c_speed * Speed_knots_i) * x_ij",
    "decision_variables": "x_ij: binary variable indicating whether ship i is assigned to mission j",
    "constraints": [
      "\u2211(x_ij) = 1 for all missions j (each mission is assigned to exactly one ship)",
      "\u2211(x_ij) \u2264 1 for all ships i (each ship is assigned to at most one mission)",
      "Tonnage_i \u2265 Min_Tonnage_j * x_ij for all ships i and missions j (ship tonnage meets mission requirement)",
      "Speed_knots_i \u2265 Min_Speed_j * x_ij for all ships i and missions j (ship speed meets mission requirement)",
      "Nationality_i = Required_Nationality_j * x_ij for all ships i and missions j (ship nationality meets mission requirement)"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "c_tonnage": {
        "currently_mapped_to": "business_configuration_logic.c_tonnage",
        "mapping_adequacy": "good",
        "description": "Cost coefficient associated with ship tonnage"
      },
      "c_speed": {
        "currently_mapped_to": "business_configuration_logic.c_speed",
        "mapping_adequacy": "good",
        "description": "Cost coefficient associated with ship speed"
      }
    },
    "constraint_bounds": {
      "Min_Tonnage_j": {
        "currently_mapped_to": "missions.min_tonnage",
        "mapping_adequacy": "good",
        "description": "Minimum tonnage required for mission j"
      },
      "Min_Speed_j": {
        "currently_mapped_to": "missions.min_speed",
        "mapping_adequacy": "good",
        "description": "Minimum speed required for mission j"
      },
      "Required_Nationality_j": {
        "currently_mapped_to": "missions.required_nationality",
        "mapping_adequacy": "good",
        "description": "Required nationality for mission j"
      }
    },
    "decision_variables": {
      "x_ij": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Binary variable indicating whether ship i is assigned to mission j",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "Decision variable x_ij indicating ship-to-mission assignment"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Define and map the decision variable x_ij to complete the linear optimization model."
  }
}
