Iteration 3 - OR_EXPERT_REFINEMENT
Sequence: 7
Timestamp: 2025-07-25 22:58:16

Prompt:
You are an Operations Research (OR) expert in iteration 3 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.


CONVERGENCE PRESSURE (Iteration 3/5):
- Focus on finalizing the linear optimization model
- Set complete=true if formulation is mathematically sound and linear
- Minimize further schema change requests


CURRENT STATE (iteration 2):
{
  "iteration": 3,
  "converged": false,
  "business_context": "A disaster response organization aims to minimize the total damage and loss of life caused by storms by optimally allocating resources to the most affected regions, ensuring linear optimization constraints are met.",
  "optimization_problem": "Minimize the weighted sum of damage and deaths caused by storms, subject to constraints on the number of cities affected, the maximum speed of storms, and the total budget available for resource allocation.",
  "objective": "minimize (w1 * \u2211Damage_millions_USD + w2 * \u2211Number_Deaths)",
  "table_count": 0,
  "key_changes": [
    "Schema changes include adding missing optimization parameters to business configuration logic and ensuring all tables meet the 3-row minimum rule. Configuration logic updated to include total_budget, max_speed, and max_cities_affected as scalar parameters."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Define total_budget, max_speed, and max_cities_affected in the schema or business configuration logic.",
  "mapping_adequacy_summary": "partially_adequate"
}

CURRENT SCHEMA:
```sql
-- Iteration 3 Database Schema
-- Objective: Schema changes include adding missing optimization parameters to business configuration logic and ensuring all tables meet the 3-row minimum rule. Configuration logic updated to include total_budget, max_speed, and max_cities_affected as scalar parameters.

CREATE TABLE resource_allocation (
  storm_id INTEGER,
  region_id INTEGER,
  is_allocated BOOLEAN
);

CREATE TABLE storm_details (
  storm_id INTEGER,
  storm_speed INTEGER,
  Damage_millions_USD FLOAT,
  Number_Deaths INTEGER
);

CREATE TABLE allocation_costs (
  storm_id INTEGER,
  region_id INTEGER,
  cost_per_allocation INTEGER
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "resource_allocation": {
      "business_purpose": "binary decision variable indicating whether resources are allocated to a region affected by a specific storm",
      "optimization_role": "decision_variables",
      "columns": {
        "storm_id": {
          "data_type": "INTEGER",
          "business_meaning": "unique identifier for the storm",
          "optimization_purpose": "identifies the storm in the decision variable",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "region_id": {
          "data_type": "INTEGER",
          "business_meaning": "unique identifier for the region",
          "optimization_purpose": "identifies the region in the decision variable",
          "sample_values": [
            101,
            102,
            103
          ]
        },
        "is_allocated": {
          "data_type": "BOOLEAN",
          "business_meaning": "indicates whether resources are allocated to the region for the storm",
          "optimization_purpose": "binary decision variable in the optimization model",
          "sample_values": [
            true,
            false,
            true
          ]
        }
      }
    },
    "storm_details": {
      "business_purpose": "details about each storm including speed, damage, and deaths",
      "optimization_role": "business_data",
      "columns": {
        "storm_id": {
          "data_type": "INTEGER",
          "business_meaning": "unique identifier for the storm",
          "optimization_purpose": "identifies the storm in the decision variable",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "storm_speed": {
          "data_type": "INTEGER",
          "business_meaning": "speed of the storm in km/h",
          "optimization_purpose": "used in speed constraint calculation",
          "sample_values": [
            100,
            120,
            80
          ]
        },
        "Damage_millions_USD": {
          "data_type": "FLOAT",
          "business_meaning": "damage caused by the storm in millions of USD",
          "optimization_purpose": "used in objective function calculation",
          "sample_values": [
            10,
            15,
            20
          ]
        },
        "Number_Deaths": {
          "data_type": "INTEGER",
          "business_meaning": "number of deaths caused by the storm",
          "optimization_purpose": "used in objective function calculation",
          "sample_values": [
            50,
            60,
            70
          ]
        }
      }
    },
    "allocation_costs": {
      "business_purpose": "costs associated with resource allocation per storm and region",
      "optimization_role": "business_data",
      "columns": {
        "storm_id": {
          "data_type": "INTEGER",
          "business_meaning": "unique identifier for the storm",
          "optimization_purpose": "identifies the storm in the decision variable",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "region_id": {
          "data_type": "INTEGER",
          "business_meaning": "unique identifier for the region",
          "optimization_purpose": "identifies the region in the decision variable",
          "sample_values": [
            101,
            102,
            103
          ]
        },
        "cost_per_allocation": {
          "data_type": "INTEGER",
          "business_meaning": "cost to allocate resources to a region for a storm",
          "optimization_purpose": "used in budget constraint calculation",
          "sample_values": [
            5000,
            6000,
            7000
          ]
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "total_budget": {
    "sample_value": 1000000,
    "data_type": "INTEGER",
    "business_meaning": "total budget available for resource allocation",
    "optimization_role": "used in budget constraint calculation",
    "configuration_type": "scalar_parameter"
  },
  "max_speed": {
    "sample_value": 120,
    "data_type": "INTEGER",
    "business_meaning": "maximum speed of storms allowed",
    "optimization_role": "used in speed constraint calculation",
    "configuration_type": "scalar_parameter"
  },
  "max_cities_affected": {
    "sample_value": 5,
    "data_type": "INTEGER",
    "business_meaning": "maximum number of cities that can be affected",
    "optimization_role": "used in cities affected constraint calculation",
    "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": "storm_record",
  "iteration": 3,
  "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": "storm_record",
  "iteration": 3,
  "business_context": "A disaster response organization aims to minimize the total damage and loss of life caused by storms by optimally allocating resources to the most affected regions, ensuring linear optimization constraints are met.",
  "optimization_problem_description": "Minimize the weighted sum of damage and deaths caused by storms, subject to constraints on the number of cities affected, the maximum speed of storms, and the total budget available for resource allocation.",
  "optimization_formulation": {
    "objective": "minimize (w1 * \u2211Damage_millions_USD + w2 * \u2211Number_Deaths)",
    "decision_variables": "is_allocated[storm_id, region_id] \u2208 {0, 1}",
    "constraints": [
      "\u2211(cost_per_allocation[storm_id, region_id] * is_allocated[storm_id, region_id]) \u2264 total_budget",
      "storm_speed[storm_id] \u2264 max_speed",
      "\u2211(is_allocated[storm_id, region_id]) \u2264 max_cities_affected"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "w1": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "weight for damage in the objective function"
      },
      "w2": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "weight for deaths in the objective function"
      },
      "Damage_millions_USD[storm_id]": {
        "currently_mapped_to": "storm_details.Damage_millions_USD",
        "mapping_adequacy": "good",
        "description": "damage caused by each storm"
      },
      "Number_Deaths[storm_id]": {
        "currently_mapped_to": "storm_details.Number_Deaths",
        "mapping_adequacy": "good",
        "description": "number of deaths caused by each storm"
      }
    },
    "constraint_bounds": {
      "total_budget": {
        "currently_mapped_to": "business_configuration_logic.total_budget",
        "mapping_adequacy": "good",
        "description": "total budget available for resource allocation"
      },
      "max_speed": {
        "currently_mapped_to": "business_configuration_logic.max_speed",
        "mapping_adequacy": "good",
        "description": "maximum speed of storms allowed"
      },
      "max_cities_affected": {
        "currently_mapped_to": "business_configuration_logic.max_cities_affected",
        "mapping_adequacy": "good",
        "description": "maximum number of cities that can be affected"
      }
    },
    "decision_variables": {
      "is_allocated[storm_id, region_id]": {
        "currently_mapped_to": "resource_allocation.is_allocated",
        "mapping_adequacy": "good",
        "description": "binary decision variable indicating whether resources are allocated to a region affected by a specific storm",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "w1",
    "w2"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Define weights w1 and w2 in the business configuration logic."
  }
}
