Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-25 22:58:16

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 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.",
  "optimization_problem": "The organization seeks to minimize the weighted sum of damage and deaths caused by storms, subject to constraints on the number of cities affected and the maximum speed of storms.",
  "objective": "minimize (w1 * \u2211Damage_millions_USD + w2 * \u2211Number_Deaths)",
  "table_count": 1,
  "key_changes": [
    "Schema changes and configuration logic updates to address missing optimization requirements and mapping gaps identified by the OR expert."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Define weights and constraint bounds in the business configuration logic",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes and configuration logic updates to address missing optimization requirements and mapping gaps identified by the OR expert.

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


```

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
          ]
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "w1": {
    "sample_value": 0.7,
    "data_type": "FLOAT",
    "business_meaning": "weight for damage cost in the objective function",
    "optimization_role": "objective coefficient",
    "configuration_type": "scalar_parameter"
  },
  "w2": {
    "sample_value": 0.3,
    "data_type": "FLOAT",
    "business_meaning": "weight for number of deaths in the objective function",
    "optimization_role": "objective coefficient",
    "configuration_type": "scalar_parameter"
  },
  "Max_cities_per_region": {
    "sample_value": 5,
    "data_type": "INTEGER",
    "business_meaning": "maximum number of cities that can be supported per region",
    "optimization_role": "constraint bound",
    "configuration_type": "scalar_parameter"
  },
  "Max_speed_limit": {
    "sample_value": 120,
    "data_type": "INTEGER",
    "business_meaning": "maximum storm speed for resource allocation",
    "optimization_role": "constraint bound",
    "configuration_type": "scalar_parameter"
  },
  "Budget": {
    "sample_value": 1000000,
    "data_type": "INTEGER",
    "business_meaning": "total budget for resource allocation",
    "optimization_role": "constraint bound",
    "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": 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": "storm_record",
  "iteration": 1,
  "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] (binary)",
    "constraints": [
      "\u2211is_allocated[storm_id, region_id] \u2264 Max_cities_per_region for each region_id",
      "\u2211is_allocated[storm_id, region_id] * storm_speed \u2264 Max_speed_limit for each storm_id",
      "\u2211is_allocated[storm_id, region_id] * cost_per_allocation \u2264 Budget"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "w1": {
        "currently_mapped_to": "business_configuration_logic.w1",
        "mapping_adequacy": "good",
        "description": "weight for damage cost in the objective function"
      },
      "w2": {
        "currently_mapped_to": "business_configuration_logic.w2",
        "mapping_adequacy": "good",
        "description": "weight for number of deaths in the objective function"
      }
    },
    "constraint_bounds": {
      "Max_cities_per_region": {
        "currently_mapped_to": "business_configuration_logic.Max_cities_per_region",
        "mapping_adequacy": "good",
        "description": "maximum number of cities that can be supported per region"
      },
      "Max_speed_limit": {
        "currently_mapped_to": "business_configuration_logic.Max_speed_limit",
        "mapping_adequacy": "good",
        "description": "maximum storm speed for resource allocation"
      },
      "Budget": {
        "currently_mapped_to": "business_configuration_logic.Budget",
        "mapping_adequacy": "good",
        "description": "total budget for resource allocation"
      }
    },
    "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": [
    "storm_speed",
    "cost_per_allocation",
    "Damage_millions_USD",
    "Number_Deaths"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Define storm_speed, cost_per_allocation, Damage_millions_USD, and Number_Deaths in the schema or business configuration logic."
  }
}
