Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-27 21:52:00

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 management agency wants to allocate resources efficiently to minimize the total damage cost from storms across different regions. The agency needs to decide how many resources to allocate to each affected region to minimize the overall damage cost while considering the number of cities affected and the maximum speed of storms.",
  "optimization_problem": "The goal is to minimize the total damage cost from storms by optimally allocating resources to affected regions. The decision variables represent the amount of resources allocated to each region. Constraints include the total available resources, the number of cities affected in each region, and the maximum speed of storms.",
  "objective": "minimize total_damage_cost = \u2211(Damage_millions_USD[i] \u00d7 resources_allocated[i])",
  "table_count": 1,
  "key_changes": [
    "Schema changes include creating a new table for decision variables and updating the business configuration logic to include total available resources as a scalar parameter. Adjustments ensure all optimization requirements are mapped and business logic is preserved."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Determine the total available resources for allocation and refine the mapping of decision variables",
  "mapping_adequacy_summary": "partially_adequate"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating a new table for decision variables and updating the business configuration logic to include total available resources as a scalar parameter. Adjustments ensure all optimization requirements are mapped and business logic is preserved.

CREATE TABLE storm (
  Damage_millions_USD FLOAT,
  Max_speed FLOAT
);

CREATE TABLE affected_region (
  Number_city_affected INTEGER
);

CREATE TABLE resource_allocation (
  resources_allocated FLOAT
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "storm": {
      "business_purpose": "Stores data about storms affecting regions",
      "optimization_role": "objective_coefficients/constraint_bounds",
      "columns": {
        "Damage_millions_USD": {
          "data_type": "FLOAT",
          "business_meaning": "Damage cost in millions USD for each storm",
          "optimization_purpose": "Coefficient in the objective function",
          "sample_values": "10.5, 20.0, 15.3"
        },
        "Max_speed": {
          "data_type": "FLOAT",
          "business_meaning": "Maximum speed of storms affecting each region",
          "optimization_purpose": "Constraint bound for resource allocation",
          "sample_values": "120.0, 150.0, 130.0"
        }
      }
    },
    "affected_region": {
      "business_purpose": "Stores data about regions affected by storms",
      "optimization_role": "constraint_bounds",
      "columns": {
        "Number_city_affected": {
          "data_type": "INTEGER",
          "business_meaning": "Number of cities affected in each region",
          "optimization_purpose": "Constraint bound for resource allocation",
          "sample_values": "3, 5, 4"
        }
      }
    },
    "resource_allocation": {
      "business_purpose": "Stores the allocation of resources to each region",
      "optimization_role": "decision_variables",
      "columns": {
        "resources_allocated": {
          "data_type": "FLOAT",
          "business_meaning": "Amount of resources allocated to each region",
          "optimization_purpose": "Decision variable in the optimization model",
          "sample_values": "100.0, 200.0, 150.0"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "total_available_resources": {
    "sample_value": "1000",
    "data_type": "INTEGER",
    "business_meaning": "Total resources available for allocation",
    "optimization_role": "Used as a constraint in the optimization model",
    "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 management agency aims to efficiently allocate resources to minimize the total damage cost from storms across different regions. The agency needs to decide how many resources to allocate to each affected region to minimize the overall damage cost while considering the number of cities affected and the maximum speed of storms.",
  "optimization_problem_description": "The objective is to minimize the total damage cost from storms by optimally allocating resources to affected regions. The decision variables represent the amount of resources allocated to each region. Constraints include the total available resources, the number of cities affected in each region, and the maximum speed of storms.",
  "optimization_formulation": {
    "objective": "minimize total_damage_cost = \u2211(Damage_millions_USD[i] \u00d7 resources_allocated[i])",
    "decision_variables": "resources_allocated[i] for each region i, where resources_allocated[i] is continuous",
    "constraints": [
      "\u2211(resources_allocated[i]) \u2264 total_available_resources",
      "resources_allocated[i] \u2264 Number_city_affected[i] \u00d7 Max_speed[i] for each region i"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Damage_millions_USD[i]": {
        "currently_mapped_to": "storm.Damage_millions_USD",
        "mapping_adequacy": "good",
        "description": "Damage cost in millions USD for each storm, used as a coefficient in the objective function"
      }
    },
    "constraint_bounds": {
      "total_available_resources": {
        "currently_mapped_to": "business_configuration_logic.total_available_resources",
        "mapping_adequacy": "good",
        "description": "Total resources available for allocation"
      },
      "Number_city_affected[i]": {
        "currently_mapped_to": "affected_region.Number_city_affected",
        "mapping_adequacy": "good",
        "description": "Number of cities affected in each region, used as a constraint bound"
      },
      "Max_speed[i]": {
        "currently_mapped_to": "storm.Max_speed",
        "mapping_adequacy": "good",
        "description": "Maximum speed of storms affecting each region, used as a constraint bound"
      }
    },
    "decision_variables": {
      "resources_allocated[i]": {
        "currently_mapped_to": "resource_allocation.resources_allocated",
        "mapping_adequacy": "good",
        "description": "Amount of resources allocated to each region",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
