Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-27 21:38:11

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 government agency wants to allocate resources to minimize the total number of casualties (killed and injured) in various locations over a year. The agency has a limited budget and resources that can be allocated to different locations to improve safety and reduce casualties.",
  "optimization_problem": "The goal is to minimize the total number of casualties (killed and injured) by optimally allocating resources to different locations. The resources are limited, and each location has a different impact on reducing casualties. The optimization will determine the optimal allocation of resources to minimize casualties while respecting budget constraints.",
  "objective": "minimize total_casualties = sum(c_killed[i] * x[i] + c_injured[i] * x[i])",
  "table_count": 2,
  "key_changes": [
    "Schema changes include creating new tables for decision variables and constraint bounds, modifying existing tables to fill mapping gaps, and updating business configuration logic for scalar parameters and formulas."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Determine the cost of resources for each location and the total budget available for allocation",
  "mapping_adequacy_summary": "partially_adequate"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating new tables for decision variables and constraint bounds, modifying existing tables to fill mapping gaps, and updating business configuration logic for scalar parameters and formulas.

CREATE TABLE perpetrator (
  Killed INTEGER,
  Injured INTEGER
);

CREATE TABLE ResourceAllocation (
  location_id INTEGER,
  amount FLOAT
);

CREATE TABLE LocationCosts (
  location_id INTEGER,
  cost FLOAT
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "perpetrator": {
      "business_purpose": "Stores casualty data for each location",
      "optimization_role": "objective_coefficients",
      "columns": {
        "Killed": {
          "data_type": "INTEGER",
          "business_meaning": "number of people killed in location i",
          "optimization_purpose": "used as coefficient in objective function",
          "sample_values": "0-100"
        },
        "Injured": {
          "data_type": "INTEGER",
          "business_meaning": "number of people injured in location i",
          "optimization_purpose": "used as coefficient in objective function",
          "sample_values": "0-200"
        }
      }
    },
    "ResourceAllocation": {
      "business_purpose": "Stores resource allocation data for each location",
      "optimization_role": "decision_variables",
      "columns": {
        "location_id": {
          "data_type": "INTEGER",
          "business_meaning": "unique identifier for each location",
          "optimization_purpose": "identifies location for resource allocation",
          "sample_values": "1-10"
        },
        "amount": {
          "data_type": "FLOAT",
          "business_meaning": "amount of resources allocated to location",
          "optimization_purpose": "decision variable in optimization model",
          "sample_values": "0-1000"
        }
      }
    },
    "LocationCosts": {
      "business_purpose": "Stores cost data for resources at each location",
      "optimization_role": "constraint_bounds",
      "columns": {
        "location_id": {
          "data_type": "INTEGER",
          "business_meaning": "unique identifier for each location",
          "optimization_purpose": "identifies location for cost association",
          "sample_values": "1-10"
        },
        "cost": {
          "data_type": "FLOAT",
          "business_meaning": "cost of resources for location",
          "optimization_purpose": "used in budget constraint",
          "sample_values": "100-10000"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "total_budget": {
    "sample_value": "1000000",
    "data_type": "FLOAT",
    "business_meaning": "represents the total budget available for resource allocation",
    "optimization_role": "used as a constraint bound in optimization model",
    "configuration_type": "scalar_parameter"
  },
  "resource_cost_formula": {
    "formula_expression": "sum(cost[i] * x[i])",
    "data_type": "STRING",
    "business_meaning": "calculates the total cost of resources allocated",
    "optimization_role": "used in constraint to ensure budget is not exceeded",
    "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": "perpetrator",
  "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": "perpetrator",
  "iteration": 1,
  "business_context": "A government agency is tasked with minimizing casualties (killed and injured) by optimally allocating limited resources across various locations. Each location has a different impact on casualty reduction, and the agency must operate within a fixed budget.",
  "optimization_problem_description": "The optimization problem aims to minimize the total number of casualties by allocating resources to different locations. The allocation must respect budget constraints, and each location has a specific cost and impact on reducing casualties.",
  "optimization_formulation": {
    "objective": "minimize total_casualties = sum((Killed[i] + Injured[i]) * amount[i])",
    "decision_variables": "amount[i]: continuous, representing the amount of resources allocated to location i",
    "constraints": [
      "sum(cost[i] * amount[i]) <= total_budget",
      "amount[i] >= 0 for all i"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Killed[i]": {
        "currently_mapped_to": "perpetrator.Killed",
        "mapping_adequacy": "good",
        "description": "number of people killed in location i"
      },
      "Injured[i]": {
        "currently_mapped_to": "perpetrator.Injured",
        "mapping_adequacy": "good",
        "description": "number of people injured in location i"
      }
    },
    "constraint_bounds": {
      "budget_constraint": {
        "currently_mapped_to": "business_configuration_logic.total_budget",
        "mapping_adequacy": "good",
        "description": "total budget available for resource allocation"
      },
      "resource_cost": {
        "currently_mapped_to": "LocationCosts.cost",
        "mapping_adequacy": "good",
        "description": "cost of resources for location i"
      }
    },
    "decision_variables": {
      "amount[i]": {
        "currently_mapped_to": "ResourceAllocation.amount",
        "mapping_adequacy": "good",
        "description": "amount of resources allocated to location i",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
