Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-25 22:41:06

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 university wants to minimize the total cost of providing allergy accommodations to students while ensuring that all students with allergies receive the necessary support. The cost varies based on the type of allergy and the city where the student resides.",
  "optimization_problem": "The objective is to minimize the total cost of providing allergy accommodations. The decision variables represent the allocation of resources to students based on their allergy type and city. Constraints ensure that all students with allergies receive at least one accommodation and that the total resources allocated do not exceed the available budget.",
  "objective": "minimize \u2211(cost[AllergyType, city_code] \u00d7 resource[AllergyType, city_code])",
  "table_count": 1,
  "key_changes": [
    "Schema changes include creating tables for cost, budget, and required resources, and updating business configuration logic with scalar parameters and formulas."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Identify and map the missing cost, budget, and required resources data to complete the optimization model.",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating tables for cost, budget, and required resources, and updating business configuration logic with scalar parameters and formulas.

CREATE TABLE cost (
  AllergyType STRING,
  city_code STRING,
  cost FLOAT,
  resource FLOAT
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "cost": {
      "business_purpose": "cost of providing accommodation for each allergy type in each city",
      "optimization_role": "objective_coefficients",
      "columns": {
        "AllergyType": {
          "data_type": "STRING",
          "business_meaning": "type of allergy",
          "optimization_purpose": "index for cost calculation",
          "sample_values": "peanut, dairy, gluten"
        },
        "city_code": {
          "data_type": "STRING",
          "business_meaning": "city where the student resides",
          "optimization_purpose": "index for cost calculation",
          "sample_values": "NYC, LA, CHI"
        },
        "cost": {
          "data_type": "FLOAT",
          "business_meaning": "cost of providing accommodation for the allergy type in the city",
          "optimization_purpose": "coefficient in the objective function",
          "sample_values": "100.0, 150.0, 200.0"
        },
        "resource": {
          "data_type": "FLOAT",
          "business_meaning": "amount of resources allocated to the allergy type in the city",
          "optimization_purpose": "decision variable",
          "sample_values": "10.0, 15.0, 20.0"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "budget": {
    "sample_value": 100000,
    "data_type": "INTEGER",
    "business_meaning": "total budget available for allergy accommodations",
    "optimization_role": "constraint bound",
    "configuration_type": "scalar_parameter"
  },
  "required": {
    "sample_value": 10,
    "data_type": "INTEGER",
    "business_meaning": "minimum required resources for each allergy type in each city",
    "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": "allergy_1",
  "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": "allergy_1",
  "iteration": 1,
  "business_context": "A university aims to minimize the total cost of providing allergy accommodations to students while ensuring that all students with allergies receive the necessary support. The cost varies based on the type of allergy and the city where the student resides. The optimization problem is linear, ensuring scalability and computational efficiency.",
  "optimization_problem_description": "The objective is to minimize the total cost of providing allergy accommodations. The decision variables represent the allocation of resources to students based on their allergy type and city. Constraints ensure that all students with allergies receive at least one accommodation and that the total resources allocated do not exceed the available budget.",
  "optimization_formulation": {
    "objective": "minimize \u2211(cost[AllergyType, city_code] \u00d7 resource[AllergyType, city_code])",
    "decision_variables": "resource[AllergyType, city_code] (continuous)",
    "constraints": [
      "\u2211(resource[AllergyType, city_code]) \u2264 budget",
      "resource[AllergyType, city_code] \u2265 required for all AllergyType, city_code"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "cost[AllergyType, city_code]": {
        "currently_mapped_to": "cost.cost",
        "mapping_adequacy": "good",
        "description": "cost of providing accommodation for each allergy type in each city"
      }
    },
    "constraint_bounds": {
      "budget": {
        "currently_mapped_to": "business_configuration_logic.budget",
        "mapping_adequacy": "good",
        "description": "total budget available for allergy accommodations"
      },
      "required": {
        "currently_mapped_to": "business_configuration_logic.required",
        "mapping_adequacy": "good",
        "description": "minimum required resources for each allergy type in each city"
      }
    },
    "decision_variables": {
      "resource[AllergyType, city_code]": {
        "currently_mapped_to": "cost.resource",
        "mapping_adequacy": "good",
        "description": "amount of resources allocated to the allergy type in the city",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
