Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-25 22:41:06

Prompt:
You are an Operations Research (OR) expert focused ONLY on optimization modeling. Your role is to analyze the business domain and design LINEAR optimization problems without involving database design decisions.

CRITICAL MATHEMATICAL CONSTRAINTS FOR LINEAR/MIXED-INTEGER PROGRAMMING:
- The optimization problem MUST be either 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
- Design business scenarios that naturally lead to linear mathematical formulations
- Generate between 2 and 20 constraints for optimization feasibility

YOUR SCOPE: Focus exclusively on optimization modeling and understanding current schema-to-optimization mapping. Do NOT propose database changes.
ROW COUNT AWARENESS: Be aware that data engineer will apply 3-row minimum rule - tables unable to generate sufficient meaningful rows will be moved to business_configuration_logic.json.

CRITICAL: Respond with ONLY a valid JSON object. No explanations, no markdown, no extra text.

Database: allergy_1

```sql
CREATE TABLE Allergy_Type (
  Allergy TEXT,
  AllergyType TEXT
);
```

```sql
CREATE TABLE Has_Allergy (
  StuID NUMBER,
  Allergy TEXT
);
```

```sql
CREATE TABLE Student (
  StuID NUMBER,
  LName TEXT,
  Fname TEXT,
  Age NUMBER,
  Sex TEXT,
  Major NUMBER,
  Advisor NUMBER,
  city_code TEXT
);
```



Current Business Configuration Logic: {} (initially empty)

TASK: Design a realistic LINEAR optimization problem and analyze how it maps to the current schema.

JSON STRUCTURE REQUIRED:

{
  "database_id": "allergy_1",
  "iteration": 0,
  "business_context": "Describe the realistic business scenario that leads to linear optimization (avoid scenarios requiring nonlinear relationships)",
  "optimization_problem_description": "Detailed description of what needs to be optimized using linear objective functions and constraints",
  "optimization_formulation": {
    "objective": "minimize/maximize specific_linear_metric with clear definition (sum of weighted variables only)",
    "decision_variables": "What linear variables can be controlled/decided (continuous or integer)",
    "constraints": "What linear limitations must be respected (no variable products or divisions) - design 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 needed for complete linear optimization model"
  ],
  
  "iteration_status": {
    "complete": false,
    "confidence": "low/medium/high",
    "next_focus": "What optimization aspects need refinement"
  }
}

Response:
{
  "database_id": "allergy_1",
  "iteration": 0,
  "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_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, representing the amount of resources allocated to a specific allergy type in a specific city",
    "constraints": [
      "\u2211(resource[AllergyType, city_code]) \u2264 budget",
      "resource[AllergyType, city_code] \u2265 required[AllergyType, city_code] for all AllergyType, city_code",
      "resource[AllergyType, city_code] \u2265 0 for all AllergyType, city_code"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "cost[AllergyType, city_code]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "cost of providing accommodation for a specific allergy type in a specific city"
      }
    },
    "constraint_bounds": {
      "budget": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "total budget available for allergy accommodations"
      },
      "required[AllergyType, city_code]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "minimum required resources for a specific allergy type in a specific city"
      }
    },
    "decision_variables": {
      "resource[AllergyType, city_code]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "amount of resources allocated to a specific allergy type in a specific city",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [
    "cost[AllergyType, city_code]: cost of providing accommodation for each allergy type in each city",
    "budget: total budget available for allergy accommodations",
    "required[AllergyType, city_code]: minimum required resources for each allergy type in each city"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "low",
    "next_focus": "Identify and map the missing cost, budget, and required resources data to complete the optimization model."
  }
}
