Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-28 00:25:08

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: protein_institute

```sql
CREATE TABLE building (
  building_id TEXT,
  Name TEXT,
  Street_address TEXT,
  Years_as_tallest TEXT,
  Height_feet NUMBER,
  Floors NUMBER
);
```

```sql
CREATE TABLE Institution (
  Institution_id TEXT,
  Institution TEXT,
  Location TEXT,
  Founded NUMBER,
  Type TEXT,
  Enrollment NUMBER,
  Team TEXT,
  Primary_Conference TEXT,
  building_id TEXT
);
```

```sql
CREATE TABLE protein (
  common_name TEXT,
  protein_name TEXT,
  divergence_from_human_lineage NUMBER,
  accession_number TEXT,
  sequence_length NUMBER,
  sequence_identity_to_human_protein TEXT,
  Institution_id 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": "protein_institute",
  "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": "protein_institute",
  "iteration": 0,
  "business_context": "The protein institute aims to optimize the allocation of research resources across different institutions to maximize the total sequence identity to human proteins, given constraints on building capacities and institutional enrollments.",
  "optimization_problem_description": "Optimize the allocation of research resources to maximize the total sequence identity to human proteins across institutions, subject to constraints on building capacities and institutional enrollments.",
  "optimization_formulation": {
    "objective": "maximize total_sequence_identity = \u2211(sequence_identity_coefficient[i] * allocation[i])",
    "decision_variables": "allocation[i]: the amount of resources allocated to institution i (continuous)",
    "constraints": [
      "\u2211(allocation[i]) \u2264 total_available_resources",
      "allocation[i] \u2264 building_capacity[i] for all i",
      "allocation[i] \u2264 enrollment[i] for all i"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "sequence_identity_coefficient[i]": {
        "currently_mapped_to": "protein.sequence_identity_to_human_protein",
        "mapping_adequacy": "partial",
        "description": "Represents the sequence identity to human proteins for institution i"
      }
    },
    "constraint_bounds": {
      "total_available_resources": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Total resources available for allocation"
      },
      "building_capacity[i]": {
        "currently_mapped_to": "building.Floors",
        "mapping_adequacy": "partial",
        "description": "Represents the capacity of the building associated with institution i"
      },
      "enrollment[i]": {
        "currently_mapped_to": "Institution.Enrollment",
        "mapping_adequacy": "good",
        "description": "Represents the enrollment capacity of institution i"
      }
    },
    "decision_variables": {
      "allocation[i]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Represents the amount of resources allocated to institution i",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [
    "Total available resources for allocation",
    "Mapping of sequence identity to a numerical coefficient",
    "Explicit mapping of building capacity to a numerical value"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Refine mapping of sequence identity and building capacity to numerical coefficients"
  }
}
