Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-25 22:33:39

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: medicine_enzyme_interaction

```sql
CREATE TABLE medicine (
  id NUMBER,
  name TEXT,
  Trade_Name TEXT,
  FDA_approved TEXT
);
```

```sql
CREATE TABLE enzyme (
  id NUMBER,
  name TEXT,
  Location TEXT,
  Product TEXT,
  Chromosome TEXT,
  OMIM NUMBER,
  Porphyria TEXT
);
```

```sql
CREATE TABLE medicine_enzyme_interaction (
  enzyme_id NUMBER,
  medicine_id NUMBER,
  interaction_type 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": "medicine_enzyme_interaction",
  "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": "medicine_enzyme_interaction",
  "iteration": 0,
  "business_context": "A pharmaceutical company wants to optimize the selection of medicines for a clinical trial based on their interactions with enzymes, aiming to maximize the overall effectiveness while minimizing adverse interactions.",
  "optimization_problem_description": "The goal is to select a combination of medicines that maximizes the total effectiveness score while ensuring that the total adverse interaction score does not exceed a specified limit. The effectiveness and adverse interaction scores are derived from the medicine-enzyme interactions.",
  "optimization_formulation": {
    "objective": "maximize \u2211(effectiveness_score[medicine_id] \u00d7 x[medicine_id])",
    "decision_variables": "x[medicine_id] (binary): 1 if medicine is selected, 0 otherwise",
    "constraints": [
      "\u2211(adverse_interaction_score[medicine_id] \u00d7 x[medicine_id]) \u2264 max_adverse_interaction_score",
      "x[medicine_id] \u2264 FDA_approved[medicine_id] for all medicine_id",
      "\u2211(x[medicine_id]) \u2264 max_number_of_medicines"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "effectiveness_score[medicine_id]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Effectiveness score of each medicine based on its interaction with enzymes"
      }
    },
    "constraint_bounds": {
      "max_adverse_interaction_score": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Maximum allowed total adverse interaction score"
      },
      "FDA_approved[medicine_id]": {
        "currently_mapped_to": "medicine.FDA_approved",
        "mapping_adequacy": "partial",
        "description": "Indicates if the medicine is FDA approved"
      },
      "max_number_of_medicines": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Maximum number of medicines that can be selected"
      }
    },
    "decision_variables": {
      "x[medicine_id]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Binary decision variable indicating if a medicine is selected",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "Effectiveness score for each medicine",
    "Adverse interaction score for each medicine",
    "Maximum allowed total adverse interaction score",
    "Maximum number of medicines that can be selected"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Define and map effectiveness and adverse interaction scores for medicines"
  }
}
