Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-27 22:27:58

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 allocation of research resources to study interactions between medicines and enzymes. The goal is to maximize the potential impact of research by focusing on interactions that are most likely to lead to significant medical advancements.",
  "optimization_problem_description": "The company needs to decide which medicine-enzyme interactions to prioritize for research, given a limited budget and resource constraints. The objective is to maximize the expected impact of the research, which is estimated based on historical data and expert opinions.",
  "optimization_formulation": {
    "objective": "maximize sum(impact_coefficient[i] * x[i]) for all interactions i",
    "decision_variables": "x[i] is a binary variable indicating whether interaction i is selected for research (1 if selected, 0 otherwise)",
    "constraints": [
      "sum(cost[i] * x[i]) <= budget",
      "sum(resource_usage[i] * x[i]) <= total_resources",
      "x[i] is binary for all i"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "impact_coefficient[i]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Estimated impact of researching interaction i"
      }
    },
    "constraint_bounds": {
      "budget": {
        "currently_mapped_to": "business_configuration_logic.budget",
        "mapping_adequacy": "missing",
        "description": "Total budget available for research"
      },
      "total_resources": {
        "currently_mapped_to": "business_configuration_logic.total_resources",
        "mapping_adequacy": "missing",
        "description": "Total research resources available"
      }
    },
    "decision_variables": {
      "x[i]": {
        "currently_mapped_to": "medicine_enzyme_interaction",
        "mapping_adequacy": "partial",
        "description": "Binary decision variable for selecting interaction i for research",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "Impact coefficients for each interaction",
    "Cost associated with researching each interaction",
    "Resource usage for each interaction",
    "Total budget and resources available"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Gather missing data for impact coefficients, costs, and resource usage to complete the optimization model"
  }
}
