Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-27 22:27:58

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 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": "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.",
  "objective": "maximize sum(impact_coefficient[i] * x[i]) for all interactions i",
  "table_count": 3,
  "key_changes": [
    "Schema changes include creating new tables for impact coefficients, costs, and resource usage, and updating business configuration logic for budget and total resources."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Gather missing data for impact coefficients, costs, and resource usage to complete the optimization model",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating new tables for impact coefficients, costs, and resource usage, and updating business configuration logic for budget and total resources.

CREATE TABLE impact_coefficients (
  interaction_id INTEGER,
  coefficient FLOAT
);

CREATE TABLE interaction_costs (
  interaction_id INTEGER,
  cost FLOAT
);

CREATE TABLE resource_usage (
  interaction_id INTEGER,
  resources FLOAT
);

CREATE TABLE medicine_enzyme_interaction (
  interaction_id INTEGER,
  selected BOOLEAN
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "impact_coefficients": {
      "business_purpose": "Stores estimated impact of researching each interaction",
      "optimization_role": "objective_coefficients",
      "columns": {
        "interaction_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each interaction",
          "optimization_purpose": "Links to decision variables",
          "sample_values": "1, 2, 3"
        },
        "coefficient": {
          "data_type": "FLOAT",
          "business_meaning": "Estimated impact coefficient",
          "optimization_purpose": "Used in objective function",
          "sample_values": "0.5, 1.2, 0.8"
        }
      }
    },
    "interaction_costs": {
      "business_purpose": "Stores cost associated with researching each interaction",
      "optimization_role": "constraint_bounds",
      "columns": {
        "interaction_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each interaction",
          "optimization_purpose": "Links to decision variables",
          "sample_values": "1, 2, 3"
        },
        "cost": {
          "data_type": "FLOAT",
          "business_meaning": "Cost of researching the interaction",
          "optimization_purpose": "Used in cost constraint",
          "sample_values": "1000, 2000, 1500"
        }
      }
    },
    "resource_usage": {
      "business_purpose": "Stores resource usage for each interaction",
      "optimization_role": "constraint_bounds",
      "columns": {
        "interaction_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each interaction",
          "optimization_purpose": "Links to decision variables",
          "sample_values": "1, 2, 3"
        },
        "resources": {
          "data_type": "FLOAT",
          "business_meaning": "Resources required for researching the interaction",
          "optimization_purpose": "Used in resource constraint",
          "sample_values": "10, 20, 15"
        }
      }
    },
    "medicine_enzyme_interaction": {
      "business_purpose": "Stores information about medicine-enzyme interactions",
      "optimization_role": "decision_variables",
      "columns": {
        "interaction_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each interaction",
          "optimization_purpose": "Primary key",
          "sample_values": "1, 2, 3"
        },
        "selected": {
          "data_type": "BOOLEAN",
          "business_meaning": "Indicates if the interaction is selected for research",
          "optimization_purpose": "Decision variable",
          "sample_values": "true, false"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "budget": {
    "sample_value": "100000",
    "data_type": "INTEGER",
    "business_meaning": "Total budget available for research",
    "optimization_role": "Constraint bound for total cost",
    "configuration_type": "scalar_parameter"
  },
  "total_resources": {
    "sample_value": "500",
    "data_type": "INTEGER",
    "business_meaning": "Total research resources available",
    "optimization_role": "Constraint bound for total resource usage",
    "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": "medicine_enzyme_interaction",
  "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": "medicine_enzyme_interaction",
  "iteration": 1,
  "business_context": "A pharmaceutical company is optimizing the allocation of research resources to study interactions between medicines and enzymes. The objective is to maximize the potential impact of research by prioritizing interactions that are most likely to lead to significant medical advancements, within budget and resource constraints.",
  "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_coefficients.coefficient[i] * medicine_enzyme_interaction.selected[i]) for all interactions i",
    "decision_variables": "medicine_enzyme_interaction.selected[i] for all interactions i, where selected is a binary variable indicating if the interaction is chosen for research",
    "constraints": [
      "sum(interaction_costs.cost[i] * medicine_enzyme_interaction.selected[i]) <= business_configuration_logic.budget",
      "sum(resource_usage.resources[i] * medicine_enzyme_interaction.selected[i]) <= business_configuration_logic.total_resources"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "impact_coefficient[i]": {
        "currently_mapped_to": "impact_coefficients.coefficient",
        "mapping_adequacy": "good",
        "description": "Estimated impact of researching each interaction"
      }
    },
    "constraint_bounds": {
      "budget_constraint": {
        "currently_mapped_to": "business_configuration_logic.budget",
        "mapping_adequacy": "good",
        "description": "Total budget available for research"
      },
      "resource_constraint": {
        "currently_mapped_to": "business_configuration_logic.total_resources",
        "mapping_adequacy": "good",
        "description": "Total research resources available"
      }
    },
    "decision_variables": {
      "selected[i]": {
        "currently_mapped_to": "medicine_enzyme_interaction.selected",
        "mapping_adequacy": "good",
        "description": "Indicates if the interaction is selected for research",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
