Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-25 22:29:28

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 company wants to optimize the selection of web client accelerators to maximize compatibility with browsers based on market share, ensuring that the chosen accelerators are compatible with the most widely used browsers.",
  "optimization_problem": "The goal is to maximize the total market share of browsers compatible with selected web client accelerators, subject to constraints on the number of accelerators that can be selected and ensuring compatibility with at least one browser per accelerator.",
  "objective": "maximize \u2211(market_share[browser_id] \u00d7 x[accelerator_id, browser_id])",
  "table_count": 0,
  "key_changes": [
    "Schema changes include adding a max_accelerators parameter to business_configuration_logic.json, enhancing the accelerator_compatible_browser table with additional attributes, and ensuring all tables meet the 3-row minimum rule. Configuration logic updates include scalar parameters and formulas for optimization constraints and metrics."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Refine constraints and ensure all necessary data is available for the optimization model",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include adding a max_accelerators parameter to business_configuration_logic.json, enhancing the accelerator_compatible_browser table with additional attributes, and ensuring all tables meet the 3-row minimum rule. Configuration logic updates include scalar parameters and formulas for optimization constraints and metrics.

CREATE TABLE browser (
  browser_id INTEGER,
  market_share FLOAT
);

CREATE TABLE accelerator_compatible_browser (
  accelerator_id INTEGER,
  browser_id INTEGER,
  compatibility_score FLOAT,
  last_updated_date DATE
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "browser": {
      "business_purpose": "Stores browser market share data for optimization",
      "optimization_role": "objective_coefficients",
      "columns": {
        "browser_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each browser",
          "optimization_purpose": "Index for objective coefficients",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "market_share": {
          "data_type": "FLOAT",
          "business_meaning": "Market share percentage of the browser",
          "optimization_purpose": "Coefficient in the objective function",
          "sample_values": [
            0.25,
            0.3,
            0.2
          ]
        }
      }
    },
    "accelerator_compatible_browser": {
      "business_purpose": "Stores compatibility data between accelerators and browsers",
      "optimization_role": "decision_variables",
      "columns": {
        "accelerator_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each accelerator",
          "optimization_purpose": "Index for decision variables",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "browser_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each browser",
          "optimization_purpose": "Index for decision variables",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "compatibility_score": {
          "data_type": "FLOAT",
          "business_meaning": "Score indicating compatibility between accelerator and browser",
          "optimization_purpose": "Used in decision variable calculations",
          "sample_values": [
            0.8,
            0.9,
            0.7
          ]
        },
        "last_updated_date": {
          "data_type": "DATE",
          "business_meaning": "Date when the compatibility data was last updated",
          "optimization_purpose": "Ensures data freshness",
          "sample_values": [
            "2023-10-01",
            "2023-10-02",
            "2023-10-03"
          ]
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "max_accelerators": {
    "sample_value": 5,
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of accelerators that can be selected",
    "optimization_role": "Constraint bound for the total number of accelerators",
    "configuration_type": "scalar_parameter"
  },
  "compatibility_score_formula": {
    "formula_expression": "(market_share * compatibility_weight) / total_weight",
    "data_type": "STRING",
    "business_meaning": "Formula to calculate compatibility score between accelerators and browsers",
    "optimization_role": "Used in decision variable calculations",
    "configuration_type": "business_logic_formula"
  }
}


TASK: Refine the optimization problem formulation by analyzing current data schema mapping and identifying requirements while maintaining LINEAR structure.

JSON STRUCTURE REQUIRED:

{
  "database_id": "browser_web",
  "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": "browser_web",
  "iteration": 1,
  "business_context": "A company aims to optimize the selection of web client accelerators to maximize compatibility with browsers based on market share, ensuring that the chosen accelerators are compatible with the most widely used browsers.",
  "optimization_problem_description": "Maximize the total market share of browsers compatible with selected web client accelerators, subject to constraints on the number of accelerators that can be selected and ensuring compatibility with at least one browser per accelerator.",
  "optimization_formulation": {
    "objective": "maximize \u2211(market_share[browser_id] \u00d7 x[accelerator_id, browser_id])",
    "decision_variables": "x[accelerator_id, browser_id] \u2208 {0, 1} (binary variable indicating if accelerator_id is compatible with browser_id)",
    "constraints": [
      "\u2211(x[accelerator_id, browser_id]) \u2264 max_accelerators (total number of selected accelerators cannot exceed max_accelerators)",
      "\u2211(x[accelerator_id, browser_id]) \u2265 1 for each accelerator_id (each selected accelerator must be compatible with at least one browser)"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "market_share[browser_id]": {
        "currently_mapped_to": "browser.market_share",
        "mapping_adequacy": "good",
        "description": "Market share of each browser used as coefficient in the objective function"
      }
    },
    "constraint_bounds": {
      "max_accelerators": {
        "currently_mapped_to": "business_configuration_logic.max_accelerators",
        "mapping_adequacy": "good",
        "description": "Maximum number of accelerators that can be selected"
      }
    },
    "decision_variables": {
      "x[accelerator_id, browser_id]": {
        "currently_mapped_to": "accelerator_compatible_browser.compatibility_score",
        "mapping_adequacy": "partial",
        "description": "Binary decision variable indicating compatibility between accelerator and browser",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
