Iteration 3 - OR_EXPERT_REFINEMENT
Sequence: 7
Timestamp: 2025-07-25 22:37:12

Prompt:
You are an Operations Research (OR) expert in iteration 3 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.


CONVERGENCE PRESSURE (Iteration 3/5):
- Focus on finalizing the linear optimization model
- Set complete=true if formulation is mathematically sound and linear
- Minimize further schema change requests


CURRENT STATE (iteration 2):
{
  "iteration": 3,
  "converged": false,
  "business_context": "Optimize the selection of basketball teams for a tournament to maximize the overall win percentage while respecting constraints on team diversity and geographical distribution.",
  "optimization_problem": "Maximize the total win percentage of selected teams for a tournament. Constraints include selecting a specific number of teams, ensuring a minimum number of teams from different conferences, and limiting the number of teams from the same location.",
  "objective": "maximize \u2211(Win_Percent \u00d7 Team_Selection)",
  "table_count": 0,
  "key_changes": [
    "Added missing constraint bounds to business configuration logic and updated data dictionary to reflect these changes. No new tables were created as the missing requirements were better suited for configuration logic."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Map the missing constraint bounds for the optimization model.",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 3 Database Schema
-- Objective: Added missing constraint bounds to business configuration logic and updated data dictionary to reflect these changes. No new tables were created as the missing requirements were better suited for configuration logic.

CREATE TABLE win_percentage (
  Team_ID INTEGER,
  Win_Percent FLOAT
);

CREATE TABLE team_selection (
  Team_ID INTEGER,
  Team_Selection BOOLEAN
);

CREATE TABLE conference_indicator (
  Team_ID INTEGER,
  Conference_Indicator STRING
);

CREATE TABLE location_indicator (
  Team_ID INTEGER,
  Location_Indicator STRING
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "win_percentage": {
      "business_purpose": "Win percentage of each team for the tournament selection optimization",
      "optimization_role": "objective_coefficients",
      "columns": {
        "Team_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each team",
          "optimization_purpose": "Index for win percentage",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "Win_Percent": {
          "data_type": "FLOAT",
          "business_meaning": "Win percentage of the team",
          "optimization_purpose": "Objective coefficient in optimization model",
          "sample_values": [
            75.5,
            80.0,
            65.3
          ]
        }
      }
    },
    "team_selection": {
      "business_purpose": "Binary decision variable indicating whether a team is selected for the tournament",
      "optimization_role": "decision_variables",
      "columns": {
        "Team_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each team",
          "optimization_purpose": "Index for decision variable",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "Team_Selection": {
          "data_type": "BOOLEAN",
          "business_meaning": "Binary indicator of team selection",
          "optimization_purpose": "Decision variable in optimization model",
          "sample_values": [
            true,
            false,
            true
          ]
        }
      }
    },
    "conference_indicator": {
      "business_purpose": "Indicator of which conference each team belongs to",
      "optimization_role": "constraint_bounds",
      "columns": {
        "Team_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each team",
          "optimization_purpose": "Index for conference indicator",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "Conference_Indicator": {
          "data_type": "STRING",
          "business_meaning": "Conference affiliation of the team",
          "optimization_purpose": "Constraint bound for conference diversity",
          "sample_values": [
            "East",
            "West",
            "South"
          ]
        }
      }
    },
    "location_indicator": {
      "business_purpose": "Indicator of the location of each team",
      "optimization_role": "constraint_bounds",
      "columns": {
        "Team_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each team",
          "optimization_purpose": "Index for location indicator",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "Location_Indicator": {
          "data_type": "STRING",
          "business_meaning": "Location of the team",
          "optimization_purpose": "Constraint bound for geographical distribution",
          "sample_values": [
            "New York",
            "Los Angeles",
            "Chicago"
          ]
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "Total_Teams_Selected": {
    "sample_value": 10,
    "data_type": "INTEGER",
    "business_meaning": "Total number of teams to be selected for the tournament",
    "optimization_role": "Constraint bound for total teams selected",
    "configuration_type": "scalar_parameter"
  },
  "Min_East_Teams": {
    "sample_value": 3,
    "data_type": "INTEGER",
    "business_meaning": "Minimum number of teams to be selected from the East conference",
    "optimization_role": "Constraint bound for East conference diversity",
    "configuration_type": "scalar_parameter"
  },
  "Min_West_Teams": {
    "sample_value": 3,
    "data_type": "INTEGER",
    "business_meaning": "Minimum number of teams to be selected from the West conference",
    "optimization_role": "Constraint bound for West conference diversity",
    "configuration_type": "scalar_parameter"
  },
  "Min_South_Teams": {
    "sample_value": 3,
    "data_type": "INTEGER",
    "business_meaning": "Minimum number of teams to be selected from the South conference",
    "optimization_role": "Constraint bound for South conference diversity",
    "configuration_type": "scalar_parameter"
  },
  "Max_New_York_Teams": {
    "sample_value": 2,
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of teams to be selected from New York",
    "optimization_role": "Constraint bound for geographical distribution",
    "configuration_type": "scalar_parameter"
  },
  "Max_Los_Angeles_Teams": {
    "sample_value": 2,
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of teams to be selected from Los Angeles",
    "optimization_role": "Constraint bound for geographical distribution",
    "configuration_type": "scalar_parameter"
  },
  "Max_Chicago_Teams": {
    "sample_value": 2,
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of teams to be selected from Chicago",
    "optimization_role": "Constraint bound for geographical distribution",
    "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": "university_basketball",
  "iteration": 3,
  "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": "university_basketball",
  "iteration": 3,
  "business_context": "Optimize the selection of basketball teams for a tournament to maximize the overall win percentage while respecting constraints on team diversity and geographical distribution.",
  "optimization_problem_description": "Maximize the total win percentage of selected teams for a tournament. Constraints include selecting a specific number of teams, ensuring a minimum number of teams from different conferences, and limiting the number of teams from the same location.",
  "optimization_formulation": {
    "objective": "maximize \u2211(Win_Percent \u00d7 Team_Selection)",
    "decision_variables": "Team_Selection[Team_ID] (binary)",
    "constraints": [
      "\u2211(Team_Selection) = Total_Teams_Selected",
      "\u2211(Team_Selection \u00d7 Conference_Indicator = 'East') \u2265 Min_East_Teams",
      "\u2211(Team_Selection \u00d7 Conference_Indicator = 'West') \u2265 Min_West_Teams",
      "\u2211(Team_Selection \u00d7 Conference_Indicator = 'South') \u2265 Min_South_Teams",
      "\u2211(Team_Selection \u00d7 Location_Indicator = 'New York') \u2264 Max_New_York_Teams",
      "\u2211(Team_Selection \u00d7 Location_Indicator = 'Los Angeles') \u2264 Max_Los_Angeles_Teams",
      "\u2211(Team_Selection \u00d7 Location_Indicator = 'Chicago') \u2264 Max_Chicago_Teams"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Win_Percent[Team_ID]": {
        "currently_mapped_to": "win_percentage.Win_Percent",
        "mapping_adequacy": "good",
        "description": "Win percentage of each team used as the coefficient in the objective function"
      }
    },
    "constraint_bounds": {
      "Total_Teams_Selected": {
        "currently_mapped_to": "business_configuration_logic.Total_Teams_Selected",
        "mapping_adequacy": "good",
        "description": "Total number of teams to be selected for the tournament"
      },
      "Min_East_Teams": {
        "currently_mapped_to": "business_configuration_logic.Min_East_Teams",
        "mapping_adequacy": "good",
        "description": "Minimum number of teams to be selected from the East conference"
      },
      "Min_West_Teams": {
        "currently_mapped_to": "business_configuration_logic.Min_West_Teams",
        "mapping_adequacy": "good",
        "description": "Minimum number of teams to be selected from the West conference"
      },
      "Min_South_Teams": {
        "currently_mapped_to": "business_configuration_logic.Min_South_Teams",
        "mapping_adequacy": "good",
        "description": "Minimum number of teams to be selected from the South conference"
      },
      "Max_New_York_Teams": {
        "currently_mapped_to": "business_configuration_logic.Max_New_York_Teams",
        "mapping_adequacy": "good",
        "description": "Maximum number of teams to be selected from New York"
      },
      "Max_Los_Angeles_Teams": {
        "currently_mapped_to": "business_configuration_logic.Max_Los_Angeles_Teams",
        "mapping_adequacy": "good",
        "description": "Maximum number of teams to be selected from Los Angeles"
      },
      "Max_Chicago_Teams": {
        "currently_mapped_to": "business_configuration_logic.Max_Chicago_Teams",
        "mapping_adequacy": "good",
        "description": "Maximum number of teams to be selected from Chicago"
      }
    },
    "decision_variables": {
      "Team_Selection[Team_ID]": {
        "currently_mapped_to": "team_selection.Team_Selection",
        "mapping_adequacy": "good",
        "description": "Binary decision variable indicating whether a team is selected for the tournament",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
