Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-25 22:37:12

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": "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": "The objective is to 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(All_Games_Percent \u00d7 Team_Selection)",
  "table_count": 3,
  "key_changes": [
    "Schema changes include creating new tables for decision variables and indicators, updating business configuration logic with scalar parameters and formulas, and ensuring all optimization requirements are mapped correctly."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Define and map additional parameters such as Total_Teams_Required, Min_Teams_Per_Conference, and Max_Teams_Per_Location to the business configuration logic.",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating new tables for decision variables and indicators, updating business configuration logic with scalar parameters and formulas, and ensuring all optimization requirements are mapped correctly.

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": {
    "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_Required": {
    "sample_value": 10,
    "data_type": "INTEGER",
    "business_meaning": "Total number of teams to be selected for the tournament",
    "optimization_role": "Constraint bound for total team selection",
    "configuration_type": "scalar_parameter"
  },
  "Min_Teams_Per_Conference": {
    "sample_value": 2,
    "data_type": "INTEGER",
    "business_meaning": "Minimum number of teams required from each conference",
    "optimization_role": "Constraint bound for conference diversity",
    "configuration_type": "scalar_parameter"
  },
  "Max_Teams_Per_Location": {
    "sample_value": 3,
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of teams allowed from the same location",
    "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": 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": "university_basketball",
  "iteration": 1,
  "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(All_Games_Percent \u00d7 Team_Selection)",
    "decision_variables": "Team_Selection[Team_ID] (binary)",
    "constraints": [
      "\u2211(Team_Selection[Team_ID]) = Total_Teams_Required",
      "\u2211(Conference_Indicator[Team_ID] == 'Conference_X' ? Team_Selection[Team_ID] : 0) \u2265 Min_Teams_Per_Conference for each Conference_X",
      "\u2211(Location_Indicator[Team_ID] == 'Location_Y' ? Team_Selection[Team_ID] : 0) \u2264 Max_Teams_Per_Location for each Location_Y"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "All_Games_Percent[Team_ID]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Win percentage of each team"
      }
    },
    "constraint_bounds": {
      "Total_Teams_Required": {
        "currently_mapped_to": "business_configuration_logic.Total_Teams_Required",
        "mapping_adequacy": "good",
        "description": "Total number of teams to be selected"
      },
      "Min_Teams_Per_Conference": {
        "currently_mapped_to": "business_configuration_logic.Min_Teams_Per_Conference",
        "mapping_adequacy": "good",
        "description": "Minimum number of teams required from each conference"
      },
      "Max_Teams_Per_Location": {
        "currently_mapped_to": "business_configuration_logic.Max_Teams_Per_Location",
        "mapping_adequacy": "good",
        "description": "Maximum number of teams allowed from the same location"
      }
    },
    "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",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "All_Games_Percent[Team_ID]"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Map the win percentage data for each team to complete the objective function."
  }
}
