Iteration 2 - OR_EXPERT_REFINEMENT
Sequence: 5
Timestamp: 2025-07-25 22:47:19

Prompt:
You are an Operations Research (OR) expert in iteration 2 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 1):
{
  "iteration": 2,
  "converged": false,
  "business_context": "A party hosting company aims to minimize the total cost of hosting parties by assigning hosts to parties while ensuring each party has a sufficient number of hosts, hosts are available, and their expertise matches the party theme.",
  "optimization_problem": "Minimize the total cost of hosting parties by assigning hosts to parties, respecting constraints on the number of hosts per party, host availability, and expertise matching.",
  "objective": "minimize \u2211(cost_per_host[Host_ID] \u00d7 assign[Party_ID, Host_ID])",
  "table_count": 1,
  "key_changes": [
    "Added decision variable table 'assign' to address missing optimization requirement. Updated business configuration logic to include scalar parameters and formulas. Ensured schema follows normalization principles and industry standards."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Add decision variable assign[Party_ID, Host_ID] to the schema for complete linear optimization model",
  "mapping_adequacy_summary": "mostly_good"
}

CURRENT SCHEMA:
```sql
-- Iteration 2 Database Schema
-- Objective: Added decision variable table 'assign' to address missing optimization requirement. Updated business configuration logic to include scalar parameters and formulas. Ensured schema follows normalization principles and industry standards.

CREATE TABLE cost_per_host (
  Host_ID INTEGER,
  cost INTEGER
);

CREATE TABLE min_hosts (
  Party_ID INTEGER,
  min_hosts INTEGER
);

CREATE TABLE max_hosts (
  Party_ID INTEGER,
  max_hosts INTEGER
);

CREATE TABLE expertise_match (
  Party_ID INTEGER,
  Host_ID INTEGER,
  match BOOLEAN
);

CREATE TABLE assign (
  Party_ID INTEGER,
  Host_ID INTEGER,
  assign BOOLEAN
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "cost_per_host": {
      "business_purpose": "Cost associated with each host",
      "optimization_role": "objective_coefficients",
      "columns": {
        "Host_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each host",
          "optimization_purpose": "Index for cost coefficient",
          "sample_values": "1, 2, 3"
        },
        "cost": {
          "data_type": "INTEGER",
          "business_meaning": "Cost of the host",
          "optimization_purpose": "Coefficient in objective function",
          "sample_values": "50, 60, 70"
        }
      }
    },
    "min_hosts": {
      "business_purpose": "Minimum number of hosts required for each party",
      "optimization_role": "constraint_bounds",
      "columns": {
        "Party_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each party",
          "optimization_purpose": "Index for minimum hosts constraint",
          "sample_values": "1, 2, 3"
        },
        "min_hosts": {
          "data_type": "INTEGER",
          "business_meaning": "Minimum number of hosts",
          "optimization_purpose": "Lower bound in constraint",
          "sample_values": "2, 3, 4"
        }
      }
    },
    "max_hosts": {
      "business_purpose": "Maximum number of hosts allowed for each party",
      "optimization_role": "constraint_bounds",
      "columns": {
        "Party_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each party",
          "optimization_purpose": "Index for maximum hosts constraint",
          "sample_values": "1, 2, 3"
        },
        "max_hosts": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum number of hosts",
          "optimization_purpose": "Upper bound in constraint",
          "sample_values": "5, 6, 7"
        }
      }
    },
    "expertise_match": {
      "business_purpose": "Binary indicator if host's expertise matches party theme",
      "optimization_role": "constraint_bounds",
      "columns": {
        "Party_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each party",
          "optimization_purpose": "Index for expertise match constraint",
          "sample_values": "1, 2, 3"
        },
        "Host_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each host",
          "optimization_purpose": "Index for expertise match constraint",
          "sample_values": "1, 2, 3"
        },
        "match": {
          "data_type": "BOOLEAN",
          "business_meaning": "Expertise match indicator",
          "optimization_purpose": "Constraint bound",
          "sample_values": "true, false"
        }
      }
    },
    "assign": {
      "business_purpose": "Binary decision variable indicating if a host is assigned to a party",
      "optimization_role": "decision_variables",
      "columns": {
        "Party_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each party",
          "optimization_purpose": "Index for assignment decision",
          "sample_values": "1, 2, 3"
        },
        "Host_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each host",
          "optimization_purpose": "Index for assignment decision",
          "sample_values": "1, 2, 3"
        },
        "assign": {
          "data_type": "BOOLEAN",
          "business_meaning": "Assignment decision indicator",
          "optimization_purpose": "Decision variable",
          "sample_values": "true, false"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "cost_per_host": {
    "sample_value": 50,
    "data_type": "INTEGER",
    "business_meaning": "Cost associated with each host",
    "optimization_role": "Objective coefficient",
    "configuration_type": "scalar_parameter"
  },
  "min_hosts": {
    "sample_value": 2,
    "data_type": "INTEGER",
    "business_meaning": "Minimum number of hosts required for each party",
    "optimization_role": "Constraint bound",
    "configuration_type": "scalar_parameter"
  },
  "max_hosts": {
    "sample_value": 5,
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of hosts allowed for each party",
    "optimization_role": "Constraint bound",
    "configuration_type": "scalar_parameter"
  },
  "expertise_match": {
    "sample_value": 1,
    "data_type": "BOOLEAN",
    "business_meaning": "Binary indicator if host's expertise matches party theme",
    "optimization_role": "Constraint bound",
    "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": "party_host",
  "iteration": 2,
  "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": "party_host",
  "iteration": 2,
  "business_context": "A party hosting company aims to minimize the total cost of hosting parties by assigning hosts to parties while ensuring each party has a sufficient number of hosts, hosts are available, and their expertise matches the party theme.",
  "optimization_problem_description": "Minimize the total cost of hosting parties by assigning hosts to parties, respecting constraints on the number of hosts per party, host availability, and expertise matching.",
  "optimization_formulation": {
    "objective": "minimize \u2211(cost_per_host[Host_ID] \u00d7 assign[Party_ID, Host_ID])",
    "decision_variables": "assign[Party_ID, Host_ID] \u2208 {0, 1} (binary decision variable indicating if host is assigned to party)",
    "constraints": [
      "\u2211(assign[Party_ID, Host_ID]) \u2265 min_hosts[Party_ID] for each Party_ID (minimum hosts per party)",
      "\u2211(assign[Party_ID, Host_ID]) \u2264 max_hosts[Party_ID] for each Party_ID (maximum hosts per party)",
      "assign[Party_ID, Host_ID] \u2264 expertise_match[Party_ID, Host_ID] for each Party_ID, Host_ID (expertise matching)"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "cost_per_host[Host_ID]": {
        "currently_mapped_to": "cost_per_host.cost",
        "mapping_adequacy": "good",
        "description": "Cost associated with each host"
      }
    },
    "constraint_bounds": {
      "min_hosts[Party_ID]": {
        "currently_mapped_to": "min_hosts.min_hosts",
        "mapping_adequacy": "good",
        "description": "Minimum number of hosts required for each party"
      },
      "max_hosts[Party_ID]": {
        "currently_mapped_to": "max_hosts.max_hosts",
        "mapping_adequacy": "good",
        "description": "Maximum number of hosts allowed for each party"
      },
      "expertise_match[Party_ID, Host_ID]": {
        "currently_mapped_to": "expertise_match.match",
        "mapping_adequacy": "good",
        "description": "Binary indicator if host's expertise matches party theme"
      }
    },
    "decision_variables": {
      "assign[Party_ID, Host_ID]": {
        "currently_mapped_to": "assign.assign",
        "mapping_adequacy": "good",
        "description": "Binary decision variable indicating if host is assigned to party",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
