Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-25 22:47:19

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 party hosting company wants to minimize the total cost of hosting parties while ensuring that each party has a sufficient number of hosts and that hosts are assigned based on their availability and expertise.",
  "optimization_problem": "The company needs to minimize the total cost of hosting parties by assigning hosts to parties in a way that respects the constraints on the number of hosts per party, the availability of hosts, and the expertise required for each party theme.",
  "objective": "minimize \u2211(cost_per_host[Host_ID] \u00d7 assign[Party_ID, Host_ID])",
  "table_count": 4,
  "key_changes": [
    "Schema changes include creating new tables for cost_per_host, min_hosts, max_hosts, and expertise_match. Business configuration logic updated with scalar parameters and formulas for optimization."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Identify and map missing data/parameters for complete linear optimization model",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating new tables for cost_per_host, min_hosts, max_hosts, and expertise_match. Business configuration logic updated with scalar parameters and formulas for optimization.

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
);


```

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"
        }
      }
    }
  }
}


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": 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": "party_host",
  "iteration": 1,
  "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] (binary: 1 if host is assigned to party, 0 otherwise)",
    "constraints": [
      "\u2211(assign[Party_ID, Host_ID]) \u2265 min_hosts[Party_ID] for each Party_ID",
      "\u2211(assign[Party_ID, Host_ID]) \u2264 max_hosts[Party_ID] for each Party_ID",
      "assign[Party_ID, Host_ID] \u2264 expertise_match[Party_ID, Host_ID] for each Party_ID, Host_ID"
    ]
  },
  "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": "missing",
        "mapping_adequacy": "missing",
        "description": "Binary decision variable indicating if a host is assigned to a party",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "Decision variable assign[Party_ID, Host_ID] is missing in the schema"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Add decision variable assign[Party_ID, Host_ID] to the schema for complete linear optimization model"
  }
}
