Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-27 22:50:07

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 museum wants to optimize the allocation of its staff across different museums to maximize visitor satisfaction while minimizing operational costs. The number of staff allocated to each museum affects the visitor experience and the operational cost.",
  "optimization_problem": "The goal is to determine the optimal number of staff to allocate to each museum to maximize visitor satisfaction, which is assumed to be proportional to the number of staff, while minimizing the total operational cost. The operational cost is a linear function of the number of staff allocated.",
  "objective": "maximize total_visitor_satisfaction = \u2211(satisfaction_coefficient[m] * staff_allocated[m]) - \u2211(cost_coefficient[m] * staff_allocated[m])",
  "table_count": 2,
  "key_changes": [
    "Schema changes include creating new tables for objective coefficients and constraint bounds, modifying existing tables to address mapping gaps, and updating business configuration logic for scalar parameters and formulas."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Gather missing data for coefficients and constraints to complete the optimization model",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating new tables for objective coefficients and constraint bounds, modifying existing tables to address mapping gaps, and updating business configuration logic for scalar parameters and formulas.

CREATE TABLE museum (
  Num_of_Staff INTEGER,
  satisfaction_coefficient FLOAT,
  cost_coefficient FLOAT
);

CREATE TABLE ObjectiveCoefficients (
  museum_id INTEGER,
  satisfaction_coefficient FLOAT,
  cost_coefficient FLOAT
);

CREATE TABLE ConstraintBounds (
  museum_id INTEGER,
  minimum_staff_required INTEGER,
  maximum_staff_capacity INTEGER
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "museum": {
      "business_purpose": "Stores information about each museum including staff allocation and coefficients",
      "optimization_role": "decision_variables/objective_coefficients",
      "columns": {
        "Num_of_Staff": {
          "data_type": "INTEGER",
          "business_meaning": "Number of staff allocated to the museum",
          "optimization_purpose": "Decision variable for staff allocation",
          "sample_values": "5, 10, 15"
        },
        "satisfaction_coefficient": {
          "data_type": "FLOAT",
          "business_meaning": "Increase in visitor satisfaction per additional staff member",
          "optimization_purpose": "Objective coefficient for satisfaction",
          "sample_values": "1.2, 1.5, 1.8"
        },
        "cost_coefficient": {
          "data_type": "FLOAT",
          "business_meaning": "Operational cost per staff member",
          "optimization_purpose": "Objective coefficient for cost",
          "sample_values": "0.8, 1.0, 1.2"
        }
      }
    },
    "ObjectiveCoefficients": {
      "business_purpose": "Stores coefficients for optimization objectives",
      "optimization_role": "objective_coefficients",
      "columns": {
        "museum_id": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for each museum",
          "optimization_purpose": "Links coefficients to specific museums",
          "sample_values": "1, 2, 3"
        },
        "satisfaction_coefficient": {
          "data_type": "FLOAT",
          "business_meaning": "Coefficient for visitor satisfaction",
          "optimization_purpose": "Used in objective function",
          "sample_values": "1.2, 1.5, 1.8"
        },
        "cost_coefficient": {
          "data_type": "FLOAT",
          "business_meaning": "Coefficient for operational cost",
          "optimization_purpose": "Used in objective function",
          "sample_values": "0.8, 1.0, 1.2"
        }
      }
    },
    "ConstraintBounds": {
      "business_purpose": "Stores bounds for staff allocation constraints",
      "optimization_role": "constraint_bounds",
      "columns": {
        "museum_id": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for each museum",
          "optimization_purpose": "Links constraints to specific museums",
          "sample_values": "1, 2, 3"
        },
        "minimum_staff_required": {
          "data_type": "INTEGER",
          "business_meaning": "Minimum staff required for operation",
          "optimization_purpose": "Constraint lower bound",
          "sample_values": "5, 6, 7"
        },
        "maximum_staff_capacity": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum staff capacity",
          "optimization_purpose": "Constraint upper bound",
          "sample_values": "15, 20, 25"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "total_available_staff": {
    "sample_value": "100",
    "data_type": "INTEGER",
    "business_meaning": "Total number of staff available for allocation",
    "optimization_role": "Used as a constraint in optimization model",
    "configuration_type": "scalar_parameter"
  },
  "minimum_staff_required": {
    "sample_value": "5",
    "data_type": "INTEGER",
    "business_meaning": "Minimum staff required for each museum",
    "optimization_role": "Used as a constraint in optimization model",
    "configuration_type": "scalar_parameter"
  },
  "maximum_staff_capacity": {
    "sample_value": "20",
    "data_type": "INTEGER",
    "business_meaning": "Maximum staff capacity for each museum",
    "optimization_role": "Used as a constraint in optimization model",
    "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": "museum_visit",
  "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": "museum_visit",
  "iteration": 1,
  "business_context": "A museum wants to optimize the allocation of its staff across different museums to maximize visitor satisfaction while minimizing operational costs. The number of staff allocated to each museum affects the visitor experience and the operational cost.",
  "optimization_problem_description": "Determine the optimal number of staff to allocate to each museum to maximize visitor satisfaction, which is assumed to be proportional to the number of staff, while minimizing the total operational cost. The operational cost is a linear function of the number of staff allocated.",
  "optimization_formulation": {
    "objective": "maximize total_visitor_satisfaction = \u2211(satisfaction_coefficient[m] * staff_allocated[m]) - \u2211(cost_coefficient[m] * staff_allocated[m])",
    "decision_variables": "staff_allocated[m] for each museum m, where staff_allocated is an integer",
    "constraints": [
      "\u2211(staff_allocated[m]) <= total_available_staff",
      "minimum_staff_required[m] <= staff_allocated[m] <= maximum_staff_capacity[m] for each museum m"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "satisfaction_coefficient[m]": {
        "currently_mapped_to": "museum.satisfaction_coefficient",
        "mapping_adequacy": "good",
        "description": "Increase in visitor satisfaction per additional staff member"
      },
      "cost_coefficient[m]": {
        "currently_mapped_to": "museum.cost_coefficient",
        "mapping_adequacy": "good",
        "description": "Operational cost per staff member"
      }
    },
    "constraint_bounds": {
      "total_available_staff": {
        "currently_mapped_to": "business_configuration_logic.total_available_staff",
        "mapping_adequacy": "good",
        "description": "Total number of staff available for allocation"
      },
      "minimum_staff_required[m]": {
        "currently_mapped_to": "ConstraintBounds.minimum_staff_required",
        "mapping_adequacy": "good",
        "description": "Minimum staff required for operation"
      },
      "maximum_staff_capacity[m]": {
        "currently_mapped_to": "ConstraintBounds.maximum_staff_capacity",
        "mapping_adequacy": "good",
        "description": "Maximum staff capacity"
      }
    },
    "decision_variables": {
      "staff_allocated[m]": {
        "currently_mapped_to": "museum.Num_of_Staff",
        "mapping_adequacy": "good",
        "description": "Number of staff allocated to the museum",
        "variable_type": "integer"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
