Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-25 22:35:37

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 coffee shop chain wants to optimize the allocation of staff during happy hours across different shops to maximize customer satisfaction while minimizing operational costs.",
  "optimization_problem": "The goal is to determine the optimal number of staff to assign to each shop during happy hours to maximize the total amount spent by members while keeping the total number of staff across all shops within a budget limit.",
  "objective": "maximize \u2211(Total_amount[HH_ID, Member_ID] * Level_of_membership[Member_ID])",
  "table_count": 1,
  "key_changes": [
    "Schema changes include creating new tables for missing constraint bounds, modifying existing tables to refine decision variable mapping, and adding business configuration logic for scalar parameters and formulas."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Define missing constraint bounds and refine decision variable mapping",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating new tables for missing constraint bounds, modifying existing tables to refine decision variable mapping, and adding business configuration logic for scalar parameters and formulas.

CREATE TABLE happy_hour_member (
  Total_amount FLOAT
);

CREATE TABLE member (
  Level_of_membership INTEGER
);

CREATE TABLE happy_hour (
  Num_of_staff_in_charge INTEGER
);

CREATE TABLE shop_staff_limits (
  Max_Staff_Per_Shop INTEGER,
  Min_Staff_Per_Shop INTEGER
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "happy_hour_member": {
      "business_purpose": "Records the amount spent by each member during happy hours",
      "optimization_role": "objective_coefficients",
      "columns": {
        "Total_amount": {
          "data_type": "FLOAT",
          "business_meaning": "Amount spent by a member during a happy hour",
          "optimization_purpose": "Coefficient in the objective function",
          "sample_values": "25.50, 30.00, 15.75"
        }
      }
    },
    "member": {
      "business_purpose": "Stores membership information for each member",
      "optimization_role": "objective_coefficients",
      "columns": {
        "Level_of_membership": {
          "data_type": "INTEGER",
          "business_meaning": "Membership level of a member",
          "optimization_purpose": "Coefficient in the objective function",
          "sample_values": "1, 2, 3"
        }
      }
    },
    "happy_hour": {
      "business_purpose": "Records the number of staff assigned to each shop during happy hours",
      "optimization_role": "decision_variables",
      "columns": {
        "Num_of_staff_in_charge": {
          "data_type": "INTEGER",
          "business_meaning": "Number of staff assigned to a shop during a happy hour",
          "optimization_purpose": "Decision variable in the optimization model",
          "sample_values": "3, 5, 7"
        }
      }
    },
    "shop_staff_limits": {
      "business_purpose": "Stores the maximum and minimum number of staff allowed per shop",
      "optimization_role": "constraint_bounds",
      "columns": {
        "Max_Staff_Per_Shop": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum number of staff allowed per shop",
          "optimization_purpose": "Constraint bound in the optimization model",
          "sample_values": "10, 12, 15"
        },
        "Min_Staff_Per_Shop": {
          "data_type": "INTEGER",
          "business_meaning": "Minimum number of staff required per shop",
          "optimization_purpose": "Constraint bound in the optimization model",
          "sample_values": "2, 3, 4"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "Total_Staff_Budget": {
    "sample_value": 100,
    "data_type": "INTEGER",
    "business_meaning": "Total budget for staff across all shops",
    "optimization_role": "Constraint bound for total staff budget",
    "configuration_type": "scalar_parameter"
  },
  "Max_Staff_Per_Shop": {
    "sample_value": 10,
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of staff allowed per shop",
    "optimization_role": "Constraint bound for maximum staff per shop",
    "configuration_type": "scalar_parameter"
  },
  "Min_Staff_Per_Shop": {
    "sample_value": 2,
    "data_type": "INTEGER",
    "business_meaning": "Minimum number of staff required per shop",
    "optimization_role": "Constraint bound for minimum staff per shop",
    "configuration_type": "scalar_parameter"
  },
  "Max_Spending_Per_Member": {
    "sample_value": 50,
    "data_type": "FLOAT",
    "business_meaning": "Maximum spending limit per member",
    "optimization_role": "Constraint bound for maximum spending per member",
    "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": "coffee_shop",
  "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": "coffee_shop",
  "iteration": 1,
  "business_context": "A coffee shop chain aims to optimize staff allocation during happy hours across different shops to maximize customer satisfaction while minimizing operational costs, ensuring the total number of staff across all shops remains within a budget limit.",
  "optimization_problem_description": "Determine the optimal number of staff to assign to each shop during happy hours to maximize the total amount spent by members, weighted by their membership level, while keeping the total number of staff across all shops within a budget limit and ensuring each shop has staff within its minimum and maximum limits.",
  "optimization_formulation": {
    "objective": "maximize \u2211(Total_amount[HH_ID, Member_ID] * Level_of_membership[Member_ID])",
    "decision_variables": "Num_of_staff_in_charge[Shop_ID] (integer)",
    "constraints": [
      "\u2211(Num_of_staff_in_charge[Shop_ID]) \u2264 Total_Staff_Budget",
      "Min_Staff_Per_Shop[Shop_ID] \u2264 Num_of_staff_in_charge[Shop_ID] \u2264 Max_Staff_Per_Shop[Shop_ID] for all Shop_ID"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Total_amount[HH_ID, Member_ID]": {
        "currently_mapped_to": "happy_hour_member.Total_amount",
        "mapping_adequacy": "good",
        "description": "Amount spent by a member during a happy hour"
      },
      "Level_of_membership[Member_ID]": {
        "currently_mapped_to": "member.Level_of_membership",
        "mapping_adequacy": "good",
        "description": "Membership level of a member"
      }
    },
    "constraint_bounds": {
      "Total_Staff_Budget": {
        "currently_mapped_to": "business_configuration_logic.Total_Staff_Budget",
        "mapping_adequacy": "good",
        "description": "Total budget for staff across all shops"
      },
      "Max_Staff_Per_Shop[Shop_ID]": {
        "currently_mapped_to": "shop_staff_limits.Max_Staff_Per_Shop",
        "mapping_adequacy": "good",
        "description": "Maximum number of staff allowed per shop"
      },
      "Min_Staff_Per_Shop[Shop_ID]": {
        "currently_mapped_to": "shop_staff_limits.Min_Staff_Per_Shop",
        "mapping_adequacy": "good",
        "description": "Minimum number of staff required per shop"
      }
    },
    "decision_variables": {
      "Num_of_staff_in_charge[Shop_ID]": {
        "currently_mapped_to": "happy_hour.Num_of_staff_in_charge",
        "mapping_adequacy": "good",
        "description": "Number of staff assigned to a shop during a happy hour",
        "variable_type": "integer"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
