Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-27 23:27:57

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 retail company wants to optimize the distribution of devices across its shops to maximize sales potential while considering stock availability and shop capacity.",
  "optimization_problem": "The goal is to maximize the total potential sales by optimally distributing available devices to various shops, considering each shop's capacity and the available stock of each device.",
  "objective": "maximize total_sales = \u2211(potential_sales[shop_id, device_id] \u00d7 allocation[shop_id, device_id])",
  "table_count": 3,
  "key_changes": [
    "Schema changes include creating new tables for missing optimization data and updating configuration logic for scalar parameters and formulas."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Gather missing data for potential sales and shop capacity 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 missing optimization data and updating configuration logic for scalar parameters and formulas.

CREATE TABLE PotentialSales (
  shop_id INTEGER,
  device_id INTEGER,
  potential_sales FLOAT
);

CREATE TABLE ShopCapacity (
  shop_id INTEGER,
  capacity INTEGER
);

CREATE TABLE Allocation (
  shop_id INTEGER,
  device_id INTEGER,
  quantity INTEGER
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "PotentialSales": {
      "business_purpose": "Estimated sales potential for each device at each shop",
      "optimization_role": "objective_coefficients",
      "columns": {
        "shop_id": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for each shop",
          "optimization_purpose": "Index for potential sales",
          "sample_values": "1, 2, 3"
        },
        "device_id": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for each device",
          "optimization_purpose": "Index for potential sales",
          "sample_values": "101, 102, 103"
        },
        "potential_sales": {
          "data_type": "FLOAT",
          "business_meaning": "Estimated sales potential",
          "optimization_purpose": "Coefficient in objective function",
          "sample_values": "500.0, 750.0, 1000.0"
        }
      }
    },
    "ShopCapacity": {
      "business_purpose": "Maximum number of devices each shop can hold",
      "optimization_role": "constraint_bounds",
      "columns": {
        "shop_id": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for each shop",
          "optimization_purpose": "Index for shop capacity",
          "sample_values": "1, 2, 3"
        },
        "capacity": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum capacity of the shop",
          "optimization_purpose": "Constraint bound",
          "sample_values": "100, 150, 200"
        }
      }
    },
    "Allocation": {
      "business_purpose": "Number of devices allocated to each shop",
      "optimization_role": "decision_variables",
      "columns": {
        "shop_id": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for each shop",
          "optimization_purpose": "Index for allocation",
          "sample_values": "1, 2, 3"
        },
        "device_id": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for each device",
          "optimization_purpose": "Index for allocation",
          "sample_values": "101, 102, 103"
        },
        "quantity": {
          "data_type": "INTEGER",
          "business_meaning": "Number of devices allocated",
          "optimization_purpose": "Decision variable",
          "sample_values": "10, 20, 30"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "shop_capacity": {
    "sample_value": "100",
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of devices each shop can hold",
    "optimization_role": "Used as a constraint in the optimization model",
    "configuration_type": "scalar_parameter"
  },
  "potential_sales_formula": {
    "formula_expression": "base_sales * demand_factor",
    "data_type": "STRING",
    "business_meaning": "Formula to calculate potential sales for each device at each shop",
    "optimization_role": "Used to determine objective coefficients",
    "configuration_type": "business_logic_formula"
  }
}


TASK: Refine the optimization problem formulation by analyzing current data schema mapping and identifying requirements while maintaining LINEAR structure.

JSON STRUCTURE REQUIRED:

{
  "database_id": "device",
  "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": "device",
  "iteration": 1,
  "business_context": "A retail company aims to optimize the allocation of devices to its shops to maximize sales potential, considering stock availability and shop capacity.",
  "optimization_problem_description": "Maximize the total potential sales by optimally distributing available devices to various shops, considering each shop's capacity and the available stock of each device.",
  "optimization_formulation": {
    "objective": "maximize total_sales = \u2211(PotentialSales.potential_sales[shop_id, device_id] \u00d7 Allocation.quantity[shop_id, device_id])",
    "decision_variables": "Allocation.quantity[shop_id, device_id] - integer variables representing the number of devices allocated to each shop",
    "constraints": [
      "\u2211(Allocation.quantity[shop_id, device_id]) \u2264 ShopCapacity.capacity[shop_id] for all shop_id",
      "Allocation.quantity[shop_id, device_id] \u2265 0 for all shop_id, device_id"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "potential_sales[shop_id, device_id]": {
        "currently_mapped_to": "PotentialSales.potential_sales",
        "mapping_adequacy": "good",
        "description": "Estimated sales potential for each device at each shop"
      }
    },
    "constraint_bounds": {
      "capacity[shop_id]": {
        "currently_mapped_to": "ShopCapacity.capacity",
        "mapping_adequacy": "good",
        "description": "Maximum number of devices each shop can hold"
      }
    },
    "decision_variables": {
      "quantity[shop_id, device_id]": {
        "currently_mapped_to": "Allocation.quantity",
        "mapping_adequacy": "good",
        "description": "Number of devices allocated to each shop",
        "variable_type": "integer"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
