Iteration 2 - OR_EXPERT_REFINEMENT
Sequence: 5
Timestamp: 2025-07-25 22:35:26

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": "Optimize bike redistribution across stations to minimize the number of unmet trip demands and the total cost of bike movements while respecting station dock capacities.",
  "optimization_problem": "Minimize the total number of unmet trip demands and the total cost of bike movements, subject to constraints on station dock capacities and bike availability.",
  "objective": "minimize \u2211(unmet_demand[s] + cost_per_bike_movement * \u2211(x[s1][s2] for all s1, s2)) where s is the station index",
  "table_count": 0,
  "key_changes": [
    "Added initial_bikes table to address missing optimization requirement, updated business configuration logic to include initial_bikes as a scalar parameter, and ensured all mappings are complete and consistent with OR expert's analysis."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Define initial_bikes[s1] in the schema or business configuration logic.",
  "mapping_adequacy_summary": "mostly_good"
}

CURRENT SCHEMA:
```sql
-- Iteration 2 Database Schema
-- Objective: Added initial_bikes table to address missing optimization requirement, updated business configuration logic to include initial_bikes as a scalar parameter, and ensured all mappings are complete and consistent with OR expert's analysis.

CREATE TABLE unmet_demand (
  station_id INTEGER,
  demand_count INTEGER
);

CREATE TABLE bike_movements (
  from_station_id INTEGER,
  to_station_id INTEGER,
  movement_count INTEGER
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "unmet_demand": {
      "business_purpose": "tracks unmet trip demands at each station",
      "optimization_role": "decision_variables",
      "columns": {
        "station_id": {
          "data_type": "INTEGER",
          "business_meaning": "unique identifier for the station",
          "optimization_purpose": "index for unmet_demand[s]",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "demand_count": {
          "data_type": "INTEGER",
          "business_meaning": "number of unmet trip demands",
          "optimization_purpose": "value of unmet_demand[s]",
          "sample_values": [
            0,
            1,
            2
          ]
        }
      }
    },
    "bike_movements": {
      "business_purpose": "tracks bike movements between stations",
      "optimization_role": "decision_variables",
      "columns": {
        "from_station_id": {
          "data_type": "INTEGER",
          "business_meaning": "station where bikes are moved from",
          "optimization_purpose": "index s1 for x[s1][s2]",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "to_station_id": {
          "data_type": "INTEGER",
          "business_meaning": "station where bikes are moved to",
          "optimization_purpose": "index s2 for x[s1][s2]",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "movement_count": {
          "data_type": "INTEGER",
          "business_meaning": "number of bikes moved",
          "optimization_purpose": "value of x[s1][s2]",
          "sample_values": [
            0,
            1,
            2
          ]
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "initial_bikes": {
    "sample_value": 15,
    "data_type": "INTEGER",
    "business_meaning": "initial number of bikes at station s1",
    "optimization_role": "used in constraints to limit bike movements",
    "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": "bike_1",
  "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": "bike_1",
  "iteration": 2,
  "business_context": "Optimize bike redistribution across stations to minimize the number of unmet trip demands and the total cost of bike movements while respecting station dock capacities and initial bike availability.",
  "optimization_problem_description": "Minimize the total number of unmet trip demands and the total cost of bike movements, subject to constraints on station dock capacities, bike availability, and initial bike counts.",
  "optimization_formulation": {
    "objective": "minimize \u2211(unmet_demand[s] + cost_per_bike_movement * \u2211(x[s1][s2] for all s1, s2)) where s is the station index",
    "decision_variables": {
      "unmet_demand[s]": "integer, number of unmet trip demands at station s",
      "x[s1][s2]": "integer, number of bikes moved from station s1 to station s2"
    },
    "constraints": [
      "\u2211(x[s1][s2] for all s2) \u2264 initial_bikes[s1] for all s1",
      "\u2211(x[s1][s2] for all s1) + unmet_demand[s2] \u2264 dock_capacity[s2] for all s2"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "unmet_demand[s]": {
        "currently_mapped_to": "unmet_demand.demand_count",
        "mapping_adequacy": "good",
        "description": "coefficient for unmet trip demands at station s"
      },
      "cost_per_bike_movement": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "cost per bike movement between stations"
      }
    },
    "constraint_bounds": {
      "initial_bikes[s1]": {
        "currently_mapped_to": "business_configuration_logic.initial_bikes",
        "mapping_adequacy": "good",
        "description": "initial number of bikes at station s1"
      },
      "dock_capacity[s2]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "dock capacity at station s2"
      }
    },
    "decision_variables": {
      "unmet_demand[s]": {
        "currently_mapped_to": "unmet_demand.demand_count",
        "mapping_adequacy": "good",
        "description": "number of unmet trip demands at station s",
        "variable_type": "integer"
      },
      "x[s1][s2]": {
        "currently_mapped_to": "bike_movements.movement_count",
        "mapping_adequacy": "good",
        "description": "number of bikes moved from station s1 to station s2",
        "variable_type": "integer"
      }
    }
  },
  "missing_optimization_requirements": [
    "cost_per_bike_movement",
    "dock_capacity[s2]"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Define cost_per_bike_movement and dock_capacity[s2] in the schema or business configuration logic."
  }
}
