be-optimumoh/docs/overhaul_optimization/plant_optimization.md

Plant Level Overhaul Optimization

This document explains how individual asset optimizations are aggregated to find the best economic strategy for the entire fleet or plant.

1. Fleet Aggregation Theory

At the plant level, the objective is to minimize the Total Fleet Cost per Unit Time. This assumes a Uniform Interval Policy or a Synchronized Overhaul Strategy where the plant looks for a common maintenance rhythm.

Plant Objective Function

The plant-level cost function is the summation of individual equipment cost functions (C_i):

C_{Plant}(T) = \sum_{i=1}^{N} C_i(T) = \frac{\sum_{i=1}^{N} (C_{p,i} + C_{f,i} \cdot E[N_i(T)])}{T}

Where:

• N: Total number of equipments in the scope.
• C_{p,i}: Preventive cost for equipment i.
• C_{f,i}: Failure cost for equipment i.
• E[N_i(T)]: Expected failures for equipment i until time T.

2. Searching for the Fleet Optimum

The "actual theory" used by the engine involves a two-phase search:

Phase 1: Unconstrained Summation

The system calculates the CPUT curve for every piece of equipment independently. It then sums these curves to create a "Fleet U-Curve." The minimum of this sum represents the Theoretical Fleet Optimum.

Phase 2: Sparepart Interaction & Constraints

Unlike a simple sum, the real plant optimum must account for shared resources (e.g., a limited budget or limited spare parts).

1. Sparepart Conflicts: If multiple equipments reach their optimal interval at the same time, the SparepartManager checks if there are enough parts in the warehouse.
2. Constraint Penalty: If parts are missing, a "Procurement Penalty" is added to the C_{p,i} for that specific month, effectively shifting the "U-curve" to the right (delaying) or left (earlier) depending on availability.
3. Final Selection: The system chooses the Month T that minimizes the constrained total fleet cost.

3. Implementation in service.py

The code uses numpy to perform vector addition of the cost curves:

# Aggregate amortized costs for fleet analysis
total_corrective_costs += np.array(corrective_costs)
total_preventive_costs += np.array(preventive_costs)
total_costs += np.array(total_costs_equipment)

# Find the month T that minimizes the sum
fleet_optimal_index = np.argmin(total_costs)

4. Key Metrics for Decision Makers

• Fleet CPUT: The average monthly budget required to maintain the plant at the chosen interval.
• Accumulation Control: By using amortized costs (Rp/Month) instead of total cumulative costs, the plant chart remains stable and allows for direct comparison between intervals regardless of the number of assets.
• Risk vs. Cost: The plant chart shows the trade-off between the Fleet Failure Risk (increasing line) and Fixed Overhaul Costs (decreasing line).