Capacity Planning

Capacity Planning

You are an expert in capacity planning and resource optimization. Your goal is to help organizations match capacity with demand, optimize resource utilization, identify bottlenecks, and make cost-effective capacity investment decisions.

Initial Assessment

Before developing capacity plans, understand:

1. Planning Context

• What type of capacity? (production, warehouse, transportation, labor)
• Planning horizon? (short-term loading, tactical planning, strategic investment)
• Current capacity utilization rates?
• Known capacity constraints or bottlenecks?

1. Demand Profile

• Demand forecast and variability?
• Seasonality patterns?
• Growth expectations?
• Product mix changes expected?

1. Current State

• Existing capacity levels?
• Equipment, facilities, headcount?
• Operating schedules (shifts, days/week)?
• Current performance (OEE, yield, throughput)?

1. Constraints & Requirements

• Service level targets?
• Budget constraints for expansion?
• Lead times for capacity additions?
• Union agreements or labor rules?
• Regulatory requirements?

---

Capacity Planning Framework

Types of Capacity Planning

1. Long-Term Strategic Capacity Planning

• Horizon: 2-5+ years
• Focus: Major investments, facility additions
• Decisions: Build new plant? Add warehouse? Outsource?
• Approach: Scenario analysis, economic modeling

2. Medium-Term Tactical Capacity Planning

• Horizon: 3-18 months
• Focus: Adjust workforce, add equipment, modify schedules
• Decisions: Hire staff? Add shift? Lease equipment?
• Approach: Aggregate planning, linear programming

3. Short-Term Operational Capacity Planning

• Horizon: Days to weeks
• Focus: Load balancing, scheduling, overtime
• Decisions: How to allocate work? Overtime? Outsource batch?
• Approach: Scheduling algorithms, queuing theory

Capacity Strategies

Leading Strategy

• Add capacity in anticipation of demand
• Ensures availability, avoids stockouts
• Higher costs, risk of underutilization
• Best for: Growing markets, high service requirements

Lagging Strategy

• Add capacity only after demand materializes
• Lower costs, minimizes waste
• Risk of lost sales, poor service
• Best for: Uncertain demand, cost-sensitive markets

Matching Strategy

• Closely match capacity to demand
• Balance of cost and service
• Requires flexible capacity options
• Best for: Moderate growth, predictable demand

Cushion Strategy

• Maintain buffer capacity above expected demand
• Handles variability and surges
• Higher fixed costs but operational flexibility
• Best for: High variability, premium service

---

Capacity Analysis Methods

Capacity Measurement

Production Capacity Metrics:

1. Design Capacity

• Maximum possible output under ideal conditions
• Theoretical maximum

2. Effective Capacity

• Capacity under normal working conditions
• Accounts for breaks, maintenance, changeovers

3. Actual Output

• What's currently achieved
• Reality of operations

Key Formulas:

def calculate_capacity_metrics(design_capacity, effective_capacity, actual_output):
    """
    Calculate capacity utilization and efficiency

    Returns:
    - utilization: actual / design capacity
    - efficiency: actual / effective capacity
    """

    utilization = (actual_output / design_capacity) * 100
    efficiency = (actual_output / effective_capacity) * 100

    return {
        'utilization': utilization,
        'efficiency': efficiency,
        'design_capacity': design_capacity,
        'effective_capacity': effective_capacity,
        'actual_output': actual_output
    }

# Example
design = 10000  # units per month
effective = 8500  # accounting for maintenance, breaks
actual = 7500  # what's produced

metrics = calculate_capacity_metrics(design, effective, actual)
print(f"Utilization: {metrics['utilization']:.1f}%")  # 75%
print(f"Efficiency: {metrics['efficiency']:.1f}%")    # 88.2%

Overall Equipment Effectiveness (OEE):

def calculate_oee(availability, performance, quality):
    """
    Calculate OEE (Overall Equipment Effectiveness)

    Parameters:
    - availability: uptime / planned production time
    - performance: actual output / theoretical output at 100% speed
    - quality: good units / total units produced

    World-class OEE: > 85%
    """

    oee = availability * performance * quality * 100

    return {
        'oee': oee,
        'availability': availability * 100,
        'performance': performance * 100,
        'quality': quality * 100
    }

# Example
availability = 0.90  # 90% uptime
performance = 0.85   # 85% of theoretical speed
quality = 0.95       # 95% good units

oee_metrics = calculate_oee(availability, performance, quality)
print(f"OEE: {oee_metrics['oee']:.1f}%")  # 72.7%

Bottleneck Analysis

Theory of Constraints (TOC):

import pandas as pd
import numpy as np

def identify_bottleneck(process_steps):
    """
    Identify bottleneck in production process

    Parameters:
    - process_steps: list of dicts with 'name', 'capacity_per_hour', 'hours_available'

    Returns bottleneck step and throughput
    """

    df = pd.DataFrame(process_steps)

    # Calculate total capacity per period
    df['total_capacity'] = df['capacity_per_hour'] * df['hours_available']

    # Identify bottleneck (minimum capacity)
    bottleneck_idx = df['total_capacity'].idxmin()
    bottleneck = df.loc[bottleneck_idx]

    # System throughput limited by bottleneck
    system_throughput = bottleneck['total_capacity']

    # Calculate utilization based on bottleneck
    df['utilization'] = (system_throughput / df['total_capacity']) * 100

    return {
        'bottleneck_step': bottleneck['name'],
        'system_throughput': system_throughput,
        'bottleneck_capacity': bottleneck['total_capacity'],
        'process_analysis': df
    }

# Example: Manufacturing process
process = [
    {'name': 'Cutting', 'capacity_per_hour': 100, 'hours_available': 160},
    {'name': 'Assembly', 'capacity_per_hour': 80, 'hours_available': 160},
    {'name': 'Testing', 'capacity_per_hour': 120, 'hours_available': 160},
    {'name': 'Packaging', 'capacity_per_hour': 90, 'hours_available': 160}
]

bottleneck_analysis = identify_bottleneck(process)
print(f"Bottleneck: {bottleneck_analysis['bottleneck_step']}")
print(f"System Throughput: {bottleneck_analysis['system_throughput']:,.0f} units/month")
print("\nProcess Analysis:")
print(bottleneck_analysis['process_analysis'])

Drum-Buffer-Rope (DBR) Scheduling:

class DrumBufferRope:
    """
    Theory of Constraints scheduling method

    - Drum: Bottleneck sets the pace
    - Buffer: Protect bottleneck from disruptions
    - Rope: Pull mechanism to control material release
    """

    def __init__(self, bottleneck_capacity, buffer_time_days=3):
        self.bottleneck_capacity = bottleneck_capacity
        self.buffer_time = buffer_time_days

    def calculate_schedule(self, demand, lead_times):
        """
        Create production schedule based on DBR

        Parameters:
        - demand: array of daily demand
        - lead_times: dict of process step lead times
        """

        schedule = []

        for day, daily_demand in enumerate(demand):
            # Bottleneck sets the pace (DRUM)
            bottleneck_output = min(daily_demand, self.bottleneck_capacity)

            # Buffer: Start production earlier to protect bottleneck
            buffer_start_day = max(0, day - self.buffer_time)

            # Rope: Material release tied to bottleneck schedule
            material_release = bottleneck_output

            schedule.append({
                'day': day,
                'demand': daily_demand,
                'bottleneck_output': bottleneck_output,
                'buffer_start': buffer_start_day,
                'material_release': material_release
            })

        return pd.DataFrame(schedule)

# Example usage
dbr = DrumBufferRope(bottleneck_capacity=800, buffer_time_days=3)

# Daily demand for next 10 days
demand = np.array([750, 850, 800, 900, 700, 800, 950, 800, 850, 800])
lead_times = {'cutting': 1, 'assembly': 2, 'testing': 1}

schedule = dbr.calculate_schedule(demand, lead_times)
print(schedule)

---

Capacity Planning Models

Aggregate Planning (Linear Programming)

Objective: Minimize total costs while meeting demand

Decision Variables:

• Production quantity per period
• Workforce levels
• Overtime hours
• Inventory levels
• Subcontracting quantities

Costs:

• Regular time production
• Overtime production
• Hiring and firing
• Inventory holding
• Stockout/backorder
• Subcontracting

from pulp import *
import pandas as pd
import numpy as np

def aggregate_planning(demand, costs, constraints, periods=12):
    """
    Aggregate production planning optimization

    Parameters:
    - demand: array of demand by period
    - costs: dict with cost parameters
    - constraints: dict with capacity constraints
    - periods: planning horizon

    Returns optimal plan
    """

    # Create problem
    prob = LpProblem("Aggregate_Planning", LpMinimize)

    # Decision variables
    P = LpVariable.dicts("Production", range(periods), lowBound=0)
    W = LpVariable.dicts("Workforce", range(periods), lowBound=0, cat='Integer')
    O = LpVariable.dicts("Overtime", range(periods), lowBound=0)
    I = LpVariable.dicts("Inventory", range(periods), lowBound=0)
    H = LpVariable.dicts("Hire", range(periods), lowBound=0, cat='Integer')
    F = LpVariable.dicts("Fire", range(periods), lowBound=0, cat='Integer')
    B = LpVariable.dicts("Backorder", range(periods), lowBound=0)
    S = LpVariable.dicts("Subcontract", range(periods), lowBound=0)

    # Objective function
    prob += lpSum([
        # Regular production cost
        costs['regular_cost'] * P[t] +
        # Workforce cost
        costs['labor_cost'] * W[t] +
        # Overtime cost
        costs['overtime_cost'] * O[t] +
        # Inventory holding cost
        costs['holding_cost'] * I[t] +
        # Hiring cost
        costs['hiring_cost'] * H[t] +
        # Firing cost
        costs['firing_cost'] * F[t] +
        # Backorder cost
        costs['backorder_cost'] * B[t] +
        # Subcontracting cost
        costs['subcontract_cost'] * S[t]
        for t in range(periods)
    ])

    # Constraints

    # Initial conditions
    initial_workforce = constraints['initial_workforce']
    initial_inventory = constraints['initial_inventory']

    for t in range(periods):
        # Production capacity constraint
        prob += P[t]  threshold].copy()
        overloads = overloads.sort_values(['period', 'work_center'])

        return overloads

    def plot_capacity_profile(self, requirements):
        """Visualize capacity requirements vs. available"""

        work_centers = requirements['work_center'].unique()

        fig, axes = plt.subplots(len(work_centers), 1,
                                figsize=(12, 4 * len(work_centers)),
                                squeeze=False)

        for i, wc in enumerate(work_centers):
            wc_data = requirements[requirements['work_center'] == wc]

            ax = axes[i, 0]

            # Plot capacity line
            ax.axhline(y=wc_data['capacity'].iloc[0],
                      color='green', linestyle='--',
                      linewidth=2, label='Capacity')

            # Plot requirements
            ax.bar(wc_data['period'], wc_data['hours_required'],
                  alpha=0.7, label='Required')

            # Highlight overloads
            overload = wc_data[wc_data['utilization'] > 100]
            if not overload.empty:
                ax.bar(overload['period'], overload['hours_required'],
                      color='red', alpha=0.7, label='Overload')

            ax.set_title(f'{wc} - Capacity Profile')
            ax.set_xlabel('Period')
            ax.set_ylabel('Hours')
            ax.legend()
            ax.grid(True, alpha=0.3)

        plt.tight_layout()
        return fig

# Example usage
work_centers = {
    'Cutting': {'capacity': 160, 'efficiency': 0.90},
    'Welding': {'capacity': 160, 'efficiency': 0.85},
    'Assembly': {'capacity': 160, 'efficiency': 0.92},
    'Inspection': {'capacity': 160, 'efficiency': 0.95}
}

crp = CapacityRequirementsPlanning(work_centers)

# Production schedule
schedule = pd.DataFrame({
    'product': ['A', 'A', 'B', 'B', 'C', 'C'] * 3,
    'period': [1, 2, 1, 2, 1, 2] * 3,
    'quantity': [100, 120, 80, 90, 60, 70] * 3
})

# Routings: hours per unit at each work center
routings = {
    'A': [('Cutting', 0.5), ('Welding', 0.8), ('Assembly', 1.0), ('Inspection', 0.3)],
    'B': [('Cutting', 0.6), ('Assembly', 1.2), ('Inspection', 0.4)],
    'C': [('Cutting', 0.4), ('Welding', 1.0), ('Assembly', 0.8), ('Inspection', 0.2)]
}

# Calculate requirements
requirements = crp.calculate_requirements(schedule, routings)
print("Capacity Requirements:")
print(requirements)

# Identify overloads
overloads = crp.identify_overloads(requirements)
if not overloads.empty:
    print("\nOverloaded Resources:")
    print(overloads[['period', 'work_center', 'utilization', 'variance']])
else:
    print("\nNo overloads detected")

# Plot
crp.plot_capacity_profile(requirements)

---

Capacity Expansion Analysis

Economic Analysis of Capacity Investments

Net Present Value (NPV) Analysis:

import numpy as np

def npv_capacity_investment(initial_investment, annual_benefits,
                           annual_costs, discount_rate, years):
    """
    Calculate NPV of capacity investment

    Parameters:
    - initial_investment: upfront cost
    - annual_benefits: revenue increase per year
    - annual_costs: operating costs per year
    - discount_rate: cost of capital (e.g., 0.10 for 10%)
    - years: investment horizon
    """

    cash_flows = [-initial_investment]

    for year in range(1, years + 1):
        net_benefit = annual_benefits - annual_costs
        discounted_benefit = net_benefit / ((1 + discount_rate) ** year)
        cash_flows.append(discounted_benefit)

    npv = sum(cash_flows)

    # Calculate IRR (Internal Rate of Return)
    irr = np.irr([-initial_investment] + [annual_benefits - annual_costs] * years)

    # Payback period
    cumulative = -initial_investment
    payback = None
    for year in range(1, years + 1):
        cumulative += (annual_benefits - annual_costs)
        if cumulative > 0 and payback is None:
            payback = year

    return {
        'npv': npv,
        'irr': irr * 100,
        'payback_years': payback,
        'total_investment': initial_investment,
        'annual_net_benefit': annual_benefits - annual_costs
    }

# Example: Evaluate new production line
investment_analysis = npv_capacity_investment(
    initial_investment=5_000_000,
    annual_benefits=2_000_000,    # Increased revenue
    annual_costs=800_000,          # Operating costs
    discount_rate=0.12,            # 12% cost of capital
    years=10
)

print("Investment Analysis:")
print(f"  NPV: ${investment_analysis['npv']:,.0f}")
print(f"  IRR: {investment_analysis['irr']:.1f}%")
print(f"  Payback: {investment_analysis['payback_years']} years")

if investment_analysis['npv'] > 0:
    print("\n✓ Investment is financially viable")
else:
    print("\n✗ Investment is not viable at this discount rate")

Decision Tree Analysis for Capacity Timing

import matplotlib.pyplot as plt
import numpy as np

class CapacityDecisionTree:
    """
    Decision tree for capacity expansion timing
    under demand uncertainty
    """

    def __init__(self):
        self.scenarios = []

    def add_scenario(self, name, probability, demand_growth,
                    expand_now_cost, expand_later_cost,
                    revenue_per_unit, shortage_cost):
        """Add

…

## Source & license

This open-source skill is cataloged on AgentStack and links to its original source — we do not rehost the code.

- **Author:** [kishorkukreja](https://github.com/kishorkukreja)
- **Source:** [kishorkukreja/awesome-supply-chain](https://github.com/kishorkukreja/awesome-supply-chain)
- **License:** MIT

Install and usage instructions live in the source repository linked above.