Step 7: What-If Analysis¶

In this final step, we extend Step 4’s multi-period production planning model with comprehensive what-if analysis capabilities for interactive tactical decision support.

Overview¶

What-if analysis enables quick exploration of “what if we changed this parameter?” questions without setting up full scenarios. This is ideal for tactical decision-making, investment planning, and risk assessment.

What’s New in Step 7¶

Building on Step 4¶

Step 7 uses the same optimization model as Step 4 (multi-period production planning) but adds comprehensive what-if analysis on top:

Aspect	Step 4	Step 7
Optimization Model	Multi-period with setup costs	Same model
Problem Scale	9 products × 4 periods (~1,600 vars)	Same scale
After Optimization	Display results, save to DB	Extensive what-if analysis
HTML Report	4 tabs (Summary, Schedule, etc.)	5 tabs (+ What-If Analysis)
Business Insights	Operational (what to produce)	Tactical (investments, scenarios)

New Features¶

Feature	Description	Business Value
Capacity Change Scenarios	Test impact of adding/removing resources	Quick ROI assessment
Bottleneck Identification	Systematically test all resources	Investment prioritization
Sensitivity Ranges	Show profit vs capacity curves	Optimal capacity sizing
Investment Comparison	Compare ROI of different options	Capital allocation
Risk Assessment	Test downside scenarios	Contingency planning

Key Business Questions Answered¶

Step 7 helps answer tactical questions like:

What if we add 50 hours to cutting machine capacity?
- How much will profit increase?
- What’s the marginal value per hour?
Which resource is the biggest bottleneck?
- Which capacity expansion gives best ROI?
- Where should we invest first?
How sensitive is profit to capacity changes?
- At what capacity do we see diminishing returns?
- What’s the optimal capacity level?
What if we lose machine capacity (equipment failure)?
- How much profit would we lose?
- Which failures are most costly?
Should we invest in machines or materials?
- Which gives better ROI per dollar?
- How do different investment amounts compare?

Running the Example¶

Step 1: Populate the Database¶

cd tutorials/production_planning/step7_whatif_analysis
python sample_data.py

Output:

================================================================================
PRODUCTION PLANNING DATABASE SETUP - STEP 7 (WHAT-IF ANALYSIS)
================================================================================

Scale: 9 products × 6 machines × 9 materials × 4 periods
Expected variables: ~1,600

[Database population details...]

Database populated successfully!

Step 2: Run Optimization with What-If Analysis¶

python production_whatif.py

The program will:

Initialize database and create ORM session
Build multi-period production model (same as Step 4)
Solve for baseline optimal solution
Run comprehensive what-if analysis:
- Test machine capacity changes
- Test material availability changes
- Identify all bottlenecks systematically
- Generate sensitivity ranges
- Compare investment options
- Assess downside risk scenarios
Display all results to console
Save baseline solution to database
Generate enhanced HTML report with what-if visualizations

Expected solve time: 10-30 seconds for baseline + 30-60 seconds for what-if analysis

Step 3: View the Enhanced HTML Report¶

# macOS
open production_whatif_report.html

# Linux
xdg-open production_whatif_report.html

# Windows
start production_whatif_report.html

Report Features (5 tabs):

Summary Dashboard (from Step 4)
- Total profit and key metrics
- Profit by period
- Resource efficiency gauges
- Order fulfillment by priority
What-If Analysis (NEW)
- Capacity change scenarios table
- Bottleneck identification and ranking
- Sensitivity ranges with charts
- Investment ROI comparison
- Risk assessment matrix
- Key insights and recommendations
Production Schedule (from Step 4)
Resource Utilization (from Step 4)
Customer Orders (from Step 4)

Console Output Walkthrough¶

1. Baseline Optimization¶

================================================================================
LumiX Tutorial: Production Planning - Step 7 (WHAT-IF ANALYSIS)
================================================================================

Building large-scale multi-period production model (ORM)...
  Scale: 9 products × 4 periods

Solving baseline model with ortools...

================================================================================
MULTI-PERIOD PRODUCTION PLAN (BASELINE)
================================================================================
Status: optimal
Total Objective Value: $45,234.56

Week 1:
--------------------------------------------------------------------------------
Product              Production      Inventory       Profit Contrib
--------------------------------------------------------------------------------
Chair                50.00           0.00            $2,250.00
Table                25.00           5.00            $3,000.00
...

2. Machine Capacity What-If¶

--------------------------------------------------------------------------------
1. MACHINE CAPACITY WHAT-IF SCENARIOS
--------------------------------------------------------------------------------

What if we add 50 hours to Cutting Machine in Week 1?
  Original Profit:  $45,234.56
  New Profit:       $45,734.56
  Change:           $500.00 (+1.11%)
  Marginal Value:   $10.00 per hour

Interpretation: Adding 50 hours of cutting machine capacity would increase
profit by $500, yielding $10 per hour marginal value.

3. Bottleneck Identification¶

--------------------------------------------------------------------------------
3. BOTTLENECK IDENTIFICATION
--------------------------------------------------------------------------------

Testing impact of adding 10 units to each resource constraint...

Resource                                 Marginal Value       Priority
--------------------------------------------------------------------------------
Cutting Machine (Week 1)                 $10.00              HIGH
Assembly Station (Week 1)                $5.50               HIGH
Wood (Week 1)                            $3.25               MEDIUM
Finishing Station (Week 2)               $2.10               MEDIUM
Metal (Week 1)                           $0.00               LOW
...

Top bottleneck: Cutting Machine (Week 1) with $10/unit marginal value
Recommendation: Prioritize expanding cutting machine capacity

4. Sensitivity Range Analysis¶

--------------------------------------------------------------------------------
4. SENSITIVITY RANGE ANALYSIS
--------------------------------------------------------------------------------

Analyzing sensitivity: Cutting Machine capacity in Week 1
Range: 100 - 250 hours (baseline: 160)

Capacity (hrs)       Profit               vs Baseline
--------------------------------------------------------------------------------
100                  $42,234.56           -6.64%
120                  $43,434.56           -3.98%
140                  $44,334.56           -1.99%
160                  $45,234.56           +0.00% (baseline)
180                  $46,034.56           +1.77%
200                  $46,734.56           +3.32%
220                  $47,234.56           +4.42%
240                  $47,534.56           +5.08%

Observation: Linear increase up to 200 hours, then diminishing returns

5. Investment Comparison¶

--------------------------------------------------------------------------------
5. INVESTMENT COMPARISON
--------------------------------------------------------------------------------

Comparing different capacity expansion options:

Investment Option                                  Profit Increase      ROI/Unit
--------------------------------------------------------------------------------
Cutting Machine +50hrs (Week 1)                    $500.00             $10.00
Cutting Machine +100hrs (Week 1)                   $900.00             $9.00
Assembly Station +50hrs (Week 1)                   $275.00             $5.50
Wood +100 units (Week 1)                           $325.00             $3.25
Wood +200 units (Week 1)                           $550.00             $2.75

--------------------------------------------------------------------------------
INVESTMENT RECOMMENDATION
--------------------------------------------------------------------------------

Best Investment Option:
  Cutting Machine +50hrs (Week 1)
  Profit Impact: $500.00
  ROI: $10.00 per unit

If cost per hour < $10, this investment is profitable.

6. Risk Assessment¶

--------------------------------------------------------------------------------
6. RISK ASSESSMENT (Downside Scenarios)
--------------------------------------------------------------------------------

What if Cutting Machine loses 50 hours in Week 1 (equipment failure)?
  Original Profit:  $45,234.56
  New Profit:       $44,734.56
  Loss:             -$500.00 (-1.11%)
  ⚠ Risk: Equipment failure would cost $500.00

What if Wood supply decreases by 20% in Week 1?
  Original Profit:  $45,234.56
  New Profit:       $44,584.56
  Loss:             -$650.00 (-1.44%)
  ⚠ Supply Risk: 20% shortage would cost $650.00

Recommendation: Prepare contingency plans for cutting machine backup
and wood supply diversification.

What-If Analysis Types¶

1. Capacity Change Scenarios¶

Quick assessment of resource changes:

from lumix import LXWhatIfAnalyzer

# Create analyzer
whatif = LXWhatIfAnalyzer(model, optimizer, baseline_solution=baseline)

# Add 50 hours to machine capacity
result = whatif.increase_constraint_rhs("machine_1_period_1", by=50)
print(f"Profit increase: ${result.delta_objective:,.2f}")

# Increase material by 100 units
result = whatif.increase_constraint_rhs("material_3_period_1", by=100)

Use Cases:

Quick tactical decisions (should we add overtime?)
ROI analysis (is capacity expansion worth it?)
Resource reallocation (move resources between periods?)

2. Bottleneck Identification¶

Systematically test all constraints to find bottlenecks:

# Test adding 10 units to every resource
test_amount = 10.0
improvements = []

for machine in machines:
    for period in periods:
        constraint_name = f"machine_{machine.id}_period_{period.id}"
        result = whatif.increase_constraint_rhs(constraint_name, by=test_amount)
        marginal_value = result.delta_objective / test_amount
        improvements.append((constraint_name, marginal_value))

# Sort by marginal value
bottlenecks = sorted(improvements, key=lambda x: x[1], reverse=True)

Use Cases:

Investment prioritization (which capacity to expand first?)
Process improvement (where to focus efforts?)
Capacity planning (long-term expansion strategy)

3. Sensitivity Range Analysis¶

Analyze how profit varies across range of capacity values:

# Test multiple capacity levels
capacity_values = [100, 120, 140, 160, 180, 200, 220, 240]

for capacity in capacity_values:
    result = whatif.increase_constraint_rhs("machine_1_period_1", to=capacity)
    print(f"Capacity: {capacity}, Profit: ${result.new_objective:,.2f}")

Use Cases:

Optimal capacity sizing (where are diminishing returns?)
Understanding profit elasticity
Budget allocation (how much capacity is enough?)

4. Investment Comparison¶

Compare ROI of different capacity investments:

investment_options = [
    ("machine_1", 50, "Cutting Machine +50hrs"),
    ("machine_1", 100, "Cutting Machine +100hrs"),
    ("material_1", 100, "Wood +100 units"),
]

for constraint, amount, description in investment_options:
    result = whatif.increase_constraint_rhs(constraint, by=amount)
    roi_per_unit = result.delta_objective / amount
    print(f"{description}: ROI = ${roi_per_unit:.2f}/unit")

Use Cases:

Capital budgeting (limited investment budget)
Trade-off analysis (machines vs materials vs labor)
Strategic planning (multi-year investment roadmap)

5. Risk Assessment¶

Test downside scenarios (capacity reduction):

# Equipment failure scenario
result = whatif.decrease_constraint_rhs("machine_1_period_1", by=50)
print(f"Equipment failure would cost: ${abs(result.delta_objective):,.2f}")

# Supply chain disruption
result = whatif.tighten_constraint("material_3_period_1", by_percent=0.2)
print(f"20% supply shortage would cost: ${abs(result.delta_objective):,.2f}")

Use Cases:

Contingency planning (what if equipment fails?)
Risk quantification (how much would disruption cost?)
Mitigation priorities (which risks to address first?)

Key LumiX What-If Features¶

Create What-If Analyzer¶

from lumix import LXWhatIfAnalyzer

# Create analyzer with model and optimizer
whatif = LXWhatIfAnalyzer(model, optimizer, baseline_solution=baseline)

# Get baseline (cached automatically)
baseline = whatif.get_baseline_solution()

Increase Constraint RHS¶

# Add 50 units
result = whatif.increase_constraint_rhs("capacity_labor", by=50)

# Set to specific value
result = whatif.increase_constraint_rhs("capacity_labor", to=1500)

# Increase by percentage
result = whatif.increase_constraint_rhs("capacity_labor", by_percent=0.2)

Decrease Constraint RHS¶

# Subtract 50 units
result = whatif.decrease_constraint_rhs("capacity_machine", by=50)

# Decrease by percentage
result = whatif.decrease_constraint_rhs("capacity_machine", by_percent=0.15)

Relax/Tighten Constraints¶

# Make constraint less restrictive
result = whatif.relax_constraint("capacity", by=100)

# Make constraint more restrictive
result = whatif.tighten_constraint("capacity", by_percent=0.2)

Access Results¶

result.description           # Description of change
result.original_objective    # Baseline profit
result.new_objective        # New profit after change
result.delta_objective      # Change in profit
result.delta_percentage     # Percentage change
result.original_solution    # Baseline solution
result.new_solution         # New solution

Model Copying with ORM Detachment¶

Critical Implementation Detail¶

What-if analysis requires copying the model to apply changes without affecting the original. When using ORM (SQLAlchemy/Django), this presents a challenge:

Problem: ORM objects are bound to database sessions and cannot be pickled/deep copied directly.

Solution: LumiX implements an ORM detachment strategy in __deepcopy__ methods:

from copy import deepcopy

# This works even with ORM data!
modified_model = deepcopy(model)

How It Works¶

Detect ORM Objects: Check for SQLAlchemy (_sa_instance_state) or Django (_state, _meta) markers
Materialize Data: Force-load lazy relationships before copying
Detach from Session: Create plain Python objects with same attributes
Handle Lambda Closures: Inspect function closures for captured ORM objects and detach them
Deep Copy: Use standard deepcopy with detached objects

Implementation¶

The strategy is implemented in:

lumix.utils.copy_utils: Utility functions for ORM detachment
LXModel.__deepcopy__: Model-level copying
LXVariable.__deepcopy__: Variable-level copying with closure handling
LXConstraint.__deepcopy__: Constraint-level copying

Example:

from lumix.utils.copy_utils import detach_orm_object

# Detach single ORM object
product = session.query(Product).first()
detached = detach_orm_object(product)
# Now safe to pickle/deepcopy

# Automatically handled in model copying
modified_model = deepcopy(model)  # Works with ORM data

For complete details, see Model Copying and ORM Detachment.

Business Decision Examples¶

Example 1: Capacity Investment Decision¶

# Test capacity increase
result = whatif.increase_constraint_rhs("machine_1_period_1", by=50)

# Decision logic
cost_per_hour = 100.0  # Equipment rental cost
total_cost = cost_per_hour * 50
roi = result.delta_objective - total_cost

if roi > 0:
    print(f"✓ INVEST: ROI = ${roi:,.2f}")
    print(f"  Payback: {total_cost / result.delta_objective:.1f} periods")
else:
    print(f"✗ DON'T INVEST: Loss = ${abs(roi):,.2f}")

Example 2: Bottleneck Prioritization¶

# Find top bottleneck
bottlenecks = sorted(
    [(name, marginal_value) for name, marginal_value in all_constraints],
    key=lambda x: x[1],
    reverse=True
)

top_bottleneck = bottlenecks[0]
print(f"Priority 1: {top_bottleneck[0]}")
print(f"  Marginal Value: ${top_bottleneck[1]:.2f}/unit")
print(f"  Action: Expand this resource first")

Example 3: Risk Mitigation¶

# Test equipment failure scenario
result = whatif.decrease_constraint_rhs("machine_1_period_1", by=50)

expected_loss = abs(result.delta_objective)
insurance_cost = 200.0  # Annual insurance premium

if insurance_cost < expected_loss:
    print(f"✓ BUY INSURANCE: Net benefit = ${expected_loss - insurance_cost:.2f}")
else:
    print(f"✗ SELF-INSURE: Insurance too expensive")

Comparison: Step 4 vs Step 7¶

Aspect	Step 4	Step 7
Problem Type	Multi-period production planning	Same
Optimization	Solve once, display results	Solve + extensive what-if
Analysis Time	10-30 seconds	10-30s baseline + 30-60s what-if
Console Output	Production plan	What-if scenarios, bottlenecks, ROI
HTML Report	4 tabs	5 tabs (+ What-If Analysis)
Business Value	Operational plan	Tactical decisions, investments
Use Case	What to produce	Where to invest, what-if questions
Time Horizon	Weekly execution	Weekly + tactical planning

Key Learnings¶

1. What-If vs Scenario Analysis¶

What-If Analysis (Step 7):

Quick tactical changes
Single parameter at a time
Interactive exploration
Minutes to hours decisions
ROI-focused

Scenario Analysis (Step 5):

Strategic planning
Multiple coordinated changes
Pre-defined scenarios
Long-term decisions
Comprehensive comparison

When to use What-If: Quick tactical decisions, testing specific changes, finding bottlenecks, ROI assessment

When to use Scenario: Strategic planning, complex multi-parameter changes, formal reporting

2. Marginal Value for Investment Decisions¶

Marginal value = profit increase per unit of resource

Use marginal value to:

Set maximum willingness to pay for capacity
Compare investment options
Prioritize resource expansion
Assess ROI

Rule of thumb: If cost per unit < marginal value → profitable investment

3. Bottleneck Discovery¶

Test all constraints systematically
Rank by marginal value
Focus on high marginal value constraints first
Non-bottlenecks have zero marginal value (excess capacity)

4. Diminishing Returns¶

Sensitivity ranges reveal:

Linear region (constant marginal value)
Diminishing returns region (decreasing marginal value)
Saturation point (zero marginal value)

Use this to: Determine optimal capacity levels, avoid over-investment

5. Risk Quantification¶

Test downside scenarios to:

Quantify potential losses
Prioritize mitigation efforts
Justify insurance/contingency costs
Build resilience

Troubleshooting¶

What-If Analysis Takes Too Long¶

Symptom: What-if analysis takes > 2 minutes

Possible Causes:

Too many scenarios tested
Solver not optimized
Large model

Solutions:

Test fewer scenarios
Use faster solver (CPLEX, Gurobi)
Reduce model size for exploratory analysis

Marginal Values Are Zero¶

Symptom: All bottlenecks have zero marginal value

Possible Causes:

Constraints are not binding (excess capacity)
Goal constraints are limiting profit
Test amount is too small

Solutions:

Check resource utilization
Relax goal constraints
Increase test amount (10 → 50 units)

Results Don’t Match Expectations¶

Symptom: What-if results contradict intuition

Possible Causes:

Other constraints become binding
Non-linear effects from binary variables
Goal programming trade-offs

Solutions:

Check which constraints are binding
Examine solution details
Test multiple increment sizes

Use Cases¶

Tactical Capacity Planning: Should we rent additional equipment?
Overtime Decision: Should we run overtime shifts?
Supply Chain Negotiation: Maximum price for additional materials?
Equipment Investment: Which machine to upgrade first?
Risk Management: What’s the cost of equipment downtime?
Budget Allocation: How to allocate $100K investment budget?

Next Steps¶

You’ve completed the Production Planning tutorial with what-if analysis!

✅ Step 1: Basic linear programming ✅ Step 2: Database integration with SQLAlchemy ORM ✅ Step 3: Goal programming with customer orders ✅ Step 4: Large-scale multi-period planning ✅ Step 5: Scenario analysis (if completed) ✅ Step 6: Sensitivity analysis (if completed) ✅ Step 7: What-if analysis and tactical decision support

Advanced Topics to Explore:

Combine what-if with Monte Carlo simulation
Build interactive dashboards with what-if capabilities
Automate what-if analysis for recurring decisions
Integrate what-if into decision support systems

Related Documentation:

What-If Analysis Example - Standalone what-if example
What-If Analysis - What-if analysis guide
Model Copying and ORM Detachment - ORM-safe copying guide
Step 4: Large-Scale Optimization with Room Types - Large-scale scheduling

Step 7: What-If Analysis¶

Overview¶

What’s New in Step 7¶

Building on Step 4¶

New Features¶

Key Business Questions Answered¶

Running the Example¶

Step 1: Populate the Database¶

Step 2: Run Optimization with What-If Analysis¶

Step 3: View the Enhanced HTML Report¶

Console Output Walkthrough¶

1. Baseline Optimization¶

2. Machine Capacity What-If¶

3. Bottleneck Identification¶

4. Sensitivity Range Analysis¶

5. Investment Comparison¶

6. Risk Assessment¶

What-If Analysis Types¶

1. Capacity Change Scenarios¶

2. Bottleneck Identification¶

3. Sensitivity Range Analysis¶

4. Investment Comparison¶

5. Risk Assessment¶

Key LumiX What-If Features¶

Create What-If Analyzer¶

Increase Constraint RHS¶

Decrease Constraint RHS¶

Relax/Tighten Constraints¶

Access Results¶

Model Copying with ORM Detachment¶

Critical Implementation Detail¶

How It Works¶

Implementation¶

Business Decision Examples¶

Example 1: Capacity Investment Decision¶

Example 2: Bottleneck Prioritization¶

Example 3: Risk Mitigation¶

Comparison: Step 4 vs Step 7¶

Key Learnings¶

1. What-If vs Scenario Analysis¶

2. Marginal Value for Investment Decisions¶

3. Bottleneck Discovery¶

4. Diminishing Returns¶

5. Risk Quantification¶

Troubleshooting¶

What-If Analysis Takes Too Long¶

Marginal Values Are Zero¶

Results Don’t Match Expectations¶

Use Cases¶

Next Steps¶

See Also¶