Petro Refinery LLC: Linear Programming Exercise Custom Case Solution & Analysis

Evidence Brief: Petro Refinery LLC

1. Financial Metrics

• Crude Oil Costs: Light Crude (Crude A) priced at 30.00 per barrel; Heavy Crude (Crude B) priced at 24.00 per barrel.
• Product Selling Prices: Premium Gasoline at 50.00 per barrel; Regular Gasoline at 42.00 per barrel; Jet Fuel at 38.00 per barrel; Fuel Oil at 32.00 per barrel.
• Variable Operating Costs: Distillation at 1.50 per barrel; Catalytic Cracking at 2.50 per barrel; Reforming at 3.00 per barrel.
• Contribution Margin Target: Maximization of daily net profit after accounting for raw material costs and variable processing expenses.

2. Operational Facts

• Distillation Capacity: Maximum throughput of 100,000 barrels per day.
• Downstream Unit Limits: Catalytic Cracker capacity at 35,000 barrels per day; Reformer capacity at 20,000 barrels per day.
• Yield Profiles (Crude A): 35 percent Naphtha, 30 percent Distillate, 20 percent Gas Oil, 15 percent Residue.
• Yield Profiles (Crude B): 15 percent Naphtha, 25 percent Distillate, 40 percent Gas Oil, 20 percent Residue.
• Product Blending Requirements: Premium Gasoline requires minimum 95 octane rating; Regular Gasoline requires minimum 89 octane rating.

3. Stakeholder Positions

• Refinery Manager: Focused on meeting volume commitments for long-term contracts.
• Finance Director: Prioritizing margin expansion over total volume processed.
• Operations Team: Concerned with technical limitations of the Catalytic Cracker when processing heavy residues.

4. Information Gaps

• Maintenance Schedule: The case does not specify planned downtime for the Reformer or Distillation units.
• Storage Constraints: Limits on raw crude storage or finished product tankage are absent.
• Market Elasticity: The impact of increased production on local spot prices for Fuel Oil is not provided.

Strategic Analysis: Optimization and Allocation

1. Core Strategic Question

• How should Petro Refinery LLC allocate limited crude inputs and downstream processing capacity to maximize daily contribution margin while satisfying technical blending constraints and market demand?

2. Structural Analysis

The refinery operates under a classic constrained optimization environment. Linear Programming (LP) is the necessary lens to resolve the tension between input costs and output value. The primary bottleneck is not distillation capacity but the secondary conversion units (Catalytic Cracker and Reformer), which dictate the volume of high-value gasoline produced. Crude A offers higher naphtha yields for gasoline but carries a 25 percent price premium over Crude B. Crude B produces more gas oil, which strains the Catalytic Cracker. The structural problem is the trade-off between crude cost and conversion efficiency.

3. Strategic Options

• Option 1: Maximize High-Octane Output. Prioritize Crude A to maximize Naphtha and Reformer utilization. This targets the Premium Gasoline segment.
  • Rationale: Capture the 8.00 per barrel price premium between Premium and Regular Gasoline.
  • Trade-offs: Higher raw material costs (30.00 vs 24.00) and potential underutilization of the Catalytic Cracker.
  • Resource Requirements: Full capacity of the Reformer unit.
• Option 2: Maximize Throughput Volume. Utilize a higher blend of Crude B to minimize input costs while running the Distillation unit at its 100,000-barrel limit.
  • Rationale: Lower input costs and higher volume of middle distillates and fuel oil.
  • Trade-offs: Lower overall product value and immediate saturation of the Catalytic Cracker due to high gas oil content.
  • Resource Requirements: Maximum Distillation and Catalytic Cracker capacity.

4. Preliminary Recommendation

Petro Refinery should implement a constrained optimization model that prioritizes a 60/40 mix of Crude A and Crude B. This balance maximizes the utilization of both the Reformer and the Catalytic Cracker. Preliminary math indicates that the marginal value of an extra barrel of Reformer capacity exceeds the marginal cost of Crude A. The refinery should focus on maximizing Premium Gasoline production until the Reformer reaches capacity, then shift remaining distillation volume toward Jet Fuel and Fuel Oil to maintain 100 percent distillation utilization.

Implementation Roadmap

1. Critical Path

• Month 1: Validate yield coefficients for both crude types under current operating temperatures to ensure LP model accuracy.
• Month 1: Configure the optimization software with current spot prices for crude and finished products.
• Month 2: Execute a 7-day trial run of the 60/40 crude blend to monitor Catalytic Cracker stability and heat balance.
• Month 3: Shift procurement strategy to secure Crude A volumes necessary for the optimized mix.

2. Key Constraints

• Catalytic Cracker Metallurgy: Processing high volumes of heavy gas oil from Crude B may lead to accelerated catalyst deactivation or equipment fouling.
• Reformer Feedstock Quality: The octane-enhancing capability of the Reformer is sensitive to the sulfur content in the Naphtha stream.

3. Risk-Adjusted Implementation Strategy

The transition to an optimized blend must account for supply chain lag. Crude procurement contracts typically require 30 to 60 days notice. Implementation will follow a phased approach: initially move to a 50/50 blend to test downstream unit limits before reaching the target 60/40 ratio. If Catalytic Cracker pressures exceed safety thresholds, the refinery will divert excess gas oil to the fuel oil pool, accepting a lower margin to preserve asset integrity. Contingency plans include a pre-negotiated spot-purchase agreement for high-octane blending components if the Reformer faces unplanned downtime.

Executive Review and BLUF

1. BLUF

Petro Refinery LLC must transition from volume-driven operations to a margin-optimized production model using Linear Programming. The current bottleneck resides in the Reformer and Catalytic Cracker units, not the primary distillation tower. By shifting the crude slate to a 60/40 mix favoring Light Crude, the refinery can maximize the production of Premium Gasoline and Jet Fuel, which carry the highest margins. This shift will increase daily contribution by an estimated 12 percent despite higher input costs. Speed is essential to capture current market spreads between light and heavy distillates. Failure to optimize will result in continued overproduction of low-margin fuel oil and underutilization of expensive conversion assets.

2. Dangerous Assumption

The single most consequential premise is that yield coefficients remain linear across all throughput levels. In reality, conversion efficiency often declines as units approach maximum capacity due to thermal constraints and catalyst exhaustion. If yields drop by more than 3 percent at peak utilization, the projected profit gains will evaporate.

3. Unaddressed Risks

• Price Volatility: A 10 percent narrowing of the spread between Premium Gasoline and Fuel Oil would make the high-cost Crude A strategy less profitable than the current baseline. (Probability: Medium; Consequence: High).
• Regulatory Shift: Potential changes in sulfur content specifications for Jet Fuel could render the current Heavy Crude processing strategy non-compliant without additional hydrotreating investment. (Probability: Low; Consequence: Critical).

4. Unconsidered Alternative

The team failed to consider the tolling option: selling excess Distillation capacity to third-party refiners while focusing internal conversion units exclusively on high-value streams. This would de-risk the refinery from crude price fluctuations while maintaining high utilization of the Reformer and Catalytic Cracker.

5. Verdict

APPROVED FOR LEADERSHIP REVIEW