Case Competition: Algorithmic Summary of Flat-Book Multi-Route Trading Optimization Model

Author: Divyam Kamboj
Date: March 2025

📌 Introduction

This project provides a comprehensive algorithmic and mathematical summary of a flat-book, multi-route trading optimization model. The objective is to route trades (long and short) across different months, locations, and sell options while maintaining zero net market exposure (flat book).

The model accounts for:

• Pipeline and storage costs
• Inventory limits
• Forecast adjustments

Python code (using LP solvers like PuLP) implements the model for practical optimization.

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📊 Input Data and Parameters

• Monthly Prices:
  • Midland: P^M(m)
  • Houston: P^H(m)
• Sour Differentials (for WTS):
  • Midland: Δ_M(m), Houston: Δ_H(m)
• Forecast Adjustments:
  Applied to Houston prices for futures routes (set to 0 in this example)
• Trading Days & Daily Capacity:
  • WTI: 80,000 barrels/day
  • WTS: 20,000 barrels/day
• Storage Cost: $0.26 per barrel per month held
• Pipeline Cost: $0.55 fixed + 0.2% of effective buying price if buying and selling locations differ
• Inventory Capacity:
  3,000,000 barrels per location (Midland, Houston)

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🧠 Derived Data Computation

Monthly Capacity

$$Capacity_p(m) = DailyCapacity_p × TradingDays(m)$$

Effective Buying Cost

For WTI:

$$C_buy^WTI(m, L) = P^M(m) or P^H(m)$$

For WTS:

$$C_buy^WTS(m, L) = P^M(m) - Δ_M(m) or P^H(m) - Δ_H(m)$$

Pipeline Cost

If L ≠ S:

$$PipelineCost = 0.55 + 0.002 × EffectiveBuyingPrice$$

Sale Price

Includes adjustments and premiums/discounts for refinery routes:

$$P_sell^WTI(n, S) = P^M(n), P^H(n) + adj., or P^H(n) + adj. + 0.05 P_sell^WTS(n, S) = P^M(n) - Δ_M(n), etc.$$

Storage Cost

$$StorageCost(m, n) = 0.26 × (n - m)$$

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💰 Profit Per Barrel for a Route

$$π(p, m, n, L, S) = SalePrice - [BuyPrice + PipelineCost (if any)] - StorageCost$$

• If π ≥ 0: profitable long trade
• If π < 0: profitable short trade (profit = |π|)

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📏 Flat-Book Constraint

To ensure zero net exposure:

$$∑ x^+ = ∑ x^−$$

For every product p, the total volume of long trades equals that of short trades.

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🔁 Decision Variables (Routing)

Each route is defined by:

• Product: WTI or WTS
• Buy Month m, Sell Month n
• Buy Location L: Midland or Houston
• Sell Option S: Midland, Houston, or Refinery

Decision Variables:

• x^+_{L,S}(m,n): long trade volume
• x^-_{L,S}(m,n): short trade volume

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✅ Constraints

Monthly Capacity

For every month m (buy) and n (sell):

$$∑ x^+ + x^- ≤ Capacity_p(m or n)$$

Flat-Book

$$∑ x^+ = ∑ x^−$$

Inventory Constraint (Optional)

Cumulative barrels stored at each location should not exceed 3,000,000 per month.

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🎯 Objective Function

Maximize total profit:

$$Maximize ∑ π(p, m, n, L, S) × (x^+ - x^-)$$

Allocate long trades for positive profits and short trades for negative profits (i.e., positive arbitrage opportunities).

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⚙️ Step-by-Step Algorithm

Step 1: Data Input

• Load all prices, trading days, and cost parameters
• Compute monthly capacities

Step 2: Route Generation

• Enumerate all possible routes (m, n, L, S)

Step 3: Profit Computation

For each route, calculate:

• Effective buying cost
• Pipeline cost (if needed)
• Sale price
• Storage cost
• Net profit π

Step 4: Define Decision Variables

• For each route, define x^+ and x^-

Step 5: Add Constraints

• Monthly capacity
• Flat-book
• Optional storage constraint

Step 6: Set Objective

• Maximize:

$$∑ π × (x^+ - x^-)$$

Step 7: Solve LP

• Use an LP solver like PuLP's CBC to solve for optimal volumes

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✅ Conclusion

This model:

• Computes trading and storage economics for multiple oil grades and routes
• Maintains net market neutrality via flat-book constraint
• Uses linear programming to select the most profitable trade volumes
• Can be extended with additional constraints like inventory rollover, dynamic pricing, etc.

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Let me know if you'd like this in a file or need a sample Python script as part of the README.md.