Linear Programming Model Leads to $2.3 Million Annual Savings in Delivery Costs: Analysis

Delivery costs can have a significant impact on a business's bottom line. Whether you're delivering goods to customers or transporting products from one location to another, the cost of transportation
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What is linear programming?

Linear Programming is a mathematical technique that provides an optimized solution to problems with multiple constraints. In the context of reducing delivery costs, this model is used to find the most cost-effective delivery routes and schedules while considering various factors such as distance, delivery volume, capacity of delivery trucks, and time windows.

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How it Works in Understanding Delivery Costs

In the context of reducing delivery costs, a linear programming model could be used to optimize the routes of delivery trucks and minimize the cost of transportation. The model considers factors such as the distance of each delivery route, the volume of goods being delivered, the capacity of the delivery trucks, and any other constraints such as time windows for deliveries.

The objective of the linear programming model is to find the combination of delivery routes that minimizes the total cost of transportation, while satisfying all the constraints. This can be done by using linear optimization algorithms that search for the optimal solution by exploring the feasible region defined by the constraints.

benefits to using linear programming in optimizing delivery

  • Reduced Delivery Costs: By finding the most cost-effective delivery routes and schedules, companies can reduce their transportation expenses and improve their bottom line.
  • Improved Delivery Schedules: The model can help companies find the best delivery schedules that meet the needs of their customers and operations. This can result in improved customer satisfaction and more efficient delivery operations.
  • Increased Efficiency: By optimizing their delivery operations, companies can improve their overall efficiency and reduce the time and resources required to manage their delivery processes.
  • Adaptability: The model can be updated and adapted as business needs change, allowing companies to continually optimize their delivery operations.

While linear programming can be a valuable tool for understanding and reducing delivery costs, there are also some disadvantages to consider:

  • Model Complexity: Linear programming models can be complex and require a significant amount of data and information to be effective. This can be a challenge for companies with limited resources or expertise in mathematical modeling.
  • Assumptions: The model makes certain assumptions about the delivery system that may not always hold in the real world. This can result in inaccurate solutions or suboptimal results.
  • Limited Flexibility: The model is based on linear equations, which may not always accurately reflect the non-linear complexities of a delivery system. This can limit the flexibility of the model and the solutions it can provide.
  • Data Accuracy: The results of the linear programming model are only as accurate as the data that is used. If the data is incorrect or outdated, the results of the model may not reflect the reality of the delivery system.
  • Limited Time Horizon: The model typically considers only a limited time horizon, which may not always accurately reflect the long-term costs and benefits of different delivery routes and schedules.


In this project

Based on our data analysis, we recommended changes to the client’s understanding of delivery cost in order to optimize it. The primary objective was to reduce the delivery cost and improve the overall efficiency of the delivery system. To achieve this goal, we used linear programming as a tool to optimize the delivery process.


Our data analysis revealed that the client’s delivery system was not as efficient as it could be, and that there were opportunities to reduce the delivery costs. We used this information to make recommendations to the client on how they could optimize their delivery system. These recommendations were based on the results of the linear programming analysis, and took into account the client’s specific needs and constraints.

Here are some results of the changes we did-

  • Improved Delivery Operations: By optimizing their delivery routes and schedules, the client can improve the efficiency of their delivery operations and reduce the time and resources required to manage the delivery process.
  • Reduced Delivery Costs: The linear programming model can help the client minimize their transportation expenses by finding the most cost-effective delivery routes and schedules. This can result in significant cost savings for the business.
  • Increased Customer Satisfaction: By improving their delivery schedules and reducing delivery times, the client can increase customer satisfaction and build stronger relationships with their clients.
  • Improved Data Management: The linear programming model may require the client to collect and analyze large amounts of data about their delivery operations. This can help the client improve their data management practices and gain a better understanding of their delivery system.
  • Better Decision Making: By providing valuable insights into the costs associated with delivery, the linear programming model can help the client make informed decisions about their delivery operations.

By implementing the recommended changes, the client was able to reduce their delivery costs by a factor of 1.6% with annual savings of $2.3M. The project implemation costed $80 k.

Project Implementation Cost


Overall, the implementation of a linear programming model can result in improved delivery operations, reduced costs, increased customer satisfaction, better data management, and improved decision-making. By carefully considering the limitations of the model and ensuring that the data used in the model is accurate, the client can get the most out of their linear programming efforts and improve their delivery operations


In conclusion, by using linear programming to optimize delivery, the client was able to achieve the goal of improving their base cost. The recommended changes, combined with the optimization of the delivery system, helped the client to better understand and control the costs associated with their delivery operations

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