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Maximizing Margins in Margarine Production

Optimizing Inventory, Procurement Timing, Quality Standards

Prepared by Viktor Plamenov

1. Introduction and Motivation


Mathematical programming has profoundly influenced the food industry, offering systematic approaches to optimize critical processes such as food formulation, oil blending, and supply chain management. By minimizing costs while maintaining or improving quality, these techniques have become indispensable for large fast-moving consumer goods (FMCG) companies. For instance, Unilever has successfully utilized mathematical programming to optimize oil blending in margarine production, achieving cost efficiency while adhering to strict quality standards for attributes like spreadability and melting point [1]. Similarly, Nestle has ´ applied these approaches to enhance supply chain operations, optimizing raw material procurement to reduce waste and improve responsiveness [2]. The application of mathematical programming in margarine production exemplifies its ability to improve efficiency across multiple dimensions. By enabling precise ingredient selection and blending, it ensures:


  • Cost Optimization: Minimizing raw material costs by dynamically responding to market price fluctuations.

  • Quality Consistency: Ensuring final products meet stringent standards for key attributes, such as spreadability and melting point, while reducing the risk of rework or recalls.

  • Inventory Management: Balancing purchases, usage, and storage to lower holding costs and prevent stockouts or overstocking.

  • Sustainability: Supporting the use of sustainable or locally sourced ingredients to reduce waste and carbon footprint.

  • Production Efficiency: Streamlining the production process by minimizing trial-and-error approaches, reducing downtime, and increasing throughput.


2. Margarine Example Study


This study focuses on margarine production as a classic example of a blending problem, highlighting how mathematical programming can effectively balance ingredient selection, inventory management, and quality control. By integrating cost considerations with product specifications, the presented framework provides a practical and profitable solution to challenges faced in real-world food manufacturing. Using synthetically generated data, we demonstrate the mathematical programming setup. The main quality attributes of the raw ingredients and final product are outlined below.


  • Margarine production requires careful control of quality attributes such as spreadability and melting profile, as well as the solid fat content (SFC) at specific temperatures (e.g., 5°C and 20°C). These characteristics influence the usability and stability of the product under storage and consumption conditions.

  • Spreadability: Indicates the ease of spreading margarine at room temperature. Higher values denote a softer, more spreadable product, while lower values indicate a firmer texture.

  • Melting Profile: Refers to the temperature range within which the margarine transitions from solid to liquid. This is crucial for consumer experience and functional applications.

  • Solid Fat Content (SFC): The SFC represents the proportion of fat that remains solid at a given temperature. It directly impacts the texture, structure, and stability of the final product.


In the current setup, an assumption of linearly additive ingredients is imposed, meaning that the attributes of the final product are a weighted average of the attributes of the ingredients used. For example:

This case study demonstrates the application of mathematical optimization in margarine production with the goal of maximizing profits over a six-month planning horizon by:

3. Mathematical Model


This section outlines a mathematical framework for optimizing margarine production over a six-month horizon. The model defines decision variables to manage production volumes, raw material procurement, and inventory levels, ensuring operational efficiency and product quality. The objective is to maximize profit by strategically balancing production costs, raw material expenses, storage fees, and sales revenue. The subsequent subsections detail the decision variables, objective function, and constraints that structure the optimization problem.


Decision Variables


The decision variables represent the key operational factors, including the quantities of fats used, fats purchased, inventory levels, and margarine produced each month, enabling precise control over production and resource allocation.

Objective Function


The objective is to maximize total profit over six months:

where:

Constraints


The constraints define the system’s operational and quality requirements, encompassing mass conservation, demand fulfillment, product quality attributes, inventory dynamics, and non-negativity, ensuring feasibility and compliance with production standards. New constraints could be potentially incorporated into the workflow without significant difficulty to address further business requirements.


  1. Mass Conservation: Ensure the total fats used equals margarine production:

  1. Demand Fulfillment: Meet the monthly demand for margarine:

  1.  Solid Fat Content (SFC): Ensure the blended margarine meets SFC requirements:

  1. Quality Attributes: Maintain spreadability and melting profile within bounds:


    • Spreadability:

  • Melting Profile:

  1. Inventory Dynamics: Inventory evolves as:

  1. Non-Negativity: All variables must be nonnegative:

4. Numerical Example

Table 4.1: Ingredients initial inventory, costs per kg, and margarine demand over a six months period.
Table 4.2: Properties of fats utilized in the margarine production.
Figure 4.1: Left: Optimal policy sensitivity with respect to price fluctuations of the raw ingredients. Right: Profit as a function of selling price.

4.1 Solution Overview


  1. Purchasing Strategy: Large purchases of Palm Oil in early months ensured stability for consistent usage throughout the period. Rice Bran Oil and Sunflower Oil were purchased in bulk as needed, reducing inventory costs.

  2. Inventory Utilization: Efficient inventory management minimized surplus while ensuring availability for production. Pumpkin Seed Oil effectively relied on initial stock, highlighting the strategic use of available resources.

  3. Blending Priorities: Palm Oil and Sunflower Oil played critical roles in the blend due to their favorable attributes and availability. Secondary fats (Rice Bran and Pumpkin Seed Oil) were used sparingly to meet specific quality and cost considerations.

  4. Sensitivity: The optimal policy demonstrates significant sensitivity to palm oil price fluctuations. A 20% increase in the cost of palm oil results in a substantial 40% reduction in overall profits (see Figure 4.1), highlighting its critical role in the cost structure. In contrast, price variations in other ingredients have a notably smaller impact on profitability, underscoring the relative dominance of palm oil in influencing the financial outcomes.

  5. Breakeven Price: Analysis reveals that when selling prices fall below 16.4, total costs surpass revenue, leading to a negative net income. Since the current model does not incorporate price elasticity, profitability increases in a strictly linear manner as prices rise, assuming all other factors remain constant.


Table 4.3: Optimal production policy over six months. The table details the quantities used in production, purchases, inventory, and total demand for each month.
Figure 4.2: Optimal production and inventory policy over a six-month planning horizon. The figure illustrates the quantities of fats used in production, purchased, and held in inventory each month, aligned with total demand requirements and cost minimization objectives.
Table 4.4: Summary of Total Purchases and Usage of Fats Over Six Months in the Optimal Policy

5. Conclusion and Business Impact


This study highlights the transformative role of mathematical programming in margarine production and the broader FMCG industry. By optimizing ingredient selection, inventory management, and quality control, businesses can achieve significant cost savings, enhance operational efficiency, and deliver consistent product quality. Real-world examples, such as Unilever’s oil blending optimization and Nestle’s supply ´ chain enhancements, underscore the practical and profitable applications of these techniques.


Steps to Improve Efficiency


The examined methodology can improve efficiency across multiple dimensions:


  1. Cost Optimization: By identifying the ideal combination of fats and oils, blending minimizes raw material costs. This ensures profitability even during market fluctuations.

  2. Quality Consistency: Blending ensures that the final product meets predefined standards for spreadability, melting point, and solid fat content, reducing risks of rework or recalls.

  3. Inventory Management: Effective blending integrates inventory dynamics, balancing purchases, usage, and storage to reduce holding costs and prevent stock issues.

  4. Adaptability to Market Changes: The process is flexible, dynamically responding to ingredient availability, cost changes, and regulatory requirements.

  5. Sustainability: Incorporating environmental considerations, blending supports the use of sustainable ingredients, reducing waste and the carbon footprint.

  6. Production Efficiency: By reducing trial-and-error in formulations, blending optimization minimizes downtime and increases throughput, enabling maximum capacity utilization.


The results of this study demonstrate how data-driven decision-making can align production strategies with market demands, ensuring adaptability, quality, and profitability. For FMCG leaders, this approach provides a competitive edge by delivering actionable insights and tangible benefits.


References


[1] H. P. Williams and A. C. Redwood, A Structured Linear Programming Model in the Food Industry, Operational Research Quarterly (1970-1977) , Dec., 1974, Vol. 25, No. 4 (Dec., 1974), pp. 517-527


[2] The Key to Inventory Optimisation at Nestle. , Procurement Magazine, (Feb., 2024)


[3] Williams, H. P. (2013). Model Building in Mathematical Programming. Wiley.

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