Every company has to choose between ordering often and paying for each order, or ordering in bulk and paying to store the extra. This paper turns that balancing act into the behavior of a simple mechanical system. Companies increasingly need to reduce costs and maximize profits, and inventory management plays a crucial role by optimizing the storage and transportation of materials.

The study introduces an optimization model for deciding order sizes based on a physical system approach. The central idea is to treat the supply problem like a row of objects linked by flexible connectors: the best arrangement is the one that settles into the lowest total cost.

This approach determines order sizes that minimize the combined ordering and inventory holding costs in a significantly shorter time, eliminating the need for heuristic methods. The study addresses the cost optimization problem in ordering and storage within the lot-sizing model.

It establishes that the material supply problem is like a one-dimensional mechanical system of point particles connected by elastic elements. That analogy enables the natural derivation of cost optimization conditions, leading to an exact solution without relying on heuristic methods.

The proposed model determines order sizes that minimize the combined ordering and inventory holding costs while significantly reducing computational time. To validate its effectiveness, the model was applied to a real-world case study and compared with classical lot-sizing algorithms.

The results demonstrate superior cost optimization and reduced execution time, underscoring the potential to improve material lot-sizing strategies in practical applications. The total-cost expression corresponds, apart from a constant, to the potential energy of the one-dimensional system shown in the figure.

That system is an array of particles connected by springs, with the total length fixed. For a given number of orders, the lowest total cost corresponds to the lowest-energy arrangement. Figure 2 shows the minimum total cost as the number of orders changes across a planning horizon of twelve periods.

The accumulated cost adds ordering and holding costs over each day, allowing the three purchasing strategies to be compared over time. The figure compares the classical model, the company’s strategy, and this model. The classical model and this model behave very similarly, with only a small difference in total cost at the end of the cycle.

The company’s strategy appears highly inefficient, highlighting the importance of adopting an appropriate purchasing strategy to improve production costs. The widening separation between the company’s steadily rising costs and the two closely tracking alternatives makes the financial penalty of its strategy immediately visible.

The model was applied to a real-world case and compared with well-established classical algorithms. Its solution achieves excellent cost optimization and also exhibits the shortest execution time. The study introduces new insights into optimization methods for material order sizing using an elastic system.

The results are promising, and the theoretical model can be extended to incorporate additional complexities. Future research will focus on variable material demands, quantity discounts, and items that deteriorate over time. The model finds order sizes that reduce both ordering and storage costs, while taking less time than the compared approaches.

For a real company, that can mean faster purchasing decisions and lower production costs.