One of the most consolidated models in inventory management theory is the Economic Purchase Lot (LEC), which optimally answers the questions: “how much to buy” and “when to buy”. This model presents the purchase batch that minimizes the total costs that are impacted by the batch: annual resupply cost and annual inventory holding cost. And, from that lot, the point of order and the frequency of revision or cycle time are unfolded.
The purpose of this post is not to teach the calculation of the LEC, but to show that, in practice, the LEC works as a good starting point for decision making, but it should not necessarily be followed, since other practical issues can make it difficult. it impracticable to be implemented. If you are not familiar with LEC theory and point of order, I suggest reading this classic article on inventory management fundamentals. Figure 1 presents a summary of the theory and demonstrates the algebraic calculation of the Economic Purchase Lot (LEC).
Figure 1: Summary of Economic Purchase Lot Theory (LEC). Source: ILOS
The point of discussion in this post is about the feasibility of adopting the algebraic calculation of the LEC in practice, since it is based on strong assumptions, which often do not reflect reality, such as unlimited transport and storage capacities, lack of quantity discounts, infinite planning horizon, non-perishables, etc. To illustrate the issue, let's introduce an example:
Suppose a factory consumes 20 kg of a certain raw material per year, which costs R$50 per kg. The factory pays R$380 for transportation inbound per order, regardless of order size, and has an annual holding cost of 15% of the product acquisition cost, which already includes capital and storage costs. Figure 2 illustrates the example and demonstrates the calculation of the LEC, which is 1.424kg, which presents a minimum total annual cost of R$10.677.
Figure 2: Graphic Illustration of the Example and Calculation of the LEC. Source: ILOS
Now we are going to include some restrictions that are imposed by our reality, such as capacities, minimum lots, unit boxes, agreed order placement frequency, etc. Based on these constraints, let's do some sensitivity analysis, adapting our batch to the constraint and looking at the effect of adaptation on the total cost. Our conclusion will be that changes in the LEC do not affect costs in the same magnitude, which gives this tool great freedom to adapt the theoretical calculation to our management reality.
Examples of restrictions and their impact on the result:
- Restriction of unit boxes: assume that this raw material is supplied in 100kg boxes. In this case, orders of 1.424kg are unfeasible and the closest viable alternative is to order lots of 1.400kg (1,7% LEC reduction). The total cost of the 1.400 kg batch is R$10.679, resulting in an increase of 0,01% in cost. That is, a 1,7% adjustment in the LEC had almost no impact on the total cost.
- Order frequency restriction: now let's assume that the contract with this supplier establishes that an order is placed per month, always on the first Monday of the month. Considering the annual demand of 20 kg and that there is no seasonal variation in consumption, the batch should be 1.667 kg, in practice. This represents an increase of 17% in the LEC, which results in a negligible increase of 1,25% in the cost, becoming R$10.810 per year.
- Transport capacity restriction: imagine now that the delivery of this product is made by small vehicles, with the capacity to transport only one ton, limiting the purchase lot to a thousand kg to keep the transport cost at R$380. Considering the reduction of almost 30% in the LEC (from 1.424 to 1.000kg), costs would increase to R$11.350, representing an increase of only 6,3% in costs.
- quantity discount: Assuming that the supplier offers a 10% discount if you order multiples of 3 kg, as this is your supplier's optimal production batch. In this case, we are increasing the lot by 110% and the total annual costs are now R$12.658, which represents a 19% increase in costs. Despite being a relevant cost increase, it is far from being in the same magnitude as the increase in the purchase lot and will still generate savings in the acquisition of PM, since now the 20 thousand kg purchased annually will no longer cost R$1 million and will cost 900 thousand. The extra operating cost of R$1.980 is more than offset by the R$100 savings from raw material acquisition.
Figure 3 illustrates the adjustments made in the four examples above and shows how this model is not very sensitive to changes in the LEC, being a theory with a high degree of freedom to adapt to the practical reality of the operation. As the total cost curve presents a long range of costs close to the minimum, there is great flexibility to change the LEC without causing major cost impacts.
Figure 3: Graphic illustration of the effect of the 4 batch adaptation examples. Source: ILOS
The Economic Purchase Lot, at first glance, seems to be a concept detached from reality, as it is based on strong theoretical assumptions. However, knowing how to use it to your advantage, adapting the algebraic result to the company's management reality, the LEC presents itself as an easy-to-use and powerful tool, since these adaptations do not cause great damage to the expected cost result.
References:
– ILOS articles – Key aspects of inventory management in the supply chain
– Live Online Course – Inventory management in the supply chain