# Optimal lot size and economic lot sizing procedures

Andreas Kemmner

For the optimal lot size, let’s take a look at economic lot sizing procedures.

## Optimal lot size and economic lot-sizing procedures – how do they work?

Economic lot-sizing procedures for the total cost reduction of warehousing and procurement or set-up costs offer a large, mostly untapped potential for cost reduction. In order to apply economic lot-sizing procedures correctly, users must understand the principle and limits of economic lot-sizing procedures.

### Goals of the lot-sizing procedures for optimal lot sizes

Economic lot-sizing procedures aim to minimise the total costs for a given article, consisting of inventory costs on the one hand and procurement costs for purchased articles or set-up costs for in-house production articles on the other. This optimises a small, essential component within the entire supply chain that is often overlooked in practice.

Larger batch sizes in procurement or production lead to higher inventories and thus higher warehousing costs. These generally rise in proportion to the batch size, while the ordering costs or set-up costs – generally referred to as batch initiation costs – fall in inverse proportion. A simple example: If the same absolute transport costs are incurred for a part for lot size x as well as for lot size 2x, then with twice as many parts ordered, each part only bears half the transport costs.

If certain costs rise in proportion to the batch size and others fall in inverse proportion to the batch size, then there must be a minimum total cost at a certain batch size (cf. Fig. 1).

### The classic economic batch sizing methods

One of the first to recognise the connection between inventory costs and batch circulation costs was Kurt Andler. He developed a formula for calculating an economic lot size in 1929. The Andler formula is still widely used today. In calculating the optimal lot size, Andler assumed that the total required quantity of an article in a planning horizon, e.g. one year, is known. From inventory costs on the one hand and procurement costs on the other, the formula now derives the lot size with which orders should always be placed. Since the lot size remains constant over the planning period, this is also referred to as a static economic lot-sizing procedure.

In practice, however, production or order requirements are rarely evenly distributed over the planning horizon. Rather, they follow one another irregularly and vary in size (Fig. 2). The decisive answer to how to determine economic lot sizes for “dynamic” requirements was given by two Americans as early as 1958. Mr Wagner and Mr Whitin developed an economic lot-sizing procedure with which dynamic lot sizes could be calculated. This mathematical solution takes into account that with the decision on a first lot size in the planning horizon, the leeway for the design of the subsequent lot sizes is automatically limited. The Wagner-Whitin method determines a sequence of lots with different sizes and different time intervals that minimises the total costs. The result is a scientifically precise answer to the question of the right lot sizes for single-stage, single-product production without capacity limitations.

The Wagner-Whitin method was too complex to be used by hand or with the calculating machines of the time. Thus, in the course of the following years, approximation methods were developed which, at the expense of theoretical accuracy, could manage with little computational and storage capacity. In 1968, for example, the Part Period method and the moving economic lot size method were introduced, in 1973 the Silver-Meal method and in 1979 the Groff method, both named after their developers, followed. These are the “classic” economic lot-sizing procedures offered in many ERP systems. In addition, there are a large number of other methods for determining optimal lot sizes that have not yet found much resonance in practice.

### The challenge for optimal or economical lot size is selecting the right lot sizing procedure

If economic lot sizes are calculated for the same demand situation of an article using different methods, the resulting lot sizes usually differ significantly from each other. This leads to great irritation in practice. However, the question of which economic lot-sizing method actually leads to the lowest total costs under real conditions can be answered with modern, powerful software tools

What is your experience on optimal lot size and economic lot sizing procedures. Send us an e-mail!

Part 2 of this blog series will show that there is no such thing as “the” best method. The right lot sizing procedure depends on the individual planning situation of each and every article.

On our Knowledge-Page you will find more helpful tips.

Andreas Kemmner

##### Autor | Author

Prof. Dr Kemmner has carried out well over 150 national and international projects in over 25 years of consultancy work in supply chain management and reorganisation.

In 2012, he was appointed honorary professor for logistics and supply chain management by the WHZ.