Integral Logistics Management — Operations Management and Supply Chain Management Within and Across Companies

11.4.2 Optimum Batch Size: The Classic Economic Order Quantity (EOQ)

Intended learning outcomes: Explain the concept of the economic order quantity (EOQ). Explain variables for the EOQ formula.

Most methods for determining batch sizes minimize the expected total costs. In dependency upon batch size, these are essentially composed of the costs mentioned in Section 11.4.1:

  1. Batch-size-dependent unit costs. Mostly the price per produced or procured unit quanti­ty does not change with increasing batch size. However, this is not true in case of allo­wance for discounts or changes in the production process from a certain batch size upward.
  2. Inventory costs. These are all the costs incurred in connection with ordering and holding inventory. Thus, inventory costs are the following costs:
    a.    Setup and ordering costs: These are incurred only once per production or procurement event. In the simplest and most common case, they are independent of the batch size. Thus, the larger the batch size, the smaller is the share in such costs that accrues to each unit. However, there may be an upward jump in costs if a certain batch size requires the choice of another production procurement structure (such as a different machine or means of transport).
    b.    Carrying cost: With increasing batch size, the average physical inventory in­creases, together with carrying cost. For the sake of simplicity, these costs are often set as proportional to batch size, that is, proportional to the value of goods in storage. As was shown in Section 11.4.1, this is only valid provided that the following restrictions hold: Firstly, the carrying cost must be independent of the storage duration. Secondly, an entry in stock only occurs following the issue of the last piece. Issues occur regularly along the time axis. Thus, if X is the batch size, on average, X/2 pieces are in stock. Thirdly, there must be sufficient warehouse space. This means that the size of the batch does not necessitate new installations.

In the simplest case, application of these principles leads to the so-called economic order quantity.

The economic order quantity (EOQ), or the optimum batch size, or the economic lot size, is the optimal amount of an item to be purchased or manufactured at one time.

The economic order quantity is calculated with respect to a particular planning period, such as one year. The variables for its calculation are listed in Figure

Fig.       Variables for the EOQ formula.

The equation for calculating total costs is shown in Figure

Fig.       EOQ formula: total costs equation.

Since the objective is to minimize the total costs, the target function is as shown in Figure

Fig.       EOQ formula: target function.

Continuation in next subsection (11.4.2b).

Course section 11.4: Subsections and their intended learning outcomes