# 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 11.4.2.1.

Fig. 11.4.2.1       Variables for the EOQ formula.

The equation for calculating total costs is shown in Figure 11.4.2.2.

Fig. 11.4.2.2       EOQ formula: total costs equation.

Since the objective is to minimize the total costs, the target function is as shown in Figure 11.4.2.3.

Fig. 11.4.2.3       EOQ formula: target function.

Continuation in next subsection (11.4.2b).

## Course section 11.4: Subsections and their intended learning outcomes

• ##### 11.4 Batch Sizing, or Lot Sizing

Intended learning outcomes: Produce an overview on production or procurement costs, batch-size-dependent unit costs, setup and ordering costs, and carrying cost. Explain optimum batch size, optimum length of order cycle, the classic economic order quantity formally and in practical application. Disclose extensions of the batch size formula.

• ##### 11.4.1 Production or Procurement Costs: Batch-Size-Dependent Unit Costs, and Setup and Ordering Costs

Intended learning outcomes: Differentiate between batch-size-dependent production or procurement costs and batch-size-independent production or procurement costs.

• ##### 11.4.1b Carrying Cost

Intended learning outcomes: Explain carrying cost and carrying cost rate. Produce an overview on costs of financing or capital costs, storage infrastructure costs and the risk of depreciation.

• ##### 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.

• ##### 11.4.2b The Economic Order Quantity (EOQ) Formula

Intended learning outcomes: Explain the economic order quantity (EOQ) formula. Describe the cost curves as a function of batch size.

• ##### 11.4.2c Optimum Length of Order Cycle

Intended learning outcomes: Present the optimum length of order cycle.

• ##### 11.4.3 Economic Order Quantity (EOQ) Formula: Sensitivity Analysis

Intended learning outcomes: Present in detail the sensitivity analysis of the EOQ calculation.

• ##### 11.4.3b Economic Order Quantity (EOQ) and Optimum Length of Order Cycle in Practical Application

Intended learning outcomes: Produce an overview on the practical implementation of the EOQ formula. Identify several factors that influence a maximum or minimum order quantity.

• ##### 11.4.4 Extensions of the EOQ Formula: Lead-Time Orientation and Discount Levels

Intended learning outcomes: Present lead-time-oriented batch sizing. Describe batch sizing considering discount levels.

• ##### 11.4.4b Extensions of the EOQ Formula: Joint Replenishment

Intended learning outcomes: Produce an overview on joint replenishment: kit materials management and collective materials management.