# 11.4.2c Optimum Length of Order Cycle

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

Continuation from previous subsection (11.4.2b)

Instead of an optimum batch size, we can also calculate an optimal time period for which an order or a batch covers demand.

The optimum order interval or optimum length of order cycle is an optimum period of time for which future demand should be covered.

This length is defined according to the formula in Figure 11.4.2.6. From this formula, it is immediately apparent that the optimum length of the order cycle — and the optimum batch size in Figure 11.4.2.4 — rises less than proportionally with increasing setup costs, and declines less than propor­tionally with increasing turnover. Thus, for example, if we set the value for the root of (2 × CS/p) at 40, the characteristic figures for optimum length of order cycle as a function of the value of turnover are those in Figure 11.4.2.7.

Fig. 11.4.2.6       Optimum length of order cycle.

Fig. 11.4.2.7       Sample characteristic figures for length of order cycle as a function of the value of turnover.

Unless we can reduce setup costs decisively, a very large length of order cycle will result in low turnover. In practice, however, when the range of demand coverage is very long, the depreciation risk increases disproportion­ally. For this reason, upward limits are set for the length of the order cycle, and thus as well for the batch sizes, for items with a small turnover. This is, incidentally, the simplest and most common method in practice to control nonlinear patterns of carrying cost: for example, carrying cost that jumps steeply when inventory exceeds a particular volume. The conside­ration of the length of order cycle is also an important batch-sizing policy in deterministic materials management (see Section 12.4).

## 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.