*Intended learning outcomes: Present lead-time-oriented batch sizing. Describe batch sizing considering discount levels. Produce an overview on joint replenishment: kit materials management and collective materials management.*

1. *Lead-time-oriented batch sizing* is a generalization of the simplified approach using the EOQ formula for production, taking the cost of work in process into consideration.

As a complement to the variables in Figure 11.4.2.1, we add the variables shown in Figure 11.4.4.1. Most of these data come from the route sheet.

**Fig.
11.4.4.1** Additional
variables for lead-time-oriented batch sizing.

The EOQ has results according to the formula given in Figure 11.4.4.2. For details of the derivation, see [Nyhu91], p. 103. The denominator under the radical is significantly larger than the one in classic batch sizing only for a long manufacturing lead time.

**Fig.
11.4.4.2** Lead-time-oriented
batch sizing: determination of the minimum.

2. *Batch sizing considering discount levels* is a generalization of the simplified approach using the EOQ formula.

Figure 11.4.4.3 illustrates the decreasing batch-size-dependent unit costs as a function of the lot size, as well as the resulting total costs curves.

**Fig.
11.4.4.3** Total
costs curves, taking discount levels into consideration.

Batch-size-dependent unit costs CU are dependent on the purchased quantity. This is particularly valid for procured goods.

A *quantity discount* is a price reduction allowance on orders over a certain minimal order quantity or value.

For example, a supplier may offer a quantity discount for the whole order quantity with
three discount levels; that is, reduced unit costs CU2 as
soon as the quantity exceeds X_{m}2, CU3 as soon as the quantity
exceeds X_{m}3, CU4, as soon as the quantity exceeds X_{m}4.

Every total costs curve for the
various values of cost per piece demonstrates a minimum within the range of
its validity. This is either the minimum of the corresponding total costs curve
(X_{0}2 in Figure 11.4.4.3), or it lies on the border of a discount level
curve (X_{m}3 in Figure 11.4.4.3). If discounts are not large, we may
also argue that the batch sizes for the different discount levels according to
the EOQ formula will lie very close to each other. We may thus calculate the
optimum batch size by selecting a particular mean cost per piece, and then
rounding it up to the next discount level.

A similar line of thinking is followed when evaluating economic efficiency and batch sizing in the case of alternative (less expensive) production processes using larger batch sizes.

3. *Joint replenishment* is joint planning for a group of related items, treating them as an item family.

Two examples of management of sets of items follow.

3a. In *kit materials management*, various goods are combined into a so-called *(material) kit* (because of their joint use in particular assemblies or products) and managed as a group.

The individual optimum batch size for an element i from a kit S with annual consumption AC of S results from the formula in Figure 11.4.4.4.

**Fig.
11.4.4.4** Individual
optimum batch sizes for an element i of kit S with annual consumption AC_{S}.

Instead of these individual batch
sizes, we may determine a kit batch size X_{S} using the compromise
formula in Figure 11.4.4.5.

**Fig.
11.4.4.5** Kit
batch size X_{S}.

If the component kits are very heterogeneous with respect to the two factors in the batch size formulas above, we can form more homogeneous planning subgroups that are then used for separate batch sizings. Another possibility is to form an economic batch for the most value-intensive components. We then set the batch size of less value-intensive materials positions as whole-number multiples of this batch for correspondingly less frequent procurement.

3b. In *collective materials management*, we form material groups, or planning groups, whose setup and ordering costs can be reduced, if the batches are ordered collectively.

Valid criteria for collective materials management include:

- The same supplier for purchased parts (taking advantage of simplified administration and/or a total invoice discount)
- The same production technique for in-house production (e.g., for a product family), whereby simplified machine setup achieves a reduction in the total setup costs

In the case of collective materials management, within a planning group materials managers must determine an average reduction in the setup and ordering costs as a percentage. As soon as an item is to be ordered, a check is made of all other items of the same planning group. If the order of a batch is due in the near future anyway, it can be ordered now through an *early order release*. This should be a reduced batch size, which is calculated by using the reduced setup and ordering costs.

## 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, Setup and Ordering Costs, and Carrying Cost

Intended learning outcomes: Differentiate between batch-size-dependent production or procurement costs and batch-size-independent production or procurement costs. 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 and Optimum Length of Order Cycle: The Classic Economic Order Quantity (EOQ)

Intended learning outcomes: Explain economic order quantity (EOQ), variables for the EOQ formula and the EOQ formula. Describe the cost curves as a function of batch size. Present the optimum length of order cycle.

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

Intended learning outcomes: Present in detail the sensitivity analysis of the EOQ calculation. 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 Economic Order Quantity (EOQ) Formula

Intended learning outcomes: Present lead-time-oriented batch sizing. Describe batch sizing considering discount levels. Produce an overview on joint replenishment: kit materials management and collective materials management.