# 12.4.1 Combining Net Requirements into Batches by Policies such as Lot-for-lot, Economic order quantity (EOQ), the Period Order Quantity (or Optimum Length of Order Cycle), Part Period Balancing (PPB), Dynamic Optimization

### Intended learning outcomes: Disclose various batch sizing policies, namely lot-for-lot, optimum number of (merged) demands, optimum number of partial lots, optimum batch size (economic order quantity, EOQ), the period order quantity (or optimum length of order cycle), part period balancing (PPB), dynamic optimization. Explain the “blowthrough” technique linked with the lot-for-lot sizing policy.

A batch-sizing policy or lot-sizing policy is a set of tech­niques that create production or procurement batches from net requirements.

In practice, there are various possible batch sizing policies:

1. Lot-for-lot: every net requirement translates into just one planned order. Variation: if the component batch sizes fall below a certain quantity, a “blow­through” of the component requirements right into the requirements given by its bill of material and its routing sheet may take place (see description below).
2. A dynamic lot size, made up of an optimum number of merged demands. If this number is 1, then the situation is again one of make to order.
3. A dynamic lot size with an optimum number of partial lots. This policy suggests splitting the demand into several orders. Another attribute determines the minimum deferral time between two of these orders.
4. A fixed order quantity, known as the optimum batch size, either de­termined manually or calculated using the EOQ (economic order quantity) formula, for example (see Section 11.4.2). If two orders are closer together than the specified minimum deferral time, they are procured in a single batch (multiples of the EOQ).
5. A dynamic lot-sizing technique, known as period order quantity, which combines various demands into one batch over the course of an optimum number of time buckets. This corresponds to the opti­mum period of time for which future demand should be covered, that is, the optimum order interval or the optimum length of order cycle in Figure 11.4.2.6. It is calculated, in principle, by di­vi­ding the optimum batch size by the average annual consumption.
6. Part period balancing (PPB), another dynamic lot-sizing technique. For the first period’s demand, an order is planned. For every further period’s demand, the carrying cost that will be incurred from the time of the last planned order is calculated. If these costs are lower than the setup and ordering costs, then every further period’s demand is added onto the last planned order. Other­wise, a new order is scheduled for every further period’s demand. Variant: If the cumulative carrying costs of all the period demands incurred from the time of the last planned order are higher than the setup and ordering costs, a new order is scheduled.
Variant: If the cumulative carrying costs of all the period’s demand since the last planned order are greater than the setup and ordering costs, a new order is scheduled.
7. Dynamic optimization (as described by [WaWh58]). This relatively complicated technique calculates the various totals for setup and carrying costs resulting from different combinations of net requirements to form batches and determines the minimum costs from these totals. This technique for identifying minimum costs is illustrated in the example below.

All batch-sizing policies, except the fourth, result in so-called discrete order quantities.

A discrete order quantity is an order quantity that represents an integer number of periods of demand. That means that any inventory left over from one period is sufficient to cover the full demand of a future period.

The following additional aspects of the various batch-sizing policies should be considered:

• The “blowthrough” technique linked with the lot-for-lot sizing policy: Designers tend to define structural levels that correspond to the modules of a product. How­ever, in the production flow, the modules are not always meaningful, since some products are manufactured in one go. This is often the case with single-item production, and requires — de facto — extended phantom bills of material. The blow­through technique drives requirements straight through the phantom bill of material to its components and combines the operations in a meaningful order. Thus, the technique converts several design structure levels to a single production struct­ure level (see the definitions of these terms in Sections 1.2.2 and 1.2.3). At the same time, the multilevel design bill of material is transferred to the associated single-level produc­tion bill of material. Figures 12.4.1.1 and 12.4.1.2 show as an example product X, which is made up of two longitudinal parts L and two transverse parts Q, each made from the same raw material. The information is shown before and after the “blow­through” of requirements through L and Q. See also [Schö88a], p. 69 ff.

Fig. 12.4.1.1       Bills of material and route sheets for a product X from the viewpoint of design.

Fig. 12.4.1.2       Bills of material and route sheets for a product X: structure from the production viewpoint, after “blowthrough” of requirements through L and Q.

• For the 2nd to the 5th batch-sizing policies, you can also specify whether the optimum values should be calculated or set manually. Maximum and minimum values can be assigned to restrict these optimum values if the calculation returns unusual values.
• The 2nd and the 3rd batch-sizing policies are particularly important for harmonious or rhythmic production, in which a certain quantity leaves production during each unit of time. The components should be procured at a similar rate.
• The 3rd batch-sizing policy, or batch splitting, is used if the specified requirement in total is not needed all at the same time. For an assembly batch of 100 machines, for example, not all the components will be needed at once, since the machines are assembled one after the other. Thus, two partial batches could be created, if necessary, for producing or procuring components, and the second partial batch could be channeled into the assembly process some time after assembly starts.
• With the 4th batch-sizing policy, or fixed order quantity, physical inventory is inevitable, since more items are generally procured than are needed to satisfy demand. This policy should therefore only be used if the inventory level will actually be reduced, that is, when it is safe to assume that demand will really occur in the future. This is the case if future demand can be determined on the basis of past consumption — at least where demand is regular. This batch-sizing policy is therefore not economically viable for lumpy demand.
• 5th, 6th, and 7th batch-sizing policies: policies 5 and 6 are generally used in determi­nis­tic materials management. Policy 7 is the most complica­ted, and, although it produces a precise and optimum solution, it is unfortunately not very robust. The accuracy obtained and thus the economic viability of policies 5, 6, and 7 increase in ascending order. Unfortunately, the complexity and processing power required also increase accordingly, especially if the techniques are applied to precise events, rather than time periods. On the other hand, the robustness decreases in ascending order, which means that, if the quantity or date of a demand within the planning horizon changes, policy 7 will require complete re-calculation, while a change in demand will not necessarily have severe consequences for policy 5.
• 7th batch-sizing policy: Figure 12.4.1.3 shows the steps of the dynamic optimization technique described by [WaWh58]. They should be studied in conjunction with the example in Figure 12.4.2.1.

Fig. 12.4.1.3       Dynamic optimization technique as described by [WaWh58].

## Course section 12.4: Subsections and their intended learning outcomes

• ##### 12.4 Batch Sizing, or Lot Sizing

Intended learning outcomes: Explain combining net requirements into batches. Differentiate between different batch-sizing policies.

• ##### 12.4.1 Combining Net Requirements into Batches by Policies such as Lot-for-lot, Economic order quantity (EOQ), the Period Order Quantity (or Optimum Length of Order Cycle), Part Period Balancing (PPB), Dynamic Optimization

Intended learning outcomes: Disclose various batch sizing policies, namely lot-for-lot, optimum number of (merged) demands, optimum number of partial lots, optimum batch size (economic order quantity, EOQ), the period order quantity (or optimum length of order cycle), part period balancing (PPB), dynamic optimization. Explain the “blowthrough” technique linked with the lot-for-lot sizing policy.

• ##### 12.4.2 Comparison of Four Different Batch-Sizing Policies, Namely Dynamic Optimization, Part Period Balancing (PPB), the Period Order Quantity (or Optimum Length of Order Cycle), and the Economic Order Quantity (EOQ)

Intended learning outcomes: Explain, using an example, the comparison of various batch-sizing policies, namely dynamic optimization, part period balancing (PPB), the period order quantity (or optimum length of order cycle), and the optimum batch size (economic order quantity, EOQ).