*Intended learning outcomes: Disclose various batch sizing policies, namely **the period order quantity (or optimum length of order cycle), part period balancing (PPB), dynamic optimization.*

*Continuation from previous subsection (12.4.1)*

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.

5^{th}, 6^{th}, and 7^{th} batch-sizing policies also result in so-called discrete order quantities.

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

*For the 5 ^{th} batch-sizing policy, *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.

*5 ^{th}, 6^{th}, and 7^{th} 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, Optimum Number of Merged Demands or Partial Orders, and Economic order quantity (EOQ)

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). Explain the “blowthrough” technique linked with the lot-for-lot sizing policy.

##### 12.4.1b Batch Sizing Policies such as Period Order Quantity (or Optimum Length of Order Cycle), Part Period Balancing (PPB), Dynamic Optimization

Intended learning outcomes: Disclose various batch sizing policies, namely the period order quantity (or optimum length of order cycle), part period balancing (PPB), dynamic optimization.

##### 12.4.2 Comparing Dynamic Optimization, Part Period Balancing (PPB), Period Order Quantity (or Optimum Length of Order Cycle), and 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).