Integral Logistics Management — Operations Management and Supply Chain Management Within and Across Companies

12.4 Batch 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

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 demands taken together. 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, 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.
  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, with no explicit identification or storage of the intermediate product levels. This is often the case with single-item production, where an additional objective is to create as few order documents as possible, and results — de facto — in phantom items and extended phantom bills of material. The blow­through technique, however, drives requirements straight through the phantom item to its components and combines the operations in a meaningful order. Applying the technique means that several design structure levels can be converted to a single production structure level.[note 1204] 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 usedin 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].


12.4.2  Comparison of the Different Batch-Sizing Policies

Batch-sizing policies 7, 6, 5, and 4 described in Section 12.4.1 are compared below. These policies are

  • Dynamic optimization
  • The cost-leveling technique
  • Comparison of the carrying cost for a single net requirement per period with the batch-size-independent production or procurement costs
  • Comparison of the cumulative carrying cost with the batch-size-independent production or procurement costs
  • The optimum length of order cycle or the optimum order interval
  • The optimum batch size (economic order quantity, EOQ)

The following assumptions apply:

  • Net requirement: 300 units of measure divided between six periods (for example, 2-month periods) giving 10, 20, 110, 50, 70, 40 units
  • Batch-size-independent production or procurement costs: 100 cost units
  • Carrying cost
  • Per unit of measure and period: 0.5 cost units
  • Per unit of measure over six periods: 3 cost units
  • An order receipt is assumed at the start of a period. Carrying cost is always incurred at the start of the next period.

Based on these assumptions, you can thus calculate the following values:

  • Optimum batch size using the economic order quantity (EOQ) (see Figure 11.4.2.4):
  • Optimum length of order cycle or the optimum order interval (see Figure 11.4.2.6):

In Figure 12.4.2.1, the total setup and ordering costs as well as the carrying cost are calculated for the various batch-sizing policies.

Fig. 12.4.2.1          Comparison of various batch-sizing policies.

Every policy yields a different result in specific cases, although this is not necessarily so in the general case. The results obtained with these techniques tend to improve in the order given above. Indeed, the optimum batch-size technique can be used only if the quantity of the last batch does not exceed the net requirement. But, even under these circumstances, the technique produces unsatisfactory results when applied deterministically.



Course sections and their intended learning outcomes

  • Course 12 – Deterministic Materials Management

    Intended learning outcomes: Produce an overview on demand and available inventory along the time axis. Describe deterministic determination of independent demand. Explain in detail the deterministic determination of dependent demand (Material Requirements Planning, MRP). Differentiate various lot sizing techniques. Disclose how to analyze the results of the MRP.

  • 12.1 Demand and Available Inventory along the Time Axis

    Intended learning outcomes: Explain the projected available inventory and its calculation. Describe scheduling and cumulative projected available inventory calculation. Produce an overview on operating curves for stock on hand.

  • 12.2 Deterministic Determination of Independent Demand

    Intended learning outcomes: Present the customer order and distribution requirements planning (DRP). Disclose the consumption of the forecast by actual demand.

  • 12.3 Deterministic Determination of Dependent Demand

    Intended learning outcomes: Describe characteristics of discontinuous dependent demand. Explain material requirements planning (MRP) and planned orders. Disclose the determination of the timing of dependent demand and the load of a planned order.


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