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

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.


Lot-size inventory is inventory that results whenever quantity price discounts, shipping costs, setup costs, or similar considerations make it more economical to purchase or produce in larger lots than are needed for immediate purposes ([APIC16]).

Batch sizes that are not specified by the user lead to longer lead times and procurement deadlines and should therefore be avoided, as discussed in the Lean/JIT concept. Even there, batch sizes have to be accepted because of setup costs. In this section, we will examine the arguments that tend to favor either smaller or larger batch sizes.

There are batch-size-dependent production or procurement costs for every produced or procured unit of measure of the order, that is, the batch-size-dependent unit costs.

Batch-size-dependent production or procurement costs are

  • In the case of external procurement, acquisition cost per procured unit quantity plus eventual additional costs that are proportional to quantity (for example, customs, shipping, and so on).
  • In the case of in-house production, the sum of the costs of the components and operations needed to produce a unit quantity. The unit cost for an operation are calculated as “run load per unit  cost rate for internal labor costs,” whereby the cost rate generally includes full costs (fixed and variable costs).
Batch-size-independent production or procurement costs are incurred with the order, even with a batch size of one.

Batch-size-independent procurement costs are mainly:

  • Ordering costs for procurement, which are the administrative costs of purchasing divided by the number of purcha­ses. Administrative costs of purchasing also include the costs of receiving stock and stock control. Batch-size-independent procurement costs also include all costs per order that are independent of quantity, such as shipping and handling costs. In the extreme case, these are dependent on the suppliers and the delivered items. To avoid large volumes of data, however, these costs are often added to purchasing costs.
    • Procurement costs can also be tapped by item class, such as according to the ABC classification. This results in varying batch- size-independent procurement costs for each ABC category (for example, higher costs for A parts than for C parts). For a more precise determination, see Section 16.4 (activity-based costing).

Batch-size-independent production costs are mainly:

  • Ordering costs for production, that is, the administrative costs of planning & control and other office functions.
  • Possible overhead costs of production that are independent of quantity (transportation, control, putting into and issuing from stock). Usually, they also count as part of the ordering costs.
  • Setup costs (= setup load ∙ the cost unit rate for internal labor costs) for the various operations (machine adjustments, tool assembly, start-up process, loss of materials at start-up, and so on). For this, management must decide whether to include full costs or only variable costs (essentially wages) in the calculations; this may influence the batch sizes.
Carrying cost, or holding costs, are all costs incurred in connection with holding inventory.
Carrying cost rate, or holding cost rate, is the rate for the carrying cost, usually defined as a percentage of the dollar value of inventory per unit of time (generally one year).

See also Section 1.1.3. Carrying cost includes:

  • The costs of financing or capital costs: Inventory ties up financial resources. Cal­cu­lation using an interest rate yields the costs of immobilizing money in inventory. This rate corresponds to either the percentage of the mean return on investment if the inventories are financed using internal capital resources, or to the bank interest rate, if the inventories are financed by a third party. For calculation purposes, take interest rate values between 5 and 15% of the average value of the inventory.
  • The storage infrastructure costs are incurred for the infra­structure necessary to store a particular product: buildings, installations, warehouse employees, insurance, and so on. The costs for inventory transactions, in contrast, are seen as ordering costs.
    • The first cost driver for storage infrastructure costs is batch size, as enough surface area or volume for the whole batch size must be provided. In a first approach, it is possible to express storage infrastructure costs proportio­nally, as a percentage related to the average inventory, because the average inventory corresponds — apart from safety stock — to half of the batch size, according to the formula in Figure 11.3.1.2. More commonly used is a percentage related to the mean inventory value. In the machine tool industry, percentages between 1 and 3% are common.
    • Further cost drivers are storage type and valuation basis (see Section 11.1.1). The storage infrastructure costs rate can be much higher for inexpensive and voluminous products (insulation materials and other construction materials) than for very expensive and possibly easy-to-store products. For more precise figures, then, the calculation should include at least some separate values, such as for information and documents, raw materials, purchased parts, semifinished goods, and end products. However, there are limits to diversifying storage infrastructure costs into as many different storage unit cost rates as possible, due to the expense involved in recording the incurred costs per separate category as well as for data maintenance, if, for example, a separate storage cost percentage were kept for each item.
    • A large part of these costs is out of proportion to the value of the stored goods. Since warehouses involve specialized construc­tions, building a warehouse represents a long-term investment. A company will make the investment if it has exhausted exis­t­ing warehouse volumes. This leads to a jump in costs. In contrast, reducing in­ven­tory value does not automatically lead to a reduction of personnel needed for ware­house management. Even so, in practice, a proportional relationship is common.

  • The risk of depreciation: This is again expressed as a percentage of the inventory value. It includes, firstly, technical obsolescence that results from changes in standards or the emergence of improved products on the market. Secondly, it inclu­des expiration due to perishability: Certain items can be stored only for a particular, limited period of time (shelf life). This is the case with “living” products such as groceries or biological pharma­ceuticals, but also with “nonliving” products such as certain electronics items. Thirdly, it includes damage, spoilage,or destruction due to unsuitable handling or storage such as, for example, the rusting of sheet metals.
    • The percentage of the risk of depreciation may be very large under certain circumstances. For short-lived items, it must be set at 10% or more. However, the percentage is generally dependent on the duration of storage.

It is not unusual for the carrying cost rate to be on the order of 20%. For goods with a high risk of depreciation, it may reach 30% and higher.



Course section 11.4: Subsections and their intended learning outcomes

  • 11.4.4 Extensions of the Batch Size Formula

    Intended learning outcomes: Identify additional variables for lead-time-oriented batch sizing. Present lead-time-oriented batch sizing. Describe total costs curves, considering discount levels. Produce an overview on joint replenishment: kit and collective materials management.

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