# 11.4.3 Economic Order Quantity (EOQ) Formula: Sensitivity Analysis

### Intended learning outcomes: Present in detail the sensitivity analysis of the EOQ calculation.

Unfairly, the EOQ formula has recently been held responsible for large batches. However, a closer look at practice reveals that the formula was often used with carrying cost unit rates that were much too low, or it was applied to deterministic materials management, for which other techniques are better suited (see Section 12.4).

In any case, the EOQ formula basically provides “only” an order of magnitude, not a precise number. The total costs curve shown in Figure 11.4.2.5 is very flat in the region of the minimum, so that deviations from the optimum batch size have only a very small effect on costs. The following sensitivity analysisshows this “robust” effect. Beginning with a quantity deviation as given in Figure 11.4.3.1, and the fact that the formula in Figure 11.4.3.2 holds for the optimum batch size X0, the cost deviation formula is shown in Figure 11.4.3.3.

Fig. 11.4.3.1       Sensitivity analysis: quantity deviation.

Fig. 11.4.3.2       Sensitivity analysis: carrying cost rates for optimum batch size.

Fig. 11.4.3.3       Sensitivity analysis: cost deviation.

For example, a cost deviation of b = 10% results for v = 64% as well as for v = 156%, which means that the relationship shown in Figure 11.4.3.4 is valid:

Fig. 11.4.3.4       Sensitivity analysis: quantity deviation given a cost deviation of 10%.

This sensitivity analysis reveals the surprising robustness of the calculation technique, which indeed rests on very simplified assumptions. Extending batch size formulas to include additional influencing factors produces an improvement in results that is practically relevant only in special cases. In any event, we may round off the calculated batch size, adapt it to practical considerations, and, in particular, make it smaller if a shorter lead time is desirable.

This robustness increases even further if we include not only C2 and C3, but also the actual costs of production or procurement C1 in the division for b given in Figure 11.4.3.3. If C1 is much larger than C2 + C3 — which is usually the case — even bigger changes to batch size do not have a strong effect on the total production or procurement costs.

In a similar way, we can show that errors in determining setup and ordering costs, the carrying cost rates, or the annual consumption in the cost deviations make as little difference as a quantity deviation does. Among other things, the EOQ formula is thus not very sensitive to systematic forecast errors. This means that very simple forecasting techniques, such as moving average value calculation, will generally suffice when determining batch sizes.

In the case of produced items, the reduction in costs for in-process inventory achieved through smaller batches is thus negligible in most cases. More significant is the fact that smaller batches may lead to shorter lead time. In addition to this improvement in the target area of delivery, there are also positive effects in the target areas of flexibility and costs. The positive effects discussed in Chapter 6 are lacking in the classic EOQ formula. However, as we will show in Section 13.2, smaller batches only result in shorter lead time if — on the one hand — the run time is long in relation to the lead time, particularly in line production (in classic job shop production this pro­portion is likely to be of the order of magnitude of 1:10 and less), and — on the other hand — the saturation of a work center does not have the effect of creating longer queues for the entire collection of batches.

Thus, the longer the run times — often required when much value is added — the higher the costs for goods in process are. In such cases we should choose rather lower values for batch sizes than those recommended on the basis of the EOQ formula (see also lead-time-oriented batch sizing in Section 11.4.4). For work-intensive operations especially, shorter operation times can contribute to harmonizing the content of work, which in turn leads to a further reduction in wait times, and thus lead times, as explained in Section 13.2.2. As Figure 6.2.6.2 illustrated, at lower production structure levels a reduction in lead time is likely to result in lower safety stocks, and thus cost savings. If for some reason storage is not possible at all, shorter lead times can even achieve additional sales.

Continuation in next subsection (11.4.3b).

## 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, and Setup and Ordering Costs

Intended learning outcomes: Differentiate between batch-size-dependent production or procurement costs and batch-size-independent production or procurement costs.

• ##### 11.4.1b Carrying Cost

Intended learning outcomes: 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: The Classic Economic Order Quantity (EOQ)

Intended learning outcomes: Explain the concept of the economic order quantity (EOQ). Explain variables for the EOQ formula.

• ##### 11.4.2b The Economic Order Quantity (EOQ) Formula

Intended learning outcomes: Explain the economic order quantity (EOQ) formula. Describe the cost curves as a function of batch size.

• ##### 11.4.2c Optimum Length of Order Cycle

Intended learning outcomes: Present the optimum length of order cycle.

• ##### 11.4.3 Economic Order Quantity (EOQ) Formula: Sensitivity Analysis

Intended learning outcomes: Present in detail the sensitivity analysis of the EOQ calculation.

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

Intended learning outcomes: 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 EOQ Formula: Lead-Time Orientation and Discount Levels

Intended learning outcomes: Present lead-time-oriented batch sizing. Describe batch sizing considering discount levels.

• ##### 11.4.4b Extensions of the EOQ Formula: Joint Replenishment

Intended learning outcomes: Produce an overview on joint replenishment: kit materials management and collective materials management.