# 13.4.3 An Extended Formula for Manufacturing Lead Time (*)

### Present an extended operation lead time. Explain the corresponding extended lead time formula in ist first and second version. Disclose the influence of overlapping of operations upon lead time.

The following lists the definitions set out in Section 13.3.2 for the components of operation time. Here, we have added the following abbreviations for the elements defined above.

LOTSIZE          :=  lot size ordered
ST[i]                 :=  setup time for operation i
RT[i]                 :=  run time per unit produced for operation i
SPLFAC[i]        :=  splitting factor for operation i
SPLOFST[i]      :=  split offset factor expressed as a percentage
RTOFST[i]        :=  run time offset for operation i expressed as a percentage
MAXOFST[i]    :=  maximum offset of the operation immediately following operation i (a duration)

We can express the operation time for an operation i, OT[i], by the formula shown in Figure 13.4.3.1. This formula is much more complex than the one in Section 13.3.2.

Fig. 13.4.3.1       Extended operation lead time.

For a sequence of operations as the order of the operations, the formula in Figure 13.4.3.2 yields the lead time for the order.

Fig. 13.4.3.2       Extended lead time formula (first version).

LTI represents the lead time for LOTSIZE and will vary when lot sizes are different. In Figure 13.4.3.3, we attempt to define partial sums to express lead time as a linear function of lot size.

As in Figure 13.3.2.3, we can store the partial sums in the lead time formula as attributes of the product and recalculate them after each modification of the routing sheet. Correspondingly, the formula according to Figure 13.3.2.4 holds.

Fig. 13.4.3.3       Extended partial sums for the lead time formula.

Fig. 13.4.3.4       Extended lead time formula (second version).

Because of the overlapping of operations, which is expressed in the formula for LTI in Figure 13.4.3.2 as a minimization, LTI is not equivalent to LTI': For either one or the other operation, the maximum offset of the next operation is smaller than the sum of the other time elements (the “normal” time period until the beginning of the next operation).

Figure 13.4.3.5 shows a possible plotting of the two lead times as functions of lot size.

Fig. 13.4.3.5       Influence of overlapping of operations upon lead time.

In most circumstances LTI' is precise enough and certainly suffices for rough-cut planning. If necessary, we can set a lot size limit for the lead time formula.If the lot size is less than or equal to this quantity, we calculate lead time according to the “quick” lead time formula (the second version in Figure 13.4.3.4). Other­wise, we apply the more involved, “slow” formula in Figure 13.4.3.2.

In a directed network of operations as the order of the operations, similar considerations to those examined in Section 13.3.2 apply.