*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

STREFAC := lead-time-stretching factor

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.

## Course section 13.4: Subsections and their intended learning outcomes

##### 13.4 Order Splitting, Order Overlapping, and Extended Scheduling Algorithms

Intended learning outcomes: Explain order or lot splitting, and overlapping. Present an extended formula for manufacturing lead time and extended scheduling algorithms.

##### 13.4.1 Order Splitting, or Lot Splitting

Intended learning outcomes: Explain reducing lead time for operation i by using a splitting factor > 1. Describe how the split offset factor offsets the split lots in time.

##### 13.4.2 Operation Overlapping and Overlapping Within an Operation

Intended learning outcomes: Explain te principle of overlapping within an operation. Describe the principle of operation overlapping.

##### 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.

##### 13.4.4 Extended Scheduling Algorithms (*)

Intended learning outcomes: Identify various possible extensions of the scheduling algorithms. Describe possible cases arising in process industries.