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

We can now extend the scheduling algorithms presented in Section 13.3.3 to include the definitions introduced in the subsections above. These include:

- The introduction of a lead-time-stretching factor that multiplies interoperation times
- The introduction of splitting and overlapping and an expanded formula for lead time
- The inclusion of multiple partial orders for each production order
- The inclusion of divergent product structures, as — for example — the case of temporary assembly
- Ongoing planning for released orders with work remaining to be done

We can derive a generalized algorithm
from the algorithm presented in Section 13.3.3, for both a sequence of
operations and for a *directed* network
of operations. This would complicate the algorithm further, and we will not
present it here in detail.

The extensions introduced thus far
may not be sufficient for lead time scheduling in every potential scenario. A
first case is the *undirected network of
operations* with
a *repetition of operations*.
During a chemical process or in the production of electronic components, for
example, production has to repeat certain operations. This may be because inspection
has uncovered defects in quality. Here, the number of iterations and the
individual operations to be repeated become evident only during the course of
work and cannot be planned in advance. In this case, it is not possible to
calculate lead time precisely. Instead, we have to use expected mean values for
the number of iterations and accompanying deviation. However, we have to take
into account that each calculation of lead time itself is based on estimations
of the time elements, particularly wait time in front of the work center.

Another case arises in process industries. The processor-oriented concept implemented in these industries may require sequencing or, more precisely, the planning of optimum sequences of operations, as early as the phase of long- and medium-term planning. Because of the extremely high setup costs, planners should establish suitable lots even prior to order release to keep changeover costs at a minimum. To this category belongs, for example, cut optimizations for glass, sheet metals, or other materials. The scheduling of an individual order will depend on whether it may be combined with other orders and with what orders, to achieve optimal usage of the raw material, the reactors, or processing containers.

## 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 the 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 its 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.