*Intended learning outcomes: Explain central point scheduling. Describe several possible solutions in a directed network of operations.*

*Central point scheduling* is a combination of forward and backward scheduling. Figure 13.3.5.1 shows the underlying concept.

**Fig. 13.3.5.1:** Central point scheduling.

The central point date is the start date for a particular operation. This is usually a critical operation (i.e., an operation at a fully utilized work center — often a bottleneck capacity). The critical operation determines the order schedule and therefore both the start and the completion dates. The relationship of this technique to the two scheduling techniques introduced earlier is as follows:

- For the critical operation and all subsequent operations, we use forward scheduling; for the operations previous to the critical operation, we use backward scheduling.

In this way, central point scheduling provides the latest start date and the earliest completion date. This proves to be quite simple in the case of a sequence of operations with exactly one central point as shown in Figure 13.3.5.1.

Other cases are more complicated and lead us to several possible solutions. For example:

- If a sequence of operations has more than one central point, it is unclear whether planning should apply forward or backward scheduling between two central points.

In a directed network of operations, there are several possible solutions:

- If there is one central point and it lies on the critical path, the latest start date and the earliest completion date appear as they do in a sequence of operations. Planners schedule the network operations that are not time critical using either forward scheduling beginning with the latest start date or backward scheduling beginning with the earliest completion date.
- If there is a central point lying on a path that is not time critical, it will affect either the forward scheduling branch or the backward scheduling branch of the time-critical network path. Here, the simplest procedure is to choose between the following two basic options. Firstly, backward scheduling beginning with the central point — this will provide a latest start date, and the entire network is scheduled forward from this date. Secondly, forward scheduling beginning with the central point — this will provide an earliest completion date, and the entire network is scheduled backward from this date.
- Where there are multiple central points located arbitrarily within the network, central point scheduling becomes more complex.

To eliminate ambiguities in central point scheduling within networks, it is useful to determine a so-called mid-level rather than a central point. The mid-level consists of a number of operations for which a start date is chosen in such a way that, without these operations, the beginning and end are no longer connected.

## Course section 13.3: Subsections and their intended learning outcomes

##### 13.3 Scheduling of Orders and Scheduling Algorithms

Intended learning outcomes: Describe the manufacturing calendar and the calculation of the manufacturing lead time. Differentiate between Backward Scheduling and Forward Scheduling. Explain network planning, central point scheduling, the lead-time stretching factor, and probable scheduling. Present scheduling of process trains.

##### 13.3.1 The Manufacturing Calendar, or Shop Calendar

Intended learning outcomes: Present characteristics of the manufacturing calendar, or shop calendar. Explain an example of a manufacturing calendar.

##### 13.3.2 Lead Time Scheduling: Calculating the Manufacturing Lead Time

Intended learning outcomes: Produce an overview on lead time scheduling. Identify definitions for the elements of operation time. Present the lead time formula and the start date as a function of completion date. Differentiate between manufacturing lead time, cycle time and throughput time.

##### 13.3.3 Backward Scheduling and Forward Scheduling

Intended learning outcomes: Produce an overview on lead time scheduling. Explain forward scheduling and backward scheduling. Describe a simple algorithm for backward scheduling.

##### 13.3.4 Network Planning and CPM — Critical Path Method

Intended learning outcomes: Explain network planning and the critical path method (CPM). Present an example of a scheduled network. Describe a network algorithm for backward scheduling.

##### 13.3.5 Central Point Scheduling

Intended learning outcomes: Explain central point scheduling. Describe several possible solutions in a directed network of operations.

##### 13.3.6 Probable Scheduling

Intended learning outcomes: Produce an overview on order urgency and slack time. Differentiate between forward, backward, and probable scheduling. Explain the role of the lead-time-stretching factor in probable scheduling.

##### 13.3.6b Calculating the Lead-Time-Stretching Factor

Intended learning outcomes: Describe the determination of the lead-time-stretching factor. Explain the equation for recalculation of lead-time-stretching factor.

##### 13.3.7 Scheduling Process Trains

Intended learning outcomes: Differentiate between reverse flow scheduling, forward flow scheduling, and mixed flow scheduling.