*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. *

In practice, the urgency of an order is often more important than an absolute date.

*Order urgency* is the urgency of the order’s operations compared with those of other orders.

A possible measure for order urgency is the lead-time-stretching factor, which is introduced in the following.

For backward scheduling, *slack time* is the difference between the latest (possible) start date and the earliest (acceptable) start date; for forward scheduling, it is the difference between the earliest (possible) completion date and the latest (acceptable) completion date.

Therefore, slack time provides an element of flexibility in planning. Positive slack time allows an increase in lead time, while negative slack time requires that it be shortened.

In *probable scheduling*, we take slack time into account to increase or decrease lead time.

Figure 13.3.6.1 illustrates the
principle of probable scheduling using an example with three operations (“op”)
and positive slack time. In contrast to forward or backward scheduling, the
operations are distributed evenly between the earliest start date and the
latest completion date. Then, the start or the completion date of each
operation is its *probable start date*
or *probable completion date*.

Since the technical process itself determines the duration of operations and the technical interoperation time, we can only modify slack time by increasing or reducing either the nontechnical interoperation times or the administrative times. All of these time elements are attributes of the product’s master data, its routing sheet, and the work centers. Their values are averages, determined through measuring or estimating.

**Fig. 13.3.6.1** Forward, backward, and probable scheduling.

The *lead-time-stretching factor* is a numerical factor by which the non-technical interoperation times and the administrative times are multiplied.

The choice of the lead-time-stretching factor has the following effects on the scheduling algorithm:

- A factor greater than 1 results in increased lead time.
- A factor equal to 1 results in “normal,” or average, lead time.
- A factor between 0 and 1 results in reduced lead time.
- A factor equal to 0 results in a minimal lead time, in that only the duration of the operations and technical interoperation times are strung together.
- With a factor of less than 0, the operations overlap.

Probable scheduling takes the latest completion date and the earliest start date as givens and calculates the lead-time-stretching factor. This is the starting point in the cases that follow.

*Customer production orders**with a set due date:*This due date is the latest acceptable completion date for scheduling. Because delivery dates are often very short term, the earliest start date becomes*de facto*“today.” The scheduling algorithm calculates the lead-time-stretching factor (less than 1) needed to shorten the interoperation times so that the order can be completed between “today” and the delivery date. In this case, the lead-time-stretching factor indicates the feasibility of completion of the order cycle (where sufficient capacity is available, of course).*Orders in process**:*The earliest start date for the first of all remaining operations is “today.” The latest completion date is generally the date specified when the order is released. Rescheduling calculates the lead-time-stretching factor required for order completion on time. This is very useful if, for example, there are delays after the order is released. A lower lead-time-stretching factor gives this order immediate urgency.*Early released orders*: The earliest start date is provided by the date the order is released; the latest completion date is the date on which warehouse stocks will probably fall below

the safety stock level. Again, probable scheduling will calculate the lead-time-stretching factor required for timely order completion. This factor can then serve as a priority rule for queues at the work centers (see also Section 15.3.1).

*Continuation in next subsection (13.3.6b).*

## 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.