*Intended learning outcomes: Explain forward scheduling and backward scheduling. Describe a simple algorithm for backward scheduling.*

The two most important scheduling techniques are the following:

*Backward scheduling*, or *back scheduling*, begins with the set (that is, the *latest *acceptable) *completion date* for the order (that is, the *order due date*), and calculates — for each operation — the latest (acceptable) completion date (that is, the *operation due date*) and the latest (possible) start date (that is, the *operation start date*), as well as the *latest (possible) start date* for the order.*Forward scheduling* begins with the set (that is, the *earliest *acceptable)* start date* for the order and calculates the earliest (acceptable) start date and the earliest (possible) completion date for each operation, as well as the *earliest (possible) completion date* for the order.

These two techniques assume the following definitions:

The *latest date* is a date that we cannot exceed in execution and control of operations. Similarly, we cannot allow a date to fall before the *earliest date*.

A *set date *is set “externally” and cannot be changed by means of the scheduling algorithm.

Figure 13.3.3.1 illustrates the two principles.

**Fig. 13.3.3.1** Forward scheduling and backward scheduling.

Figure 13.3.3.2 shows the simplest algorithm for backward scheduling (the algorithm for forward scheduling has a similar structure):

- The order of the operations is assumed to be a sequence of operations.
- The production order consists of one single partial order.
- All n operations are included in the lead time scheduling; that is, the order has not yet begun.
- The interoperation times are weighted with a factor of 1; that is, they are assumed to be “normal.”

The formal description of this scheduling task is as follows:

- Take a production order consisting of one partial order with n operations i, 1 ≤ i ≤ n, and m components j, 1 ≤ j ≤ m, as given. The operation numbers stand in a semiorder; if, for example, i
_{1}< i_{2}, then operation i_{1}is performed before operation i_{2}.

- Beginning with the set (that is, the latest acceptable) order completion date, we calculate the following “latest” dates:

- Start and completion dates for the individual partial order

- Start and completion dates for the individual operations

- Reservation dates (= start date) for the components

- Start date for the order, with an exception message if it is earlier than a set (earliest) start date

As data specifications, the following notations are used:

- x = order, partial order, or one position in the partial order (component or operation)
- LCD[x] = latest completion date for x
- ECD[x] = earliest completion date for x
- LSD[x] = latest start date for x
- ESD[x] = earliest start date for x
- OT[i] = operation time for operation i
- INTBEF[i] = interoperation time before operation i
- INTAFT[i] = interoperation time after the end of operation i
- INTTEC[i] = technical interoperation time after operation i
- ADMPORDBEG = administrative time for the partial order at the beginning
- ADMPORDEND = administration time for the partial order at the end

Remarks:

- For comparing the date attributes with one another, we will use the standardized “ISO” format, that is, YYYYMMDD.
- A date is calculated either by the scheduling algorithm or given as a set date. We distinguish the latter from the former by the addition of (set), for example, LCD(set)[x].

**Fig. 13.3.3.2** Simple algorithm for backward scheduling.

## 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.