# 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.

Site production, or project manufacturing, uses mainly scheduling techniques proper to project management.

Network planning is a generic term for techniques that are used to plan complex projects (cf. [APIC16]).

Project routings, a project task, or a work package have directed networks of operations, such as in Figure 13.1.1.2, instead of simple operation sequences. For network planning, the simple algorithm in Figure 13.3.3.2 will not do.

The critical path method (CPM) is used for planning and controlling the activities in a project. It determines the critical path that is the path with the longest duration, which identifies those elements that actually constrain the cumulative lead time (or critical path lead time) for a project (cf. [APIC16]).

Scheduling is done forward and backward. Figure 13.3.4.1 shows the results of scheduling the network in Figure 13.1.1.2 with set values for ESD and LCD. The difference between ESD and LSD is the lead-time margin.[note 1306] On the critical path, it always has the same value (generally close to or equal to zero) and is also called path float or slack time.

Further network work techniques are:

• The program evaluation and review technique (PERT) is a network analysis technique in which each activity is assigned a pessimistic, most likely, and optimistic estimate of its duration. The critical path method is then applied using a weighted average of these times for each node. PERT computes a standard deviation of the estimate of project duration ([APIC16]).
• The critical chain method is an extension of the critical path method that was introduced in the theory of constraints, which considers not only technological precedence but also resource constraints (cf. [APIC16]).

Fig. 13.3.4.1       Scheduled network.

Figure 13.3.4.2 shows an effective network algorithm for backward schedu­ling. It is formulated as a generalization of the algorithm in Figure 13.3.3.2. If BEGIN is the start and END the conclusion of the routing sheet, then:

• prec(i) designates the quantity of all operations, which precede operation i or END.
• succ(i) designates the quantity of all operations, which follow operation i or BEGIN.

An operation that precedes (or follows) a particular operation i bears a smaller (or larger) operation number than i. Thus, we can treat operations in an ascending (or descending) order. Usually this type of semiorder establishes itself naturally. Other­wise, it can be calculated easily by using the function prec(i) (or succ(i)).

Fig. 13.3.4.2       Network algorithm for backward scheduling.

Omitting all set dates, the above network algorithm is also able to calculate the critical path. For each operation i, the attribute CRIT[i] specifies the operation following i on the critical path. An analogous attribute specifies the first operation on the critical path in the item master data. In step 1b, all the last operations are assigned CRIT[i1]= “END.” Wherever the “<” condition appears in step 2b, CRIT[i1] is replaced with i.”