# 13.7.4 Exercise: Backward Scheduling and Forward Scheduling

### Intended learning outcomes: Explain and solve the forward and backward scheduling problems that is calculation of start and completion dates for the order and each operation, as well as the critical path and lead-time margin.

Here, you will practice some backward and forward scheduling. Figure 13.7.4.1 presents a simple network, including a legend showing the lead- time elements used.

Solve the forward and backward scheduling problems (calculation of start and completion dates for the order and each operation, as well as the critical path and lead-time margin) listed in Figure 13.7.4.2:

Fig. 13.7.4.1       Scheduled network.

a.    Common forward scheduling.
b.    Common backward scheduling.
c.    Forward scheduling with a different lead-time-stretching factor, that is, a different order urgency, to accelerate or slow down the order.
d.    Forward scheduling with lead-time-stretching factor = 0, which results in the lead time as the sum of operation times plus the technical inter­operation times.

Fig. 13.7.4.2       Various forward and backward scheduling problems.

Some common problems in the calculation process lead to the following potential errors:

• Calculating incorrect start date and due dates, not respecting inter­operation times multiplied by the stretching factor
• Multiplying technical waiting time by the stretching factor
• Incorrectly calculating the longest path in a network
• Not understanding the principle of forward or backward scheduling

Solutions:
(ESD stands for earliest start date, ECD for earliest completion date, LSD for latest start date, LCD for latest completion date.)

a.    ESD(op10) = 3, ECD(op10) = 3.5; ESD(op20) = 6.5, ECD(op20) = 7; ESD(op30) = 3, ECD(op30) = 3.5; ESD(op40) = 10, ECD(op40) = 11; ESD(order) = 0, ECD(order) = 12. Note the critical path in determi­ning the ESD(op40): The lower path is critical. The lead-time margin of the upper path is 2.

b.    LCD(op40) = 15, LSD(op40) = 14; LCD(op30) = 9.5, LSD(op30) = 9; LCD(op20) = 11, LSD(op20) = 10.5; LCD(op10) = 7.5, LSD(op10)=7; LCD(order) = 16, LSD(order) = 4. Note that — again — the lower path is critical. The lead-time margin of the upper path is again 2.

c.    ESD(op10) = 1.5, ECD(op10) = 2; ESD(op20) = 3.5, ECD(op20) = 4; ESD(op30) = 1.5, ECD(op30) = 2; ESD(op40 = 5.5, ECD(op40) =6.5; ESD(order) = 0, ECD(order) = 7. Note that both paths are critical.

d.    ESD(op10) = 0, ECD(op10) = 0.5; ESD(op20) = 0.5, ECD(op20) = 1; ESD(op30) = 0, ECD(op30) = 0.5; ESD(op40) = 3, ECD(op40) = 4; ESD(order) = 0, ECD(order) = 4. Note that the critical path has changed. The upper path is now critical. The lead-time margin of the lower path is 2.