Transcript Network & Gantt chart
Resource analysis
Project management (lecture + seminar)
Introduction
• • Sometimes one or more resources (especially skilled workers) are equally or more important than time. According to priority, there are: – time-limited and – resource-limited projects. Priority can change over time but it is not wise to have double priorities.
Basic tools came from production engineering: loading (resource allocation)
Resources
• • • Definition: anything that is scarce and required for any activity in the project. Resources are constraints for the project.
Resources can be: – Non-storable: has to be renewed for each period e.g. work – Storable: depleted only by usage (remains available if not used) e.g. money The most common resource typology, the 4Ms: – – – – Men Machines Money (cost) Material – Other
Loading (resource allocation)
• • The assignment of work to an worker, machine or unit (generally: to a workstation) in time.
A workstation can be: – underloaded (load < capacity) – fully loaded (load = capacity) – overloaded (load > capacity) • • Fully loading is nearly impossible to reach except in flow production.
Underloading is the most common, because it respects time. Overloading leads to be late.
Defining resources for projects
• • • SOW WBS Task list – Resource needs given in resource-hours (e.g. man-hour, machine-hour) – Two forms of resource specification: • Rate-constant (can be changed to a constant function/pattern): constant usage rate defines the duration, too • Total constant: to finish the activity
What to do with non-linear duration-resource functions?
• • Use a computer Focus on quasi-linear parts of the functions
Capacity
• • Be realistic: – Usual efficiency – Estimated absenteeism, sickness, holidays – Existing commitments – Ancillary tasks and their resource needs – Any additional constraints (like methodology) and limitations (like work contracts) Also calculate with the possibilities (cost, time, trade-offs) to increase capacity
Optimum seeking procedures
• • Constraints: – Resource-limited projects – Time-limited projects – Resource-limited AND time-limited projects (question of priority) Methods: – Linear programming – Levelling – Allocation – Smoothing
Linear programming
• • Successful only for small networks (up to about 200 activities) Need for precise data
Levelling (simplest technique)
• • • Need for a previously produced starting
schedule.
Attempts to level out peaks and valleys in resource requirements by rescheduling some activities.
Difficulty of interactions between activities.
Allocation (for resource limited cases) • • • Allocation resources ‘Splitting’ an activity: stopping an activity, which is currently in progress, by the removal of its resources for use on an activity of higher priority.
Two procedures for allocation: – Serial: if only a few activities are splitable – Parallel: if many activities are splitable; more complicated method that needs more time and data
• •
Allocation when resources are limited
Serial procedure: 1.
2.
All activities in the project are ranked using constant priority rule. The most frequently used rule: ascending order of the LSTs with a tiebreaker of the ascending order of total floats (a kind of ‘ urgency ’ ).
Activities are scheduled in the above order at the earliest possible point in time consistent with the availability of resources and the precedence
requirements.
Step-by-step process: – – – Draw the network diagram for the logical connections Compute the activity times and total floats Plot a Gantt or time-scaled network in tandem with a resource histogram
•
Allocation when resources are limited
Parallel procedure: Activities are considered sequentially (sub-lists). Unscheduled activities are retained and ranked in the next period with new activities.
a
START
b c f g h d e k j i l
FINISH
The time-limited case
• Balancing the S-curve with milestones: Forcing early activities to start sooner
Smoothing (time limited)
• Aim is to produce a feasible schedule within the time constraints & provide as smooth a resource requirement profile as possible.
• Informational needs of smoothing: – Start time and timeframe (TPT or deadline) – Priority order of the resources required •
Prioritising
activities and
selecting
them in order for scheduling (critical activities have supreme priority).
• Finding the best place for the activity (
placing
). • Repeat the process with the next activity.
Prioritising activities
Considerables: • Resource type(s) and importance • Total work content (resource units per time multiplied with the duration for all resources used on the activity) • Available float Formula if no initial scheduling exists:
(Total work content) / (Float remaining)
In descending order (greatest first).
Placing
• The best position is the one that gives the lowest usage increase in the time span of the activity.
• Two ways of finding this position: – Visual – Sum of squares: • Calculate the sum of squared resource needs of each period within the questionable time frame (between the ES and LF time of the given activity) for every possible positioning • Choose the position with the lowest value
seminar
Defining resources for projects 2
• • • • • • SOW WBS Task list Logical connections (PNT) Gantt chart and histogram Levelling
Using the bar chart
• • • • Set up and analyse the network – Assign the resource data to the activities Draw the Gantt chart – Aggregate each resource time period by time period throughout the total project Cumulating (Summation or S Curve): Use levelling the load for optimization
Network with single resource data
0 0
START (0)
0 0 0
0
0 0 0 0
a
2
0 2
(1)
2 0 5 5 5 5
b (4) 5
10 2 2 0
c
8
0 10
(3)
10 2 5 3
d
5
3 7
(2)
10 10 10 0
e 3
0 13
(1)
13 13 0 0 13
FINISH (0)
13
0
13
activity
a b c d e Res. aggr.
Cum. res.
Resource units
11 10 9 8 7
6 5 4 3 2 1
5
5
1
1 4
Aggregation with a bar chart
(single resource, earliest start)
2
1 4
3
4 3 2
4
4 3 2
5
4 3 2
6
3 2
7
3 2
8
3
9
3
10
3
11 12 5
10
9
19
9
28
9
37
5
42
5
47
3
50
3
53
3
56 1
1
57 1
1
58
1 2 3 4 5 6 7 Time 8 9 10 11 12 13
1
1
59
13
activity
a b c d e Res. aggr.
Cum. res.
Resource units
11 10 9 8 7
6 5 4 3 2 1
1
1
1
1
Aggregation with a bar chart
(single resource, latest start)
2
1
3 4 5 6 7 8 9 10 11 12
3 3 3 4 3 2 4 3 2 4 3 2 4 3 2 4 3 2
1
2
3
5
3
8
3
11
9
20
9
29
9
38
9
47
9
56 1
1
57 1
1
58
1 2 3 4 5 6 7 Time 8 9 10 11 12 13
1
1
59
13
The S Curve analysis
• The minimum slope level is the less ‘critical’ from the viewpoint of availability
S Curve of the example
70 60 50 40 30 20 10 0 1 2 3 4 5 6 7 8 9 10 11 12 13 ES LS smoothest
Scheduling with constraints
• • • Three approaches: Allocation: Activities are scheduled so that an initially defined limit of resources or time is not exceeded. Levelling: A previously generated schedule must be given. Then it levels out the peaks and troughs without changing the TPT.
Smoothing: A start time, a TPT and resource priorities.
Other possibilities
• • • Alternative resources Alternative methods Alternative sequences (if there is no technical dependency)
•
Levelling the load
We must have a starting allocation of activities over time and a resource constraint (previous example).
• Trying to keep the original TPT unchanged means that critical activities should not be moved. Thus try to move activities with free float.
Solution
• • There are only 2 activities with free float: b & d
Which one to move and to where?
• Moving activity d 3 days in advance is eliminating the peak.
Resource units
11 10
3 2 1
9 8 7
6 5 4
1 2 3 4 5 6 7 Time 8 9 10 11 12 13
activity
a b c d e Res. aggr.
Cum. res.
1
1 4
5
5
2
1 4
3
4 3 -
4
4 3 -
5
4 3 -
6
3 2
7
3 2
5
10
7
17
7
24
7
31
5
36
5
41
8 9 10 11 12 13
3 2 3 2 3 2
5
46
5
51
5
56 1
1
57 1
1
58 1
1
59
S Curve
70 60 50 40 30 20 10 0 1 2 3 4 5 6 7 8 9 10 11 12 13 ES LS smoothest leveled
0 0 • 0
Effect of levelling
New „activity”: waiting for the resource (it is a lag, not a true activity) 0 2 0 10 0
c
(3)
0 0 2 2
8
10 0 0 0
a
2 (1)
0 10 0 13 0 2 5
START (0)
0 10
e (1)
d
(2) 0
0 0 10
3
13
5
0 0 5 5 10
b (4) 5
5 0 13 0 0 13
FINISH (0)
13
0
13 • Changes: new precedence relationship, floats, late start and finish times
Network with single resource data
0 0
START (0)
0 0 0
0
0 0 0 0
a
2
0 2
(2)
2 0 5 5 5 5
b (4) 5
10 • Resource limit: 5 2 2 0
c
8
0 10
(3)
10 2 5 3
d
5
3 7
(2)
10 10 10 0
e 3
0 13
(1)
13 13 0 0 13
FINISH (0)
13
0
13
0 0
START (0)
0
0
0
Network with multiple resource data
0 2 0 0 10 0
c (3A)
0 0 2 10 0 13
8 a (2A)
2 10
e (3B) 2 3
0 0 0 2 3 7 10 13 2 3 13 0 13
FINISH (0)
5 5 5
d (2B) 5
10 13
0
0 13 0 5 5 5 5 8
b (4B) 5
10
f (3A) 3
13 5 10 • Resource limits: 5A, 5B
Reading
• Lockyer – Gordon (2005): Chapter 17 & 18