An Activity and Arrow Arranging Algorithm for Clarity in Schedule ...

An Activity and Arrow
Arranging Algorithm for
Clarity in Schedule Network
Diagrams
by
Gunnar Lucko
Catholic University of America
ICCCBE-XI Conference
June 14, 2006

Overview
Tradition versus Software-Generated Schedules
Fonts and Colors, Space and Symbols
Arranging Algorithm
Application Example
Conclusion and
Recommendations

Introduction
“Traditional” Scheduling
developed with paper and pencil
activities and arrows (time and logic information
of schedule) arranged intuitively
schedulers had manual drafting skills
“Modern” Scheduling
ubiquitous software packages require only
entering tabular time and logic information or by
clicking into a bar chart
poor default settings for diagrams (Lucko 2005)

Software-Generated Schedules
Lucko (2005)
definition for schedule: contains time and logic
Bar (Gantt) charts since 1917
no layout guidance; ; by default do not contain
logic; imply “sequence” by stepping down;
fenced bar chart (Melin and Whiteaker 1981)
Activity-on
on-node node diagram
no layout guidance; ; focus on logic; default
grid cells squeezes activities and arrows;
poor 10:1 space distribution (Lucko 2005)

Software-Generated Sample

Fenced Bar Chart
Mob.
A
B
C
D
E
F
G
H
I
J
K
L
M
T/O
J
J
I
K
K
M
L
L
L
10 20 30 40 50 60 70 Days

Software
Software-Generated AON
Generated AON
1010
02/15/05
A
02/04/05
03/14/05
03/03/05
1000
01/26/05
Mob
01/26/05
02/04/05
02/04/05
5
1020
02/04/05
B
02/04/05
02/18/05
02/18/05
1050
02/07/05
E
02/04/05
02/28/05
02/25/05
1030
02/18/05
C
02/18/05
02/28/05
02/28/05
1070
03/02/05
G
02/25/05
03/24/05
03/21/05
1100
03/14/05
J
03/03/05
04/08/05
03/30/05
1060
02/28/05
F
02/28/05
03/24/05
03/24/05
1040
03/15/05
D
03/03/05
04/08/05
03/29/05
1080
04/12/05
H
03/24/05
04/20/05
04/01/05
1090
03/24/05
I
03/24/05
04/08/05
04/08/05
1110
04/13/05
K
03/24/05
05/04/05
04/14/05
1130
04/20/05
M
04/01/05
05/04/05
04/15/05
1120
04/08/05
L
04/08/05
05/04/05
05/04/05
1140
05/04/05
T/O
05/04/05
05/09/05
05/09/05

Font and Color
Serif-type fonts more legible
than sans-serif serif type fonts
Mixed Capitalization more legible
THAN ALL CAPITAL LETTERS
Font size matters
font size matters
Color can highlight critical path, add to
richness of information: : hue (color), value
(darkness), saturation (intensity)
Contrast can help, but may distract

Space and Symbols
Allocations of activities and arrows relative to
each other
division of space between graphical elements,
currently 10:1 imbalance as per Tufte’s s data
density (2001)
reduction of “chart fluff” in exchange for clarity
through rich information
activities should be arranged on regular grid
arrows should be funneled along a clearly
visible path along their entire length

Schedule Graphics Details

Arranging Schedule Elements
Activities
possible arrangements from left to right (semi-
time-scaled):
horizontal or diagonal “spine”
full (both sides of spine) or half (one side only)
Arrows
for displaying start-start, start, start-finish, finish-
finish, finish-start, start, intermediate (% complete),
software used several ways

Breakdown of Approach
Consider good practices for graphics design
Assign activities to grid columns
is easy - solved analogous to resource leveling
(Callahan et al. 1992)
Assign activities to grid rows
is difficult - triple objective function for arrows,
research underway at CUA
shortest + fewest bends + fewest crossings
Assign funneling of arrows through grid
fine-tune path to reduce crossings

Arranging Algorithm
Columns
C j = C i + max P 1 to i count predecessor chain
Crossings
X = ½ · k · (k - 1) Purchase (2002)
k arrows intersecting
1 ? 3

Arranging Algorithm
Step 0: Layout
Step 1: CPM calculations
Step 2: Column allocation
Step 3: Sort activities by ES; If activities have same ES then sort s
by number of
successors; Else if activities have same number of successors then sort by duration;
Else if activities have same duration then sort by name
Step 4: Draw activities into first columns from top to bottom and d connect with
predecessors
Step 5: Repeat for next column
Step 6: Move column vertically up or down activities on critical path align horizontally
(“spine”)) [Crossings[
unchanged]
Step 7: Count total number of crossings
Step 8: For non-critical activities generate [non-overlapping overlapping ] partial successor paths,
ignoring critical activities. For partial successor path, check if moving it to other side
reduces crossings; If crossings are reduced then keep move; Else do not keep move
Step 9: Counts direct predecessors and direct successors on same side of spine (DPSS
and DSSS) and direct predecessors and direct successors on different side of spine
(DPDS and DSDS) to achieve a balanced distribution, ignoring critical activities
If balance B = (DPDS+DSDS) - (DPSS+DSSS) ≥ 0 then check if moving activity to other
side reduces crossings; If crossings are reduced then keep move; Else do not keep move;
Else go to next activity

Example: Activity List
Activity
Dur.
Successors
ES
LS
EF
LF
TF
FF
Mob. 7 A, B, E 0 0 7 7 0 0
A 19 D, I, J 7 13 26 32 6 0
B 10 C 7 7 17 17 0 0
C 6 D, F, J 17 17 23 23 0 0
D 18 L 26 33 44 51 7 7
E 15 F, G 7 8 22 23 1 0
F 17 H, I, K 23 23 40 40 0 0
G 16 H, I, K 22 24 38 40 2 2
H 6 M 40 53 46 59 13 0
I 11 L 40 40 51 51 0 0
J 19 L 26 32 45 51 6 6
K 15 T/O 40 54 55 69 14 14
L 18 T/O 51 51 69 69 0 0
M 10 T/O 46 59 56 69 13 13
T/O 3 N/A 69 69 72 72 0 0
Boldface
indicates
critical path

Example: Initial Configuration
24 crossings,
entanglement
40 13 46
46 13 56
H
6
M
10
53 0 59
59 13 69
0 0 7
7 0 17
17
0 23
23 0 40
40 0 51
51 0 69
69 0 72
MOB
7
B
10
C
6
F
17
I
11
L
18
T/O
3
0 0 7
7 0 17
17 0 23
23 0 40
40 0 51
51 0 69
69 0 72
7 1 22
E
15
22 2 38
G
16
26 7 44
D
18
40 14 55
K
15
8 0 23
24 2 40
33 7 51
54 14 69
ES
TF
EF
7 6 26
26 6 45
Name
Dur.
A
19
J
19
LS
FF
LF
13 0 32
32 6 51

Example: Improved Configuration
Reduced to 9
crossings,
6 possible with
better path E-F
and swap of K-H
7 6 26
A
19
26 7 44
D
18
33 7 51
26 6 45
J
19
13 0 32
32 6 51
0 0 7
MOB
7
7 0 17
B
10
17
0 23
C
6
23 0 40
F
17
40 0 51
I
11
51 0 69
L
18
69 0 72
T/O
3
0 0 7
7 0 17
17 0 23
23 0 40
40 0 51
51 0 69
69 0 72
7
1
22
22 2 38
40 13 46
46 13 56
E
15
G
16
H
6
M
10
8 0 23
24 2 40
53 0 59
59 13 69
ES
TF
EF
40 14 55
Name
Dur.
K
15
LS
FF
LF
54 14 69

Conclusions
Goal
to automatically generate clear schedules
Recent research
investigates building up rather than permutation
replicates more human intuition in arranging
develops a comprehensive list of parameters
for 3D network structure, no crossings
examines mathematics literature to create proof
proposes to arrange activities close to “spine”
by criticality (inverse to float)

Thank you!
Do you have
any questions?