Dr. AM Nageswara Yogi, Professor and HOD Department of MCA TJ Institute of Technology, Bengaluru
51
Decision Support System for Mobilization of Army Convoys Dr. AM Nageswara Yogi, Professor and HOD Department of MCA TJ Institute of Technology, Bengaluru
Dr. AM Nageswara Yogi, Professor and HOD Department of MCA TJ Institute of Technology, Bengaluru
Dr. AM Nageswara Yogi, Professor and HOD Department of MCA TJ
Institute of Technology, Bengaluru
Slide 2
Introduction Mobilization of convoys Aim and Objective Features
in DSS Constraints Solution to the problem Shortest route between
source and destination Second shortest path User defined path Case
study Conclusions
Slide 3
Mobilization of convoys This is multidisciplinary problem
involving Mathematical modeling Operations Research Graph Theory
Simulation Software Engineering Statistics
Slide 4
Modern War involves lot of complexities War on terror in
Afghanistan Do you feel Americans and Pakistan working together?
What is the important reason in spite of many differences between
them, America still continues to align with Pakistan?
Slide 5
Reason: Logistics -- Pakistans geography helps to fight war in
Af. How to win the war? Plan Logistics to a high level of accuracy
Damage and Disrupt the Enemy Logistics
Slide 6
INTRODUCTION In Kargil (40 days war), first 22 days, many
causalities on our side. Reasons were analyzed -- 60 Kms from
Kargil, there were supply sheds of Pak army providing support to
terrorists. Logistics were destroyed by IAF with full strength (MiG
- 27 fighter squadron ) War was over within 18 days. Area of
operations 10kms X200kms
Slide 7
With the complexities of modern war, logistics is concerned not
only with the 1. movement and maintenance of forces, 2. evacuation
and hospitalization of personnel but also with storage and
distribution of weapons, food etc. The complexities of modern war
impose many strains on the logistic planners who must recognize 1.
the speed and depth of the operations, 2. vulnerability of line of
communications to air and ground attack and 3. vast organizational
need for the maintenance of modern forces.
Slide 8
Logistics planning is the intelligent forecasting of the
requirements of an operation. In early wars, armies brought
supplies with them. Men and animals like elephants, camels, horses
were used to carry the supplies. The development of motor vehicles
and railways revolutionized military transportation during WW I. WW
II was a war of logistics on a global scale. Apart from the motor
vehicles, the transport aircraft and supply through sea routes
considerably eased the situations.
Slide 9
In France, a high priority, high speed truck transport system
known as Red Ball Express between Normandy and Reims used some 100
truck companies to operate convoys in 1944. Results were excellent
in spite of wastages from accidents and breakdowns. Such huge motor
transport operations require exhaustive and meticulous
planning.
Slide 10
A Convoy is a group of vehicles with a leading vehicle called
the head of the convoy and the last vehicle is called the tail of
the convoy. Optimization of the movement of such convoys on a
network of roads between multiple sources and destinations is a
complex problem. It involves many constraints. These constraints
cannot be related mathematically and occur independently and arrive
dynamically. Move plans require a high standard of accuracy. Any
initial mistakes are likely to have cumulative effect.
Slide 11
Mobilization of convoys Evolving schedules of a number of
convoys manually and the subsequent monitoring control on a real
time basis becomes a herculean task, which needs lot of thinking
and variations in planning the moves
Slide 12
Due to reasons like Prioritization of the new movement of
convoys Natural disasters like land slide enemy actions.
Maintenance of vehicles The initial planned movement of convoys
which are on their way to various destinations will get disturbed
dynamically
Slide 13
Mobilization of convoys The convoys, which are already on move,
1. will have to wait at some places or 2. change their routes.
Therefore the problem becomes very complicated and many decisions
have to be taken. An on-line simulation model is the best avenue
for knowing and analyzing all the possible outcomes in such
situations. So there was a need to develop a DSS and a software to
simulate scenarios, which will help in training the officers
involved in such planning
Slide 14
AIM AND OBJECTIVE AIM AND OBJECTIVE The aim of the move plan of
convoys is to get men and materials at a new location quickly. The
objective was to design a DSS and develop a training software
package for scheduling of convoys so that the DSS must. 1. Help the
decision-maker to simulate and optimize routes in terms of
travelling distance from a source to the destination subject to the
various constraints. 2. Enable the decision-maker to obtain the
positions of scheduled convoys at specified date and time, so as to
keep track of the move plan. 3. Be capable of accepting the dynamic
modifications to network of roads and the convoy inputs at any
stage and generating fresh convoy schedules.
Slide 15
FEATURES IN DSS 1. It is possible to create a map of the
required portion of the area of interest by giving the positions of
the nodes and arcs (roads) joining them with all their
characteristics. 2. It is possible to schedule any number of
convoys by specifying starting date and time at the source,
destination along with the relevant information. The DSS supports
the user to schedule a convoy along a shortest path, second
shortest path or a user specified path between the source and the
destination. 3. The decision maker has the facility to find out the
status of the convoys at a specified date and time. 4. It is
possible to get total scheduled timetable of any running convoy
from the source to destination including the distance travelled,
time of arrival and departure of head and tail of the convoys at
each node, halt times along the confirmed path of the convoy.
Slide 16
5. It is possible to change convoys parameters and reschedule
all the affected convoys. 6. It is possible to change the path of a
running convoy from the next reaching node, 7. It is possible to
delete a scheduled convoy before it starts from the source node,
terminate a running convoy at the next reaching node and all the
affected convoys are automatically rescheduled. 8 It is possible to
block a road for a certain period. Those convoys passing through
this road will wait at the starting node of the blocked arc till
the arc block is lifted. User can change the convoys path provided
a route exists. 9 It is possible to estimate the starting date and
time from the source node for a convoy whose reaching date and time
at the destination node is specified.
Slide 17
1. Priority of convoys Ex: Action is progressing in the border
Providing trained personnel, medicines for injured, food and water,
equipment -- high priority Commander based on the information fix
priority to the convoys like which convoy should reach the front
area earliest. In the DSS model we assign number to convoys such as
1,2,3. DSS will assign convoy priority higher if number assigned is
lower.
Slide 18
Constraint -- Priority of convoys If two convoys of same
priority arrive at node around the same time, the DSS will allow
the convoy, which has reached earlier, to move. The following
convoy will move at a speed =Min (road speed, convoys speed) along
the common roads. -- No overtaking. If two convoys of different
priorities arrive a node around the same time and are going to
travel along common roads, then DSS will calculate the starting
time of Low priority convoy if it affects the higher priority
convoy. Algorithms are developed for two and extended to n number
of convoys. Arrival and departure times at the succeeding nodes
will be calculated as usual
Slide 19
Speed constraints Road speed (S r ) depends on the condition of
the road user will specify the gradient of road calculated as
follows If is the average road gradient in degs from starting node
to the end node of the road, Then speed of the convoy moving along
that road, Sc = Min(Sr, Sc)*(1- /90) (DSS uses radians degs are
taken for clarity), The convoy that is moving in opposite direction
will be moving along negative gradient Speed of that convoy =Sc =
0.90 * Min(Sr, Sc) Note: In case a slower moving convoy is moving
ahead of a convoy with higher or lower priority convoy, then the
speed of following convoy will restricted till the first convoy
reaches the next node, Lower priority convoy will be made to wait
at next node till tail of higher priority convoy leaves that node +
extra time.
Slide 20
Road block dynamic constraint The constraint will occur due to
Enemy action Natural calamity like Land slide Road will blocked for
a period of time. DSS will delete this road for that period of time
and re- schedules of the affected convoys. Decision maker will have
options like halting the convoys rescheduling depending on the
priorities changing destination of the affecting convoys
Slide 21
Classification of roads and convoys Road will be classified
depending max wt of a vehicle which can move on that road. For
Example a Road is classified as 9 means that vehicles more than 9
tons cannot move on that road. Convoy will be classified again
based on max wt of the vehicle. For example a convoy is classified
as 40 means that there is at least one vehicle whose wt is 40 tons.
Then this convoy cannot move on a road whose classification less
than 40. A convoy of higher classification cannot move on road of
lower classification. This is taken as a logical constraint during
modeling.
Slide 22
Restriction of movement along arcs Movement of convoys along
some roads will be restricted to Day only -- 0600 to 1800 hours
depends on location Night only 1800 to 0600 hours depends on
location Day and night only The convoys will be halted at a node
where it reaches within + or - 30 minutes of the stipulated time. +
or 30 can be changed by the commander of the move.
Slide 23
Restriction of movement of convoys Convoys themselves will
restricted move during Day only Night only Day and night only A day
only convoy can not move on night only road. This is also built as
logical constraint in DSS model.
Slide 24
One way roads constraint In this model one road means the
convoys can move from both directions but they cannot cross along
that road. If a convoy is moving along the one way road then the
convoy coming opposite will be made to halt at the node at the
other end.
Slide 25
Fatigue of the Drivers How to model this constraint ?
Slide 26
DSS model takes care of fatigue of Drivers by giving halts for
tea/coffee at specified nodes and also along the road. It is also
important that personnel breaks for lunch and dinner. Giving rest
to drivers will reduce fatigue and rest time can be utilized for
maintenance of vehicles by maintenance staff. DSS models allows the
commander to reschedule based on the requirements
Slide 27
SOLUTION TO THE PROBLEM A network of roads or a map consists of
a set of nodes connected by roads. The attributes of nodes are
name, number, longitude, latitude, node length, facilities like
parking, maintenance available or not. The attributes of each road
are starting node i, ending node j, distance (d i,j ) in km (if
there is no road between nodes i and j then d i,j = -1), road
speed, (S a,i,j -max speed of any vehicle along the arc), Road
classification (c i,j ), restriction of movement(r i,j day and
night/day only/night only), direction (one/two way)
Slide 28
Convoy attributes A scheduled convoy on the selected map is
identified by name / number, speed(S c ), total number of vehicles
(n), density (d- number of vehicles per km), restriction of
movement, classification (Cc), priority, starting date and time at
the source or the reaching date and time at the destination, source
and destination.
Slide 29
To find the shortest route between the source node and
destination node Let A = (a i,j ) be n x n matrix which defines
whether an arc exists or not between two nodes, in which a i,j = 1
if arc is available from node i to j, otherwise it is zero. Let
R=(r i,j ) be n x n matrix representing the arc restriction
regarding the movement of convoys along the arc joining the nodes i
and j. The elements are d&n or d or n as per the following
definitions: r i,j = d & n if a i,j = 1 and the arc joining i
and j is Day and Night. r i,j = d if a i,j = 1 and the arc is Day
Only. r i,j = n if a i,j = 1 and the arc is Night Only. r i,j = d
if a i,j = 0 meaning arc does not exist from i to j.
Slide 30
Let C= (c i,j ) be the arc classification matrix of order n x
n, whose elements are the maximum weight of a vehicle which can
pass through the nodes i and j. C i,j =Max. weight of the vehicle
if a i,j = 1. If a i,j = 0, then C i,j = 0. The time t i,j taken to
travel from node i to j by a convoy moving with a speed S c will be
calculated as follows provided d i,j -1. If the convoy is Day and
Night then t i,j = d i,j / S c if S c S a,i,j and C c c i,j t i,j =
d i,j / S a,i,j if S c > S a,i,j and C c c i,j If the convoy is
Day Only then t i,j = d i,j / S c if S c S a,i,j and C c c i,j and
r i,j n t i,j = d i,j /S a,i,j if S c > S a,i,j and C c c i,j
and r i,j n If the convoy is Night Only then t i,j = d i,j / S c if
S c S a,i,j and C c c i,j and r i,j d t i,j = d i,j / S a,i,j if S
c > S a,i,j and C c c i,j and r i,j d
Slide 31
If t i,j can not be calculated due to constraints like
arc/convoy classifications or restriction of movement, then the
path does not exist from i to j for the convoy to be scheduled. Now
we utilize Dijkstras algorithm to find the shortest route between
the source node and the destination node for the scheduled convoy.
The route thus found takes the minimum travelling time, excluding
the wait and routine halts. Overall journey time is the time
between the passing of the leading vehicle (Head) from the source
node and the reaching time at the destination by the last vehicle
(Tail) of the column, which includes the wait time and routine
halts.
Slide 32
To find the second shortest path Consider that the first
shortest path from the source node N1 to the destination node Nn
for a specified convoy found using Dijkstras algorithm is passing
through the nodes N0 - -N1 - -N2 - - N3- -N4.Nn-1 - -Nn. To find
the second shortest path for same convoy with starting node N1 and
destination node Nn, we follow the following procedure: 1. We first
remove the arc joining N0 - - N1. 2. We find the available route
between N0 and Nn using the Dijkstras algorithm. If the path
exists, let this path takes a travelling time t0. if the path does
not exist, we move to the next step.
Slide 33
4. Now remove the arc joining the nodes N1 - - N2 and restore
the arc between No and N1 5. We compute the route between N0 and
Nn. Let this route takes a travelling time t1, if it exists. If the
path does not exist, then continue the process till we reach the
arc joining Nn-1 - -Nn. If there is no path found, display the
message second shortest path does not exist. 6. For more details on
shortest path algorithms please refer any text book on Graph
Theory. 7. We find t* = min(t 0, t 1,, t m ), mn. The route which
takes a travelling time t* is the second shortest route.
Slide 34
To schedule a convoy along the User Defined Path from its
source to destination Commander wants to schedule the convoy on his
choice that is User Defined Path. Selected map along with roads and
nodes will be displayed on the screen All those arcs whose
classifications are less than the convoy classification are removed
from the displayed map as the scheduled convoy will not be able to
move along these arcs. If the convoy is day only or night only then
the arcs that are night only or day only respectively will be
removed from the displayed map. Now user can select the route of
the scheduled convoy from source node( in blue colour circle) to
any other intermediate node joining this node with the help of the
mouse. Then from this node select the next node joining the
previous node. continue this process till we reach the destination
node (in black colour circle). If any along selected arc, speed
restriction(arc speed is less than the convoy speed) occurs, then
suitable warning message will appear. User will have the choice of
moving the convoy with the Min (arc speed, convoy speed). Once the
user reaches the destination node user can confirm this path. The
scheduled timetable will be generated
Slide 35
To schedule a convoy whose reaching date and time at the
destination is specified Another notable feature of DSS model is
that a convoy whose reaching date and time is specified at the
destination can be scheduled. The DSS model will estimate the
approximate starting date and time of the convoy from the source
node using iteration technique so that the convoy will reach the
destination at the required reach date and time. The model takes
into account the priority, routine and node halts, lunch/dinner
time into consideration. The path of this convoy can also be
confirmed along shortest path or second shortest path or user
defined path.
Slide 36
Software project data Front-end : VB 6.0No. front-end forms :
43 Back end : MSACCESSNo tables : 10 No. of modules : 18KLOC : 8.18
No. pages of documents :258 (5 documents) No. of reports designed :
8 Estimated Effort: 45 PMs Actual Effort : 60 PMs (2 asstX6 + 1 Off
X24 + 1PDX24) Actual effort Yogi- Patil Bailey- Basili Barry Boehm
COCO MO-II Doty Walston -Felix 60501430 4836
1.01.24.342.062.011.261.7
Slide 37
DSS software is developed using in VB 6.0 with backend database
in MSACCESS. The working of the DSS system can be explained with
the help of the following example. The first step is the creation
of road map under consideration by giving the characteristics of
nodes and roads
Slide 38
Start node End noded i,j (km/hr) S a,i,j (km/hr) C i,j
Restricti on directio n Gradie nt HassanMangalore 1104570 d&n2
way HassanBangalore 2003070 n2 way KolarBangalore 704570 d1 way
TirupatiChittor 11040 d&n2 way ChittorKolar 1202518 d&n2
way ChennaiKanchipur am 755024 d&n2 way Kanchipu ram Chittor
855040 n2 way Arc characteristics
Slide 39
Notes: 1. Arc from Hassan to Bangalore is blocked from 1800 to
2000 hours on 19/04/2003. 2. Routines halts are 0140-0200,
0340-0400, 0540-0600, 0740-0800,etc., 3. Lunch time 1300-1400 and
Dinner time 2100-2200. Table 2:scheduled convoys characteristics
Name/n umber S c Km/hr n/drestri ction CcCc Priorit y
Source/starting date/time Destinatio n
C1/55535450/30d&n92Tirupathi/ 18/04/03/ 1130 Mangalore
C2/44445400/20d&n91Chennai/ 18/04/03/ 1130 Mangalore
C3/33340500/25d&n91Mangalore/ 18/04/04/ 1400 Chennai
Slide 40
Table 3(a): scheduled time table of convoy C1 NodeConvoys head
arriving date and time Heads wait time Heads departure time Convoys
Tail Arriving time Tails wait time Tails departure time Tirupathi
--00:4018/04/03/1130 02:0818/04/03/1218
Chittor18/04/03/161807:0018/04/03/221818/04/03/164607:0018/04/03/2246
Kolar19/04/03/040603:0919/04/03/065519/04/03/043403:2919/04/03/0723
Banglore19/04/03/091513:4419/04/03/205919/04/03/100313:4419/04/03/2227
Hassan20/04/03/053900:4020/04/03/053920/04/03/062700:4020/04/03/0627
mangalore20/04/03/0927 -- 20/04/03/1015 ---
Slide 41
Table 3(a): scheduled time table of convoy C1 NodeConvoys head
arriving date and time Heads wait time Heads departure time Convoys
Tail Arriving time Tails wait time Tails departure time Tirupathi
--00:4018/04/03/1130 02:0818/04/03/1218
Chittor18/04/03/161807:0018/04/03/221818/04/03/164607:0018/04/03/2246
Kolar19/04/03/040603:0919/04/03/065519/04/03/043403:2919/04/03/0723
Banglore19/04/03/091513:4419/04/03/205919/04/03/100313:4419/04/03/2227
Hassan00:4020/04/03/053920/04/03/062700:4020/04/03/0627 mangalore
-- 20/04/03/1015 --
Slide 42
Table 3(b): scheduled time table of convoy C2
chennai--00:2018/04/03/1130 01:4918/04/03/1219 Kanchipur am
18/04/03/143003:5018/04/03/180018/04/03/145903:5018/04/03/1829
Chittor18/04/03/201301:4018/04/03/201318/04/03/204200:4018/04/03/2042
Kolar19/04/03/024103:1919/04/03/060019/04/03/031003:3919/04/03/0629
Banglore19/04/03/073414:2619/04/03/200019/04/03/082314:0619/04/03/2029
Hassan20/04/03/044000:2020/04/03/044020/04/03/050900:4020/04/03/0509
Mangalore20/04/03/0726 -- 20/04/03/0815 --
Slide 43
Table 3(c): scheduled time table of convoy C3
Mangalore--00:2018/04/03/1400 01:1618/04/03/1436
Hassan18/04/03/170502:5518/04/03/180018/04/03/180102:3518/04/03/1836
Bangalore19/04/03/024007:4318/04/03/100319/04/03/031607:4319/04/03/1039
Kolar19/04/03/120801:4019/04/03/120819/04/03/124401:4019/04/03/1244
Chittor19/04/03/183601:2019/04/03/183619/04/03/191201:2019/04/03/1912
Kanchipur am
20/04/03/220300:2020/04/03/220320/04/03/223900:2020/04/03/2239
Chennai20/04/03/0016 -- 20/04/03/0052 --
Slide 44
CONCLUSIONS 1. A DSS for optimal scheduling of convoys by road
in terms of travelling distance is developed. 2. This model will be
useful for training decision-makers in simulating a large scenario
in real time planning. 3. The model is tested over a map with about
500 nodes and scheduling 55 convoys with various priorities and
from different sources to destinations. 4. The model was also
tested at two user sites for various cases and working
satisfactorily. 5. The model was used during Operation
Parakram
Slide 45
APPENDIX A South India map was created with 200 nodes and 258
roads connecting these nodes. It took about 3 days for a computer
operator to create the complete map database. The DSS model was run
on a pIII with speed of 550 Mhz. it was observed that to compute
the shortest path between a source and destination having 23 nodes
in between them, the CPU time was 6 seconds and for the second
shortest path took 9 seconds when other convoys were scheduled on
the map. It was observed that the time to compute the shortest path
and the second shortest path starts increasing as more number
convoys starts overlapping along the paths and affect the movement
of each other due to priorities, speeds, road conditions. It was
observed that, when fifteen convoys were scheduled, the computing
time to find the shortest and the second shortest path went up to
39 seconds and 190 seconds respectively. We found that more than 8
convoys were affecting the movement of this convoy.
Slide 46
Computing time for shortest path for a convoy whose reaching
date and time was given at the destination was found to be 36
seconds when five convoys were running along the some common routes
and the time increased to 104 seconds when fifteen convoys were
running along some common paths. The increase in time is due to
iterations involved in finding the starting date and time at the
source node.
Slide 47
WHAT IF SCENARIOS 1. Is there a path existing between the
specified source and destination? 2. If yes, schedule the convoy
either on a shortest path or on a second shortest path or on a
user-defined path? 3. What is total journey time? 4. When (date and
time) will the convoy reach destination? 5. What is the average
spped? 6. What is the total wait time during the journey?
Slide 48
A higher priority convoy C 2 which left some other node will be
reaching the same destination node of C 1. it will pass through the
some of the common arcs. 1. how much time will C 1 wait because of
the convoy C 2 at the first common node? 2. What is the revised
schedule timetable of C 1 ? 3. What will be the additional wait
time of C 1 ? 4. Is it possible to schedule C 1 on a different path
so that C 2 will not affect the movement of C 1 and the total wait
time of C 1 reduces? 5. Would like to change the priority of C 2
and reschedule, so that C 2 will not affect the schedule of C 1 ?
Or would like to change the priority of C 2 less than that of C 1
and reschedule? WHAT IF SCENARIOS
Slide 49
Another convoy from C 3 is moving in the opposite direction of
C 1 1. Is there a one way between source and destination? 2. Are
the convoys going to meet along this one way? 3. If so? Which
convoy will wait at the previous node to make way for other? 4.
What is the additional wait time of each convoy. A day only convoy
C 4 has to reach the destination node on 25 Aug. 2003 at 1000 whose
starting node is specified. 1. What should be starting date and
time at source node? 2. Are there convoys, which affect the
movement of C 4 ? 3. If so?, what is the additional wait time? 4.
Suppose C 4 reaches a node at 1630 and it is going to halt there,
because it will be reaching the next node around 1900 hours. Would
you like to continue journey upto next node even though it is the
day only convoy. Please note that day only convoys will travel
between 0600 hours to 1800 hours. WHAT IF SCENARIOS
Slide 50
Based on the latest information an arc was closed due to
landslide from 1000 hours on 20 June 2003 to 1500 hours on 25 June
2003. questions addressed by DSS are 1. Which are all the convoys
affected due to this change of environment? 2. How many convoys
have to wait at the previous node? 3. Would like to change their
paths if exists? 4. Would like to change the destination from this
node and get the schedule table? 5. Would you like to terminate the
convoy at the some other node? 6. Would you like to delete the
convoy if is not yet started from the source node? 7. Reschedule
all convoys after each of option mentioned in above questions ( 1 )
to ( 6 )? WHAT IF SCENARIOS
Slide 51
User can build the required scenario and feed the data to the
model in the specified input forms. Output will be generated in the
form of reports. Required reports can be generated