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

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

Mobilization of convoys This is multidisciplinary problem involving Mathematical modeling Operations Research Graph Theory Simulation Software Engineering Statistics

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?

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

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

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.

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.

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.

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.

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

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

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

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.

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.

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.

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.

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

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.

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

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.

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.

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.

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.

Fatigue of the Drivers How to model this constraint ?

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

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)

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.

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.

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

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.

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.

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.

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

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.

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

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

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

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

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 ---

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 --

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 --

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 --

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

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.

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.

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?

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

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

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

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

dr. am nageswara yogi, professor and hod department of mca tj institute of technology, bengaluru

Documents

war of logistics

enemy logistics slide

days war

bengaluru slide

complexities of modern

kms x200kms slide

logistics planning

lot of complexities