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![Page 1: Decision for the location of Intermodal terminals in a rail-road network Anupam Kulshreshtha IIM - Lucknow.](https://reader036.fdocuments.us/reader036/viewer/2022082817/56649db05503460f94a9df07/html5/thumbnails/1.jpg)
Decision for the location of Intermodal terminals in a rail-road network
Anupam KulshreshthaIIM - Lucknow
![Page 2: Decision for the location of Intermodal terminals in a rail-road network Anupam Kulshreshtha IIM - Lucknow.](https://reader036.fdocuments.us/reader036/viewer/2022082817/56649db05503460f94a9df07/html5/thumbnails/2.jpg)
Problem Background
Problem set in the context of Konkan Railway RO-RO type of Intermodal services
Services are on a linear network 21 stations covered in Konkan service from Roha to
Mangalore in 480 Kms. Currently three stations Roha(Kolad), Verna and
Mangalore are Intermodal providing services in two stretches
Different network operators are managing the two routes.
Objective is to optimally increase loading and unloading stations on these routes
![Page 3: Decision for the location of Intermodal terminals in a rail-road network Anupam Kulshreshtha IIM - Lucknow.](https://reader036.fdocuments.us/reader036/viewer/2022082817/56649db05503460f94a9df07/html5/thumbnails/3.jpg)
Railway problems in Research literature
Main Issues – Problem of routing trains through railway stations Overall time table generation Issues regarding train linking Optimal utilization of infrastructure Crossing of trains in single and multiple line tracks Blockage of lines Number of sidings required and their length Scenarios with constant as well as variable train speeds Real time scheduling and timetable changes Incorporating uncertainty in train dispatches Reforming tracks and impact on quality of time tables
![Page 4: Decision for the location of Intermodal terminals in a rail-road network Anupam Kulshreshtha IIM - Lucknow.](https://reader036.fdocuments.us/reader036/viewer/2022082817/56649db05503460f94a9df07/html5/thumbnails/4.jpg)
Railway problems in Research literature
Main Issues contd.. Expected dispatching delays Suburban rail transport systems Minimizing required fleet size of locomotives Minimizing cost incurred by unloaded running (dead
heading) of locomotives Simultaneous allocations of locomotives and rail cars Allocation of platforms
![Page 5: Decision for the location of Intermodal terminals in a rail-road network Anupam Kulshreshtha IIM - Lucknow.](https://reader036.fdocuments.us/reader036/viewer/2022082817/56649db05503460f94a9df07/html5/thumbnails/5.jpg)
Issues in Intermodal literature
Cooperation between Drayage companies Allocation of shipper and receiver locations to a terminals Redistribution of trailer chassis and load units for drayage Pricing strategies Scheduling of trucks trips Design of Intermodal terminals Capacity levels of equipments and labour Allocation of capacities to jobs Scheduling of Jobs Infrastructure network configuration and terminal locations
![Page 6: Decision for the location of Intermodal terminals in a rail-road network Anupam Kulshreshtha IIM - Lucknow.](https://reader036.fdocuments.us/reader036/viewer/2022082817/56649db05503460f94a9df07/html5/thumbnails/6.jpg)
Issues in Intermodal literature
Network pricing strategies Redistribution of railcars and load units in the network Load Order of trains Selection of routing and services for Intermodal
operators
![Page 7: Decision for the location of Intermodal terminals in a rail-road network Anupam Kulshreshtha IIM - Lucknow.](https://reader036.fdocuments.us/reader036/viewer/2022082817/56649db05503460f94a9df07/html5/thumbnails/7.jpg)
The Modeling Part
![Page 8: Decision for the location of Intermodal terminals in a rail-road network Anupam Kulshreshtha IIM - Lucknow.](https://reader036.fdocuments.us/reader036/viewer/2022082817/56649db05503460f94a9df07/html5/thumbnails/8.jpg)
Situation Details
Services on a linear network considered Some candidate nodes to serve as Intermodal terminals Some nodes already serving as Intermodal terminals
(relaxed for now) A given set of existing train services operating between
certain stations Extension of trains beyond current end points ruled out Trains can be made to serve any intermediate station
on the route Cost of such stoppages not considered as yet
![Page 9: Decision for the location of Intermodal terminals in a rail-road network Anupam Kulshreshtha IIM - Lucknow.](https://reader036.fdocuments.us/reader036/viewer/2022082817/56649db05503460f94a9df07/html5/thumbnails/9.jpg)
Situation Details
Making a node Intermodal shall involve a fixed running cost per period
The capacity of each node for outgoing as well as incoming traffic is limited
The line capacity is limited by the capacity of currently operating trains
Demand can be fulfilled only if a direct train available between a certain pair of stations
Demand and revenue between pair of stations given as parameters
Decision variables are location of terminals and demand allocation to trains for different pairs selected
![Page 10: Decision for the location of Intermodal terminals in a rail-road network Anupam Kulshreshtha IIM - Lucknow.](https://reader036.fdocuments.us/reader036/viewer/2022082817/56649db05503460f94a9df07/html5/thumbnails/10.jpg)
Modeling
Notations and sets –
i, j - Indices for origin and destination terminals (1 to n, n – no. of nodes)
k - Index for trainsyi - Binary variable for selected node (as origin terminal)
yj - Binary variable for selected node (as destination terminal)
x kij - Amount transported between selected nodes i and j through train k
dij - Demand between pair of nodes
r kij - Revenue between pair of nodes
![Page 11: Decision for the location of Intermodal terminals in a rail-road network Anupam Kulshreshtha IIM - Lucknow.](https://reader036.fdocuments.us/reader036/viewer/2022082817/56649db05503460f94a9df07/html5/thumbnails/11.jpg)
Modeling
Si - Fixed expenses per period for ith node to serve as Intermodal terminal
ciO - Handling capacity of the node for out going
trafficcj
I - Handling capacity of the node for incoming traffic
Sk - Set of origin nodes served by train kSt - Set of destination nodes served by train kCk - Capacity of train kt - index for link capacity constraint iteration nodes
ranging from 1 to n-1 (n – no. of nodes)
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Modeling
Objective Function –
kijxkij.r
kij - iSiyi
Constraints
Demand Constraints –
kxkij dij .yi i,j
kxkij dij .yj i,j
![Page 13: Decision for the location of Intermodal terminals in a rail-road network Anupam Kulshreshtha IIM - Lucknow.](https://reader036.fdocuments.us/reader036/viewer/2022082817/56649db05503460f94a9df07/html5/thumbnails/13.jpg)
Modeling
Node Capacity Constraints –
∑kjxkij ci
o. yi i
∑kix
kij cj
I . yj j
Link Capacity Constraints –
∑i∑j xkij ≤ Ck t, k (For forward trains)
i≤t, i≥Sk
j≥t+1, j≤St
![Page 14: Decision for the location of Intermodal terminals in a rail-road network Anupam Kulshreshtha IIM - Lucknow.](https://reader036.fdocuments.us/reader036/viewer/2022082817/56649db05503460f94a9df07/html5/thumbnails/14.jpg)
Modeling
Link Capacity Constraints –
∑i∑j xkij ≤ Ck t, k (For backward trains)
j≤t, i≥Sk
i≥t+1, j≤St
For current size (21 nodes) problem can be solved directly at Cplex(around 2000 continuous variables and 21 binary variables)
For larger size, need to adapt Benders Decomposition
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Suggestions and feedback –
Some additional constraints
More appropriate assumptions
![Page 16: Decision for the location of Intermodal terminals in a rail-road network Anupam Kulshreshtha IIM - Lucknow.](https://reader036.fdocuments.us/reader036/viewer/2022082817/56649db05503460f94a9df07/html5/thumbnails/16.jpg)
Thanks