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Decision for the location of Intermodal terminals in a rail-road network

Decision for the location of Intermodal terminals in a rail-road network. Anupam Kulshreshtha IIM - Lucknow. Problem Background. Problem set in the context of Konkan Railway RO-RO type of Intermodal services Services are on a linear network

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Decision for the location of Intermodal terminals in a rail-road network

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  1. Decision for the location of Intermodal terminals in a rail-road network Anupam Kulshreshtha IIM - Lucknow

  2. 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

  3. 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

  4. 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

  5. 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

  6. 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

  7. The Modeling Part

  8. 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

  9. 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

  10. Modeling • Notations and sets – i, j - Indices for origin and destination terminals (1 to n, n – no. of nodes) k - Index for trains yi - 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

  11. Modeling Si -Fixed expenses per period for ith node to serve as Intermodal terminal ciO -Handling capacity of the node for out going traffic cjI - Handling capacity of the node for incoming traffic Sk - Set of origin nodes served by train k St - Set of destination nodes served by train k Ck - Capacity of train k t - index for link capacity constraint iteration nodes ranging from 1 to n-1 (n – no. of nodes)

  12. Modeling • Objective Function – kijxkij.r kij - iSiyi • Constraints • Demand Constraints – kxkij  dij .yi i,j kxkij  dij .yj i,j

  13. Modeling • Node Capacity Constraints – ∑kjxkij cio. yii ∑kixkij cjI . yjj • Link Capacity Constraints – ∑i∑j xkij ≤ Ck t, k (For forward trains) i≤t, i≥Sk j≥t+1, j≤St

  14. 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

  15. Suggestions and feedback – • Some additional constraints • More appropriate assumptions

  16. Thanks

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