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 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

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

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

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

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

The Modeling Part

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

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

Modeling Notations and sets – i, j - Indices for origin and destination terminals (1 to n, n – no. of nodes) k - Index for trains y i - Binary variable for selected node (as origin terminal) y j - Binary variable for selected node (as destination terminal) x k ij - Amount transported between selected nodes i and j through train k d ij - Demand between pair of nodes r k ij - Revenue between pair of nodes

Modeling S i - Fixed expenses per period for i th node to serve as Intermodal terminal c i O - Handling capacity of the node for out going traffic c j I - Handling capacity of the node for incoming traffic S k - Set of origin nodes served by train k S t - Set of destination nodes served by train k C k - Capacity of train k t - index for link capacity constraint iteration nodes ranging from 1 to n-1 (n – no. of nodes)

Modeling Objective Function –  k  i  j x k ij.r k ij -  i S i y i Constraints Demand Constraints –  k x k ij  d ij.y i  i,j  k x k ij  d ij.y j  i,j

Modeling Node Capacity Constraints – ∑ k  j x k ij  c i o. y i  i ∑ k  i x k ij  c j I. y j  j Link Capacity Constraints – ∑ i ∑ j x k ij ≤ C k  t, k (For forward trains) i≤t, i≥S k j≥t+1, j≤S t

Modeling Link Capacity Constraints – ∑ i ∑ j x k ij ≤ C k  t, k (For backward trains) j≤t, i≥S k i≥t+1, j≤S t 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

Suggestions and feedback – Some additional constraints More appropriate assumptions

Thanks