an integrated train scheduling and infrastructure...

Scientia Iranica E (2017) 24(6), 3409{3422

Sharif University of TechnologyScientia Iranica

Transactions E: Industrial Engineeringwww.scientiairanica.com

An integrated train scheduling and infrastructuredevelopment model in railway networks

M. Shakibayifara, E. Hassannayebib;�, H. Mirzahosseinc, Sh. Zohrabniad andA. Shahabie

a. Department of Transportation Engineering and Planning, Iran University of Science & Technology, Tehran, Iran.b. Department of Industrial Engineering, Tarbiat Modares University, Tehran, Iran.c. Department of Civil Engineering, Faculty of Engineering, Imam Khomeini International University (IKIU), 34149, Qazvin, Iran.d. Faculty of Management and Accounting, Allameh Tabataba'i University (ATU), Tehran, Iran.e. School of Industrial Engineering, Islamic Azad University, Tehran South Branch, Tehran, Iran.

Received 7 April 2016; received in revised form 28 August 2016; accepted 1 October 2016

KEYWORDSTrain scheduling;Railway infrastructuredevelopment;Capacity expansion;Networkdecomposition;Con ict resolution.

Abstract. The evaluation of the railway infrastructure capacity is an important taskof railway companies. The goal is to �nd the best infrastructure development plan forscheduling new train services. The question addressed by the present study is how theexisting railway infrastructure can be upgraded to decrease the total delay of existing andnew trains with minimum cost. To answer this question, a mixed-integer programmingformulation is extended for the integrated train scheduling and infrastructure developmentproblem. The train timetabling model deals with the optimum schedule of trains on arailway network and determines the best stop locations for both the technical and religiousservices. We developed two heuristics based on variable �xing strategies to reduce thecomplexity of the problem. To evaluate the e�ect of railway infrastructure developmenton the schedule of new trains, a sequential decomposition is adopted for Iranian railwaynetwork. The outcomes of the empirical analysis performed in this study allow to gainbene�cial insights by identifying the bottleneck corridors. The result of the proposedmethodology shows that it can signi�cantly decrease the total delay of new trains with themost emphasis on the bottleneck sections.

© 2017 Sharif University of Technology. All rights reserved.

1. Introduction

The passengers' demand on railway transportation isexpected to increase signi�cantly in the future. Hence,the railway network capacity has to be improved to

*. Corresponding author.E-mail addresses: m [email protected] (M.Shakibayifar); [email protected] (E. Hassannayebi);[email protected] (H. Mirzahossein);[email protected] (Sh. Zohrabnia);St a [email protected] (A. Shahabi)

doi: 10.24200/sci.2017.4397

handle this future demand. Constructing or upgradingrailway infrastructure is an option for increasing thecapacity. The railway capacity varies according todi�erent factors, e.g. train heterogeneity, train speed,stop patterns, infrastructure layout, and schedule ro-bustness [1]. Train stop time de�nes the amount oftime trains spend stopped at a location. The stoppingpattern is a decisive factor to determine the operationalcapacity of the network. In Iranian railway network,trains stop at intermediate stations for load/unloadingpassenger, technical services as well as praying services.The last factor is a speci�c religious related constraintthat signi�cantly a�ects the train timetables. Based

3410 M. Shakibayifar et al./Scientia Iranica, Transactions E: Industrial Engineering 24 (2017) 3409{3422

on religious regulation, during prede�ned praying timewindows, train must stop to perform praying services.Passengers get o� the train and pray in the stationmosque during the time window. However, the prayingtime windows change over time and location due to thelocal geographic position. Thus, the optimal patternof stop for praying service has direct in uence on thecapacity of the Iranian railway system. The optimiza-tion of the railway lines' capacity plays an importantrole in railway transportation industry. The e�ectiveutilization of a railway network results in the avoidanceof resource con icts, and, at the same time, �ndingan appropriate balance between capacity utilizationand level of service [2]. This paper is concerned withRailway Network Infrastructure Development Problem(called RNIDP). The proposed approach combines thescheduling of new trains and re-scheduling of existingtrains by choosing the best railway infrastructure devel-opment scenario for decreasing train delays. The focusof this work is on the combinatorial analysis of infras-tructure con�guration optimization and timetable gen-eration. In other words, our work addresses the railwayinfrastructure planning and train timetabling problemin one integrated model. To the best of our knowledge,this approach has not been extensively investigated inliterature, and if so, not to the equivalent scope towhich it is taken in this study. In this paper, RNIDPis formulated as a Mixed-Integer Linear Programming(MILP) model. The key contribution of the study is theintegrated investigation of the train timetabling andinfrastructure development problems. The previousstudies in the literature present an independent studyof train timetabling and capacity planning problems.To deal with such a complex optimization problem,a novel network decomposition approach is presented.Furthermore, in order to solve the resulting sub-problem e�ciently, a fast heuristic based on variable�xing strategy is proposed.

The rest of the paper is as follows. In Section 2,a literature review of train timetabling problem andrelated issues is discussed. In Section 3, the problemis described in detail. In Section 4, the mathematicalprogramming formulation for RNIDP is described. InSection 5, heuristic algorithms are presented in detail.In Section 6, numerical analysis and the results aredescribed. Finally, the discussion and conclusion arestated in Sections 7 and 8, respectively.

2. Literature review

Train timetabling is one of the most interestingproblems in transportation planning systems. Traintimetabling problem basically consists of determiningthe train's departure and arrival times in each sta-tion. The assessment of train timetable is a complexprocedure due to the fact that it is subjected to the

capacity and resource constraints [3]. A majority of theapproaches to train timetabling are analytical meth-ods. Moreover, the application of exible simulationapproaches for railway systems has been recognized byprevious studies [4]. Huisman et al. [5] provided anexcellent state-of-the-art review of railway optimizationproblems. In the literature, numerous mathemati-cal formulations are presented for train timetablingproblem. Train timetabling problem is known to beNP-hard with respect to the number of con icts inthe schedule [6,7]. Thus, it is di�cult to determinethe optimum solutions to industry-sized problems in areasonable time, and this raises the need for e�cientheuristic and meta-heuristic algorithms. In the relatedliterature, several sophisticated search procedures areintroduced, such as look-ahead search [8], backtrack-ing search [9], and meta-heuristics algorithms [10-12]. D'ariano et al. [13] addressed the real-time trainscheduling problem in a railway network using ane�cient Branch and Bound (B&B) algorithm. The em-pirical test cases make evident that the B&B algorithmoutperforms the commonly-used dispatching in termsof both average and maximum secondary delays. Adecision support system, called ROMA, was designedby D'Ariano [14] based on Alternative Graph (AG)techniques to cope with real-time train reschedulingproblem with multiple delays. The aim was to improvepunctuality index through better utilization of therailway infrastructure. The system was extended byCorman et al. [15] to present an innovative distributedapproach to manage train operations more e�ectively inmulti-area dispatching areas. The performance of thedistributed approach was compared with the existingmodels in terms of computation time and reducing totaldelay. Hassannayebi and Kiaynfar [16] proposed threemeta-heuristic algorithms based on Greedy Random-ized Adaptive Search Procedure (GRASP) to �nd thenear-to-optimal train timetable in double-track railwaylines. The output results show the e�ectiveness ofthe proposed meta-heuristic algorithm in solving large-sized instances of the train timetabling problem.

In a vast majority of the previous studies, thetrain schedule is an input for railway capacity planningmodel. Some recent and related capacity planning liter-ature that is associated with aspects of train schedulingproblems is as follows: proposing a scheduling modelfor inserting additional trains into the existing timetable without any railway infrastructure expansionplan. Sajedinejad et al. [17] designed a simulation-based decision support framework called SIMARAILfor scheduling trains in railway networks. The proposedframework was used as a tool to assess the di�erenttrain dispatching policies. Lai and Shih [18] developeda capacity planning procedure for evaluation of pos-sible expansion scenarios and determine the optimalnetwork investment plan to meet the future demand.

M. Shakibayifar et al./Scientia Iranica, Transactions E: Industrial Engineering 24 (2017) 3409{3422 3411

Hasannayebi et al. [19] developed an event-drivensimulation model for train timetabling problem withconsideration of train stops for praying services. Pathrelinking algorithm was implemented to obtain goodquality solutions. Goverde et al. [20] introduced thenew indicator for dynamic infrastructure occupationassessment and analyzed infrastructure capacity underdisturbances. The capacity assessment study wasperformed on Dutch railway corridor with di�erentsignalling systems under both scheduled and perturbedtra�c circumstances. For scheduled tra�c, the UICstandard was used to compute infrastructure capac-ity, whereas Monte Carlo simulation technique wasemployed to evaluate rail capacity under disruptedconditions. Sch�obel et al. [21] proposed an optimiza-tion model for integrated timetable and infrastructuredesign of a railway system. The problem was for-mulated as a combinatorial optimization problem andsolved using mathematical programming techniquesand metaheuristics. Hassannayebi et al. [22] proposeda simulation-based optimization approach for traintimetabling in urban rail. The problem was solvedusing genetic algorithm and the outcomes verify thee�ectiveness of the solution method.

The previous studies on capacity planning inrailway are mostly dedicated to the maximization ofthe throughput without making new infrastructureinvestments. In the literature, two aspects of railwaycapacity planning problem exist. The �rst is the short-term planning of scheduling additional trains and thesecond is the long-term planning of railway infrastruc-ture upgrading. Railway infrastructure developmentis strongly related to a famous railway optimizationproblem called railway saturation problem. In therailway saturation problem, the main objective is toinsert a maximum number of additional trains in aprede�ned train set. A notable point is that the railwaysaturation problem does not deal directly with trainscheduling problem. Delorme et al. [23] developed twoheuristic approaches to evaluate the railway infrastruc-ture capacity. These models do not consider cost-basedobjective function and also service level constraints.Shih et al. [24] proposed an optimization model for theoptimal siding locations for single-track railway linessubject to the infrastructure and tra�c characteristics.The experimental results proved that the optimal plancan maximize the return on investment and achievethe desired service level. Vansteenwegen et al. [25]proposed a method for adjusting an initial in caseof planned temporary infrastructure unavailability. Atrade-o� was made between the level of service andthe capacity. The proposed model incorporates thetimetable robustness to rescheduling procedure. Thedeveloped procedure also aims to minimize the numberof cancelations. Pouryousef et al. [2] proposed a multi-objective linear programming model together with

rail simulation tools to improve capacity utilization.The developed system has the capability of automaticresource con ict resolution and train scheduling toolsfor multiple-track corridors. The methodology wasvalidated through comparison with RailSys simulationpackage. Hassannayebi et al. [26] proposed a robustmulti-objective stochastic programming approach fortrain scheduling at rapid rail transit lines. Themathematical models were developed to minimize theexpected waiting times and the cost of overcrowding.The e�ectiveness of the proposed model was validatedthrough the application to Tehran underground railwaynetwork. P�ohle and Feil [27] conducted a researchbased on integration of train scheduling and infrastruc-ture planning.

Corman et al. [28] addressed the integrated trainscheduling and delay management in real-time railwaytra�c condition. The delay management model focuseson the e�ect of rescheduling actions on the qualityof service. The result of empirical test experimentsbased on Dutch railway network con�rms that goodquality solutions can be obtained within a reasonablecomputation time. Sam�a et al. [10] applied meta-heuristic algorithms to the real-time train timetablingproblem in complex and congested railway networks.The proposed methodology is initiated with generatinga good quality solution via a Branch and Bound(B&B) algorithm. Subsequently, Variable Neighbor-hood Search (VNS) and Tabu search algorithms wereimplemented to improve the solution by re-routingof trains. The result indicated that the proposedalgorithm outperforms the solutions attained by acommercial optimization package in terms of reducedcomputation times and search performance. Qi etal. [29] designed an integrated multi-track stationlayout design and train scheduling model on railwaycorridors. The optimization model decides the numberof siding tracks or platforms within the budget con-straints. The total construction cost and total traintravel time are assumed as performance metrics. A bi-level programming model was developed to solve a trainscheduling model along with track assignment problem.The optimization models were solved almost e�cientlyby commercial software GAMS with CPLEX solverand local searching-based heuristic. As a concludingremark, a wide range of papers are devoted to the traintimetabling problem in the last decades, but there isstill lack of integrated models which combine infras-tructure upgrading issues with timetable generation.

3. Problem description

The train timetabling problem deals with the opti-mum dispatching of trains on a railway network anddetermines the best station to stop for technical andservice-based purposes including religious requests. In


the following sections, we describe the assumptions, no-tation, introduction of special constraints, and railwayinfrastructure terms in detail.

3.1. AssumptionsThe problem is concerned with a railway network witha set of linked corridors. Railway network consistsof single, double, and multiple-track routes. A trainservice is de�ned as a trip of a train that travels fromits origin station to its destination station. Each trainis assumed to have a pre-speci�ed traveling route in thenetwork. Furthermore, the free running times of trainsat segments are assumed to be constant. Train servicesare determined by a set of planned and unplannedstops. There are three categories of trains' stops:

1. Scheduled stops with �xed stop time;

2. Unscheduled stops with �xed stop time;

3. Unscheduled stops with variable stop time.

Train technical services are planned during theoperation cycle, but religious services occur duringdynamic and time-dependent intervals. Scheduledstops are permitted at any intermediate stations forany train. But, unscheduled stops are permitted in thelimited set of stations which have the required facilities,e.g. mosque. We consider a track section between twoadjacent stations. To prevent this scheduled delay, aminimum headway time needs to be considered. Aminimum headway time is the minimum time di�erencebetween dispatching of two following trains that shouldbe kept in order to satisfy tra�c safety regulations.

3.2. NotationThe notations of indices and sets used in the mathe-matical model, the notations of parameters used in themathematical model, and the decision variables used inthe mathematical formulation are presented as follows:

Indices:j Train indexk Segment indexi Station indexs index of technical stop types

(s = 1; 2; 3; :::; S)r index of praying service r (r =

1; 2; 3; :::; R)J1 Set of existing trains (J1 2 J)J2 Set of new unscheduled trains (J2 2 J)I1 Set of one-lane stations (I1 2 I)I2 Set of two-lane stations (I2 2 I)K1 Set of single track segmentsK2 Set of double track segmentsCO Set of corridors in the railway network

Parameters:�(j; k) Index of the kth traveling segment in

the route of train jKj Total number of segments on route of

train j�jk 1 if train j is an inbound train in

segment k, 0 otherwise'j1;j2;k 1 if segment k exist in route of train j1

and j2�ij 1 if train j needs to have access

to platform for loading/unloadingpassengers in station i, 0 otherwise

pjk Free running time of train j at segmentk

dwij Minimum dwell time of train j instation i

Hj1:j2:i The minimum headway betweenarrival/departure time of train j1 andj2 at station i

sts Stopping time required for technicalstop type s

ptij Passenger load and unloading time fortrain j in station i

spr The required time for praying type rmsij Scheduled stop time for train j at

station iedj Earliest departure time of train j from

its origin station (j 2 J2)ldj Latest departure time of train j from

its origin station (j 2 J2)sdj Scheduled departure time of train j

from its origin station (j 2 J1)�i 1 if the location of mosque facility is

in the inbound lane at station i, 0otherwise (i 2 I1)

v(j;k) 1 if there is an facility at kth travelingsegment of train j for technical stop, 0otherwise

�i 1 if there is an overpass facility instation i, 0 otherwise

�i 1 if there is a mosque facility in stationi, 0 otherwise

NLi Number of tracks which is notconnected with any platform in stationi

Npi Number of tracks which is connectedwith a platform in station i

Lri Lower bound of time window ofpraying service type r in station i

Uri Upper bound of time window ofpraying service type r in station i

tp Minimum time to prepare for prayingand performing praying service


C Desirable value for summation of trainstraveling time

M A large positive constantLCi Construction cost of a new track in

station iPCi Construction cost of a new platform in

station iDecision variables:xdjk Departure time of train j from

beginning of the segment kxajk Arrival time of train j at the end of

the segment kzj1;j2;k 1 if train j1 is entered before train j2

in the same direction on segment k, 0otherwise

uj1;j2;k 1 if train j1 is entered before train j2in the opposite direction on segment k,0 otherwise

ysij 1 if train j stopped for sth technicalservice at station i, 0 otherwise

wijt 1 if train j is assigned to tth track atstation i, 0 otherwise

oijt 1 if train j occupies tth platform atstation i, 0 otherwise

grij 1 if train j stopped for rth prayingservice at station i, 0 otherwise

Ali Number of additional tracks (do notconnected with platform) need to beconstructed in station i

Api Number of additional tracks (connectedwith platform) need to be constructedin station i

Construction of new platform and track in thestation is considered as infrastructure developmentoptions in the mathematical model. The optimizationmodel determines which section of the railway networkneeds to be upgraded with what type of capacityimprovement scenario. Construction of new linesand platforms in each station has a prede�ned costwhich depends on the station infrastructure character-istics.

3.3. Religious-related constraintsWe considered several religious constraints in ourmodel that appear in Iranian railway network. Trainmovements on the railway network in Iran are regulatedby the three daily prays. All trains should stopduring the praying time window for a period of 20-25 minutes. Each praying service has a dynamic timewindow to be performed. This time window dependson geographic location of station and canonical timehorizon. These time horizons consist of morning, noon,and sunset. We assume that each station has a localcanonical time horizon. So, the start time of praying

depends on the location of site and daily time horizonchanges. Praying times change daily according tothe seasons and train exact location in the railwaynetwork. Performing religious services for trains alsodepends on the dispatching time of the trains fromtheir origin stations and the arrival time to destinationstation. Finding the best station for stopping toperform religious service is a challenging optimizationproblem added to train timetabling problem. Eqs. (1)and (2) state the condition which forces the trains tostop for praying service in the intermediate stations.We denote the dispatching time of train j from theorigin station by xdj;�(j;1) and arrival time of this trainto destination station by xaj;�(j;Kj). Every prayingservice type needs to be checked before determiningthe best station to stop. If the following conditions aresatis�ed, then train j should stop in one station (whichhave mosque facility) on its route for praying servicetype r. The two conditions of praying service activationcan be expressed as the following two equations:

xdj;�(j;1) � Lr;�(j;1) + tp

8j 2 J; 8r = 1; 2; 3; (1)

xaj;�(j;Kj) � Ur;�(j;Kj+1) � tp8j 2 J; 8r = 1; 2; 3; (2)

where (Lri; Uri) is the praying time interval in station i,when trains are allowed to stop for performing prayingservice with type r. Note that, in Eq. (1), Lr;�(j;1) isde�ned as a lower bound of praying interval for prayingservice r in origin station of train j on its route. Trainsmay have to stop for all praying services, or none ofthem.

4. Mathematical formulations

In this section, we formulate the train timetablingproblem as a mixed-integer linear programming. In thefollowing, we state the details of the integrated math-ematical model for generating an extended timetableaccording to the best railway infrastructure upgradingplan. The objective function is to minimize Eq. (3) sub-ject to constraints given by Eqs. (4)-(20). The objectivefunction is the minimization of railway infrastructuredevelopment cost:

minZ =jjIjjXi=1

(Ali:LCi +Api:PCi) ; (3)

xdj:�(j:1) = sdj 8j 2 J1; (4)

edj � xdj;�(j;1) � ldj ; 8j 2 J2; (5)


xaj;�(j;k) = xdj;�(j;k) + pj;�(j;k) ;

8j; k = 1; 2; :::; kj ; (6)

xdj;�(j;k+1) � xaj;�(j;k) + dw�(j;k);j +ms�(j;k);j

8j; k = 1; 2; :::; kj ; i 2 I; (7)

ms�(j:k);j = max�pt�(j;k);j :

jjsjjXs=1

sts; ys:�(j;k);j

:jjrjjXr=1

spr; qr;�(j;k);j

�; i 2 I1; (8)

ms�(j;k);j = max�pt�(j;k);j :

jjsjjXs=1

sts:ys;�(j;k);j

:jjrjjXr=1

(spr+t0:��(j;k) :�j;�(j;k+1)):gr;�(j;k);j

�;

i 2 I2; (9)(xdj1k + pj1k +Hj1:j2:K � xdj2;k + (1� zj1;j2;k):Mxdj2:k + pj2k +Hj1;j2;k � xdj1:k + zj1;j2;k:M

8j1:j2:k; 'j1:j2;k = 1; �j1:k + �j2:k = f0:2g (10)(xdj1k+pj1k+Hj1:j2:K � xdj2:k + (1� zj1:j2:k):Mxdj1:k + pj1k +Hj1:j2:K � xdj2:k + zj1:j2:k:M

8j1:j2:k; 'j1:j2:k = 1; �j1:k + �j2:k = f0:2g (11)(xdj1k+pj1k+Hj1:j2:K � xdj2:k+(1� uj1:j2:k):Mxdj2:k + pj2k +Hj1:j2:K � xdj1:k + uj1:j2:k:M

8j1:j2:k; 'j1:j2:k = 1; �j1:k + �j2:k = 1 (12)

jjJjjXj=1

�xaj:�(j:kj) � xdj:�(j:1)

� � C; (13)

jjJjjXj=1

wijt � 1 + �i 8i 2 I; 8t 2 T; (14)

jjKj jjXk=1

��(j:k) :gr:�(j:k):j = 1; 8j 2 J; 8r 2 R; (15)

Lr:�(j:k) �M(1� grij) � xdj:�(j:k+1) � Ur:�(j:k)

+M(1� grij);8j 2 J; 8k 2 K; 8r 2 R; (16)

Kj�1Xk=1

�(j:k) :ys:�(j:k):j = 1; 8j 2 J; 8s 2 S; (17)

�ij � msij ; (18)

jjJjjXj=1

oijt:�ij � Npi +Api; 8i 2 I; 8t 2 T; (19)

oijt + wijt � 1; 8i 2 I; 8j 2 J; 8t 2 T: (20)

Constraints (4) and (5) are related to the departuretime constraints. Constraints (4) de�ne the departuretime of the train at the �rst segment. Constraints (5)ensure that the departure time of the train from theorigin is within the allowed range. Eq. (6) states therunning time constraints on segments. Eq. (7) de�nesthe minimum station dwell time constraint. Thetrain technical, passengers load/unload and religiousservices are parallel tasks which are performed inthe stations. So, the maximum stopping time of atrain in a station is the maximum time of all tasksabove. The calculated stopping time in each stationis distinguished in Constraints (8) and (9) accordingto the station characteristics. According to Eq. (8),the scheduled stop time for train j (running in theinbound direction) in station is the maximum time ofall possible technical operations or religious services.Likewise, the scheduled stop time of trains at outboundroute is formulated in Eq. (9). The minimum headwayConstraints (10)-(12) also describe the minimum safetyheadway requirements between the departure timesand arrival times of successive trains at the samesegment. More speci�cally, Constraints (10) and (11)state the overtaking con ict for trains. Constraint (12)states the crossing con ict for inbound and outboundtrains. Constraint (13) states that the total travelingtime of trains should be less than a desired value.Constraint (14) ensures that the number of trainsoccupying a station in the same time is less thanmaximum capacity of the station. Eqs. (15) and(16) are related to the situation that trains stop forpraying services. Constraints (15) ensure that only onestation is assigned to each train to perform prayingservices. Constraints (16) state that the departuretime of trains is between the allowed praying timewindows. Constraint (17) de�nes the stopping patternof trains for technical services. Trains are permitted tostop at a set of eligible stations for technical services.Constraint (18) states that a free platform shouldbe allocated to a train which stops in the station.Constraint (19) ensures that the number of trains whichneeds free platform, at any given time, is less than thetotal number of existing and additional platforms in thestations. Eq. (20) states the logical constraint aboutoccupation of a platform in the stations.


Figure 1. The overview of the proposed heuristicalgorithm.

5. Solution methodology

In this section, we present two heuristics and a de-composition approach to reduce the complexity of theproblem. The overview of the proposed decomposition-based heuristic algorithm to solve train timetablingproblem in network is illustrated in Figure 1. Heuristicalgorithms contributes to a decrease in the number ofdecision variables and constraints via variable �xingstrategies. The decomposition approach is also used fordividing the complete optimization problem into sub-problems. Each sub-problem is associated with a traintimetabling model on a separate route.

5.1. Variable �xing strategiesGiven the mathematical model presented in the previ-ous sections, the problem turns into a large-scale mixinteger program. As is well known, this type of modelis far more di�cult to solve optimally. Here, to handlethe above mixed-integer programming model with anexponential number of variables and constraints, wepresent a preprocessing algorithm for decreasing thenumber of active praying services. By applying thisprocedure, we can determine the condition of prayingservice activation before optimizing the mathematicalmodel. By changing the dispatching time of a trainbetween its earliest and latest departure times, thepraying services may become active or inactive. Thegoal is to assign the trains into a set of de�niteand inde�nite trains according to their praying serviceactivation. The notations used to describe the heuristicprocedures are presented as follows:

Drj Set of trains which their conditionsforpraying service type r are de�nitelyactive

NDrj Set of trains which their conditionsfor praying service type r are notde�nitely active

eaj Earliest possible arrival time of train jto its destination station

APrj 1 if the praying service type r is activefor train j, 0 otherwise

rj 1 if the �rst condition of prayingservice is true, 0 otherwise

�rj 1 if the second condition of prayingservice is true, 0 otherwise

eaj can be calculated as follows:

eaj=edj+Kj+1Xk=1

(pt�(j;k);j+dw�(j;k);j )+KjXk=1

pj;�(j;k) ;

8j 2 J: (21)

The praying service activation conditions can be statedby parameters eaj and ldj in the following equations:

ldj � Lr:�(j;1) + tp; (22)

eaj � Ur:�(j;Kj+1) � tp: (23)

Next, we describe the main components of our prepro-cessing in Algorithm 1.

We proposed a mathematical optimization modelwhich determines the departure time of trains from theorigin station to minimize the number of active prayingservices. This algorithm is a class of heuristics whichis based on constraint satisfaction techniques. In thefollowing, we propose the mathematical model for theMAPS algorithm:

minZ =jjJjjXj=1

RXr=1

APrj ; (24)

2APrj � rj + �rj 8j 2 J; 8r 2 R; (25)

rj + �rj � 1 +APrj 8j 2 J; 8r 2 R; (26)

xdj:�(j:1) � Lr:�(j:1) � tp �M(1� rj);

8j 2 J; 8r 2 R; (27)

xdj;�(j:1) � Lr:�(j:1) � tp > M: rj ;

8j 2 J; 8r 2 R; (28)


Algorithm 1. The main components of the proposed preprocessing.

xaj;�(j:Kj) � Ur:�(j:Kj+1) + tp �M:(�rj � 1);

8j 2 J; 8r 2 R; (29)

xaj;�(j:Kj) � Ur:�(j:Kj+1) + tp �M:�rj ;

8j 2 J; 8r 2 R; (30)

xaj:�(j:Kj) =xdj:�(j:1) +Kj+1Xk=1

�pt�(j:k):j + dw�(j:k):j

�+

KjXk=1

pj:�(j:k) 8j 2 J; 8r 2 R; (31)

�rj = (0; 1); rj = (0; 1): (32)

In the formulation, Objective (24) de�nes the numberof total active praying services. Constraints (25)and (26) ensure that if the two conditions of prayingservices are true, then the praying service will be active.Constraints (27) and (28) de�ne the relation betweenthe �rst condition of praying service activation withauxiliary variables. Similarly, Constraints (29) and(30) de�ne the relation between the second conditionof praying service activation with auxiliary variables.Constraints (31) de�ne the trains traveling time.

5.2. Physical railway network decompositionIt should be noted that large-scale train schedulingproblems with hundreds of trains, which move indi�erent routes along hundreds of stations, are farmore di�cult to solve exactly. Based on a physicaldecomposition of the railway network in sub-networks,the problem is divided into sub-problems correspondingto these sub-networks. These sub-problems are thensolved and the whole process is coordinated at a higherlevel in order to generate a global feasible solution.This decomposition procedure is performed in a hierar-chy framework. The proposed decomposition approachconsists of corridor-based decomposition, train route-based decomposition, and double-track segments de-composition. In this framework, computational e�ort

for searching the infrastructure upgrading options willdecrease.

In order to account for the evaluation of di�er-ent capacity expansion scenarios, we propose a novelheuristic algorithm, which decomposes the physicalnetwork into bottleneck and underutilized corridors.The de�nition of bottlenecks can be based on theanalysis of infrastructure, technical de�nitions, opera-tional systems, economical, spatial and social context,and travel demand forecasts. Normally, the tra�cdensity through the bottleneck sections is expected tobe very high. We de�ne the bottleneck corridor as thedemand for transport exceeding the available capacityof infrastructure. The underutilized corridors are theother railway sections with lower demand. Bottlenecksin railway transport system usually are concerned with:(1) the level of transport speed (maximum travel speed,train travel time, passenger waiting time); and (2) thecapacity (maximum number of operating trains perrailway section). The analysis to identify the existingbottlenecks corridors come up with the necessary mea-sures. On the main stream of bottleneck analysis forthe existing railway infrastructure is the evaluation ofthe train timetables to calculate the average delay timeof trains. The main idea of this heuristic algorithmis decomposition of a railway network based on ourde�nition of the level of railway capacity utilization.Di�erent policies for generating train timetables arethen applied to the two types of corridors accordingto their properties.

The scheduling strategy initiates by solving thetimetabling problem of the bottleneck corridors andthen using the result of the solved problem to gen-erate timetable for other underutilized corridors. Inbottleneck corridors, the track topology usually con-sists of single-track segments, hence there is a hugepotential for railway infrastructure development. Inthe infrastructure development problem, we test dif-ferent scenarios to decrease the tra�c density of thebottleneck corridors. In order to clarify the de�nition ofthe bottleneck corridors, we used the terms bottlenecksection and bottleneck station to quantify the tra�c


density on the railway resources. The bottleneck sec-tion and bottleneck station are de�ned by a percentageof potential tra�c density. A saturation criterionis used to quantify the tra�c density of a railwayresource. Delorme et al. [23] de�ned the capacity ofa segment of a rail system as the maximum number oftrains that can be scheduled on it within a certain unitof time (e.g., an hour). This concept is extended hereto determine the tra�c density ratio of the sections.The following notations are used for describing thesaturation criteria:

Kc Set of segments exist in corridor cIc Set of stations exist in corridor c k The minimum tra�c density ratio of

track segment k�i The minimum tra�c density ratio of

station i�c The minimum utilization ratio of a

corridor cLDjk Latest departure time of train j from

the beginning of the segment kEAjk Earliest arrival time of train j at the

end of the segment keaij Latest departure time of train j from

station ildij Earliest arrival time of train j at

station i

The theoretical expressions of the capacity of asection and station noted k and �i, respectively, canbe de�ned as:

k =PjjJjjj=1 (EAjk � LDjk)

T8k 2 Kc; (33)

�i =PjjJjjj=1 �ij : (eaij � ldij)

T8i 2 Ic; (34)

where T is the planning horizon. Now, we can calculatethe weighted average of the station and section satura-tion ratios as utilization ratio of a railway corridor asfollows:

�c =jjIcjjPi2Ic �i + jjKcjjPk2kc kjjIcjj+ jjkcjj 8c 2 CO:

(35)

Therefore, we can divide the set of corridors into thebottleneck corridors with the highest ratio of utilizationand underutilized corridors. This separation is accord-ing to a prede�ned threshold ratio of utilization (i.e.,30%).

6. Computational results

In this section, some examples taken from the Iranianrailway network are used to illustrate the proposed

Figure 2. Total number of passengers carried in theIranian rail network.

methods. Transport system of the Iranian railway isgrowing fast now (Figure 2). The length of railway aswell as expressway network have doubled during thelast 15 years. The economic aspects of this expansionplan have not been yet investigated extensively by thetransport experts; this is the main motivation of thepreset study. By 2020, the Iranian railway expectsto reach every regional capital by rail. Nevertheless,the demand is much higher than the available trains,as new rolling stock is always one step behind theopening of new lines and the tracks are shared withheavy freight tra�c.

6.1. Case dataThe decomposed mathematical formulation has beenapplied to the whole railway network which consistsof long railway corridors. The example includes 132trains and 56 stations and the network is composedof 30 double-tracked and 25 single-tracked segments(Figure 3). The Tabriz-Mashhad corridor is a double-tracked line with segments separated by stations, wherea mean of 90 daily long distance trains run fromTabriz to Mashhad, or vice versa. Because of specialinfrastructure characteristics of the railway network inIran, there is a signi�cant potential for increasing therailway capacity by upgrading railway infrastructure.The information of the existing railway network ispresented in Table 1.

6.2. Numerical analysisTo demonstrate the capabilities of the approachesdeveloped in this paper, a real case study is solved.The results of preprocessing algorithm are summarizedfor di�erent train services. The output of the algorithmis the categorization of trains according to their prayingservice activation status. In this case, there are threedaily praying services and each praying service couldbe de�nitely active or not. The trains with de�nitepraying service status can help reduce the number


Figure 3. The Iranian railway network (north corridor).

Table 1. Infrastructure information of the existing railway network.

Station # Track # PlatformCost of constructinga track with platform

($ per km)

Cost of constructinga track without platform

($ per km)

1-5 4 2 8700 7600

6-15 3 1 6900 8700

16-20 5 3 8800 4200

21-56 4 2 6400 6600

of decision variables and constraints in mathematicalmodel. The total number of decision variables de-creases 13% after implementing these algorithms in amathematical model.

The purpose of decomposition approach is toevaluate how much the average delay can be decreasedby the suggested decomposition approach and comparethe results to the outcome if the infrastructure staysunchanged. In this example, the number of the existingtrains in circulation is 100 before adding the additionaltrain services. We plan to schedule 32 new trains to therailway network in the planning horizon to satisfy theconstraints given in Section 4 by choosing the minimumcost infrastructure upgrading options. The result of thedecomposition algorithm is shown in Table 2.

Di�erent capacity expansion scenarios have beengenerated in the decomposed optimization models toincrease the utilization of the railway capacity. The

result of each sub-problem and the average delay ofthe existing and new trains are summarized in Table 3.Each of the sub-problems generated from the decom-position approach was solved by using GAMS/CPLEX12.0 on a PC equipped with a 3.3 GHz PentiumIV processor. Regarding the computation time, thedecomposed sub-problems are terminated in less than12 min for all instances. However, it should be notedthat this was due mainly to the use of the proposeddecomposition method. According to the obtainedresult given in Table 3, the existing number of tracksand platform has been expanded, on average, by about32% and 46%, respectively. The average delay of trainin the whole network after upgrading the infrastruc-ture is about 6.9 minutes. Furthermore, the totalcost of upgrading the existing infrastructure is about511000 ($). The objective value also shows a strongrelation between the construction of new platforms


Table 2. Physical decomposition of the railway network.

Corridor name Minimum utilizationratioa (�c)

Saturationstatus

Number of generatedsub-problems

Number of trainsub-route

Tehran-Mashhad 14% Ub 4 12Tehran-Tabriz 40% Bc 5 7Tehran-Ahvaz 35% B 3 5Tehran-Sarri 11% U 4 8

aThreshold ratio of utilization = 30%; bU: under-utilize; cB: bottleneck.

Table 3. Size, speci�cation, and optimal solution of the generated sub-problems.

Sub-problem

Infrastructurebefore upgrading

Infrastructureafter upgrading

% Increaseof NCT

% Increaseof NCP

Infrastructuredevelopment

cost ($)

Average delay(min)

Computationtime (sec)

NTa NSb NCTc NCPd

1 14 9 6 4 42.86% 44.44% 54000 13.4 540.442 12 10 4 3 33.33% 30.00% 24000 9.6 650.453 9 7 2 3 22.22% 42.86% 12000 10.3 300.354 10 8 4 4 40.00% 50.00% 42000 5.4 400.345 24 4 5 5 20.83% 125.00% 10000 4.2 760.766 15 9 4 6 26.67% 66.67% 20000 6.8 230.237 7 7 4 2 57.14% 28.57% 48000 4.7 320.358 21 11 3 1 14.29% 9.09% 28000 6.9 140.349 8 5 3 2 37.50% 40.00% 58000 8.3 300.4510 9 4 1 1 11.11% 25.00% 70000 2.2 130.1511 10 9 4 3 40.00% 33.33% 12000 4.5 100.6512 8 10 2 3 25.00% 30.00% 20000 6.6 70.1613 5 8 3 4 60.00% 50.00% 45000 7.2 60.5414 8 9 2 4 25.00% 44.44% 30000 5.4 50.7615 9 5 3 5 33.33% 100.00% 13000 3.1 110.5516 10 8 2 2 20.00% 25.00% 25000 11.9 260.89

aNT: The number of scheduled train; bNS: The number of existing stations;cNCT: The number of new tracks; dNCP: The number of new platforms.

and decreasing the average delay resulted from thecombination of the infrastructure development options.Also, the obtained results indicate that adding a newplatform in the station is more e�ective than addinga new track in terms of decreasing the average traindelay.

The decomposition method obtains a better ob-jective value for the instances which belong to thebottleneck corridors rather than to those in the un-

derutilized corridors (Table 4). However, the aver-age computation time of the decomposition methodfor bottleneck instances is mostly obtained from thedecomposition method for underutilized instances.

There is a need for upgrading railway infras-tructure when the number of train increases. Thedecomposition approach helps �nd the minimum costscenario for developing infrastructure and decreasingdelay systematically. As stated before, the proposed

Table 4. Improvement of the total delay by development of the bottleneck corridors.

Corridorname

Saturationstatus

Improvement intotal delay (%)

Average computationtime (sec)

Tehran-Mashhad U 13 234Tehran-Tabriz B 47 650Tehran-Ahvaz B 54 925Tehran-Sarri U 11 353


Figure 4. Average delay increases by schedulingadditional train services.

decomposition method identi�es the potential infras-tructure alternatives and chooses the near-optimumcapacity expansion plan. Figure 4 shows how theaverage delays increase exponentially when the numberof trains exceeds the saturation level. The averagedelay is computed as the ratio of the total train delayat destination to the total number of trains. This valueis computed for each test problem and the associatedbest found solution. In order to obtain each point inthis graph, we solve the optimization model to �nd thebest capacity upgrading plan. Also, the timetablingmodel is solved for the case when no capacity expansiondecisions are allowed. Then, the best found solutionsare considered and their performances are compared interms of average delay of trains at destinations.

7. Discussion

The question addressed by the present study is howthe railway infrastructure can be upgraded to decreasethe total delay of the existing and new trains. Themain �nding of the study is that developing the infras-tructure of the bottleneck corridors is more e�ectivethan upgrading underutilized corridors for reductionof total delay. In our experiments, the average delayin generated timetable relates strongly to the railwayinfrastructure. As expected, by increasing the numberof platforms in the stations, the average delay becomesshorter. However, railway development problem makescongestion issues that a�ect the resulting timetable.The experiments showed that there is a potentialimprovement for decreasing the average delay by imple-menting the decomposition approach and constructionof new platforms in the bottleneck corridors.

Evidence that our model helps the railway oper-ators in infrastructure development decisions is thatthe evaluation of several capacity expansion scenariostakes a lot of time even in the simulation softwareproducts. It should be noted that optimizing the use ofrailway infrastructure is a complex and time-consuming

task. Therefore, numerous capacity expansion scenar-ios should be evaluated in order to work out how manyextra trains can be scheduled by the existing infrastruc-ture and how much investment will be required for newinfrastructure. In other words, the railway capacity isextremely dependent on infrastructure. It is clear thatthe proposed decomposition approach does not guaran-tee for the optimal solution to complete mathematicalmodel. As a consequence, the results lend furthercredence to our earlier suggestion that decompositionapproach (especially route-based decomposition part)has short computation time as an advantage for large-scale problems. Specially, we conclusively recommendestablishing a reductionism procedure for eliminatingthe extra decision variables before optimization. Thepreprocessing helps the decomposition approach toexplore the regions in a more promising way in lesstime than the exact approaches does. The proposedmethod allows us to analyze the performance of therailway networks (e�ect of infrastructure development)on delays as it has been demonstrated in the real case.

8. Conclusion

The design and optimization of new railway infras-tructure is a complex long-term planning procedurethat involves several operational constraints. The newupgraded rail infrastructure a�ects the timetabling de-cisions as well. Thus, it is worth analyzing both tacticaland strategic aspects of this problem in an integratedapproach. Up to now, there is no optimization-baseddecision support tool to determine a minimum costinfrastructure upgrading plan by taking into accountall the constraints de�ned by the operation of traintra�c in the railway system. In this paper, wepresented a mathematical programming model for thetrain scheduling and railway infrastructure develop-ment problems. The Iranian railway network was se-lected as the test benchmark. The religious constraintsassociated with the passenger praying services wereaddressed in the timetabling model. The mathematicalmodel of the present paper was then extended to handlethe infrastructure planning issues. In our framework,the complex mathematical model was simpli�ed by twoheuristic methods based on variable �xing techniquesin order to be solved e�ciently. We also presented anetwork-wide decomposition procedure with the aim ofreducing the complexity of the complete mathematicalmodel of the centralized instance. The result of imple-menting the proposed method shows the advantagesof the methodology to design the railway networkswith minimum cost so that it makes us capable ofscheduling new trains e�ciently. We considered theconstruction of new tracks and platforms as infrastruc-ture development options to upgrade the infrastructurefor decreasing the average delay. For the future studies,


the existing mathematical model can be combined withtrain routing model to cope with real assumptions. Ourmathematical modeling approach is also capable to beincorporated with detailed evaluation of the robustnessand reliability indexes.

References

1. Abril, M., Barber, F., Ingolotti, L., Salido, M.A.,Tormos, P. and Lova, A. \An assessment of railwaycapacity", Transportation Research Part E: Logisticsand Transportation Review, 44(5), pp. 774-806 (2008).

2. Pouryousef, H., Lautala, P. and Watkins, D. \De-velopment of hybrid optimization of train schedulesmodel for N-track rail corridors", Transportation Re-search Part C: Emerging Technologies, 67, pp. 169-192(2016).

3. Hassannayebi, E., Zegordi, S.H. and Yaghini, M.,\Train timetabling for an urban rail transit line using aLagrangian relaxation approach", Applied Mathemati-cal Modelling, 40(23), pp.9892-9913 (2016).Hassannayebi, E., Zegordi, S.H. and Yaghini, M.\Train timetabling in urban rail transit line us-ing Lagrangian relaxation approach", Applied Mathe-matical Modelling, (2016). http://dx.doi.org/10.1016/j.apm.2016.06.040.

4. Hassannayebi, E., Sajedinejad, A. and Mardani, S.\Disruption management in urban rail transit sys-tem: A simulation based optimization approach", inHandbook of Research on Emerging Innovations in RailTransportation Engineering, IgI-Global. pp. 420-450(2016).

5. Huisman, D., Kroon, L.G., Lentink, R.M. and Vro-mans, M.J. \Passenger railway optimization", Hand-books in Operations Research and Management Sci-ence, 14, pp. 129-187 (2006).

6. Cai, X., Goh, C. and Mees, A.I. \Greedy heuristicsfor rapid scheduling of trains on a single track", IIETransactions, 30(5), pp. 481-493 (1998).

7. Caprara, A., Fischetti, M. and Toth, P. \Modelingand solving the train timetabling problem", OperationsResearch, 50(5), pp. 851-861 (2002).

8. S�ahin, _I. \Railway tra�c control and train schedulingbased oninter-train con ict management", Transporta-tion Research Part B: Methodological, 33(7), pp. 511-534 (1999).

9. Adenso-D�az, B., Gonz�alez, M.O. and Gonz�alez-Torre,P. \On-line timetable re-scheduling in regional trainservices", Transportation Research Part B: Method-ological, 33(6), pp. 387-398 (1999).

10. Sam�a, M., Corman, F. and Pacciarelli, D. \A variableneighbourhood search for fast train scheduling androuting during disturbed railway tra�c situations",Computers & Operations Research, 78, pp. 480-499(2017).

11. Hassannayebi, E. and Zegordi, S.H. \Variable andadaptive neighbourhood search algorithms for rail

rapid transit timetabling problem", Computers & Op-erations Research, 78, pp. 439-453 (2017).

12. Zhang, L., Tang, Y., Hua, C. and Guan, X. \A newparticle swarm optimization algorithm with adaptiveinertia weight based on Bayesian techniques", AppliedSoft Computing, 28, pp. 138-149 (2015).

13. D'ariano, A., Pacciarelli, D. and Pranzo, M. \A branchand bound algorithm for scheduling trains in a railwaynetwork", European Journal of Operational Research,183(2), pp. 643-657 (2007).

14. D'Ariano, A. \Innovative decision support system forrailway tra�c control", IEEE Intelligent Transporta-tion Systems Magazine, 1(4), pp. 8-16 (2009).

15. Corman, F., D'Ariano, A., Pacciarelli, D. and Pranzo,M. \Centralized versus distributed systems to resched-ule trains in two dispatching areas", Public Transport,2(3), pp. 219-247 (2010).

16. Hassannayebi, E. and Kiaynfar, F. \A greedy random-ized adaptive search procedure to solve the train se-quencing and stop scheduling problem in double trackrailway lines", Journal of Transportation Research,9(3), pp. 235-257 (2012).

17. Sajedinejad, A., Mardani, S., Hasannayebi, E. andKabirian, A. \SIMARAIL: simulation based optimiza-tion software for scheduling railway network", in Sim-ulation Conference (WSC), Proceedings of the 2011Winter. IEEE (2011).

18. Lai, Y.C. and Shih, M.C. \A Robust Decision Sup-port Framework for Long-Term Railway CapacityPlanning", In Proceedings of 9th World Congress onRailway Research, Lille, France (2011).

19. Hasannayebi, E., Sajedinejad, A., Mardani, S. andMohammadi, K.A.R.M. \An integrated simulationmodel and evolutionary algorithm for train timetablingproblem with considering train stops for praying", InProceedings of the 2012 Winter Simulation Conference(WSC), pp. 1-13, IEEE (2012).

20. Goverde, R.M., Corman, F. and D'Ariano, A. \Rail-way line capacity consumption of di�erent railwaysignalling systems under scheduled and disturbedconditions", Journal of Rail Transport Planning &Management, 3(3), pp. 78-94 (2013).

21. Sch�obel, A., Raidl, G.R., Grujicic, I., Besau, G.and Schuster, G. \An optimization model for inte-grated timetable based design of railway infrastruc-ture", in Proceedings of the 5th International Semi-nar on Railway Operations Modelling and Analysis-RailCopenhagen (2013).

22. Hassannayebi, E., Sajedinejad, A. and Mardani,S. \Urban rail transit planning using a two-stagesimulation-based optimization approach", SimulationModelling Practice and Theory, 49, pp. 151-166 (2014).

23. Delorme, X., Rodriguez, J. and Gandibleux, X.\Heuristics for railway infrastructure saturation",Electronic Notes in Theoretical Computer Science,50(1), pp. 39-53 (2001).


24. Shih, M.C., Lai, Y.C., Dick, C. and Wu, M.H.\Optimization of siding location for single-track lines",Transportation Research Record: Journal of the Trans-portation Research Board, pp. 71-79 (2014).

25. Vansteenwegen, P., Dewilde, T., Burggraeve, S. andCattrysse, D. \An iterative approach for reducingthe impact of infrastructure maintenance on the per-formance of railway systems", European Journal ofOperational Research, 252(1), pp. 39-53 (2016).

26. Hassannayebi, E., Zegordi, S.H., Amin-Naseri, M.R.and Yaghini, M. \Train timetabling at rapid rail transitlines: a robust multi-objective stochastic programmingapproach", Operational Research, pp. 1-43 (2016).

27. P�ohle, D. and Feil, M. \What are new insights usingoptimized train path assignment for the developmentof railway infrastructure? ", in Operations ResearchProceedings, Springer. pp. 457-463 (2016).

28. Corman, F., D'Ariano, A., Marra, A.D., Pacciarelli,D. and Sam�a, M., \Integrating train scheduling anddelay management in real-time railway tra�c control",Transportation Research. Part E: Logistics and Trans-portation Review, 105, pp. 213-239 (2017).

29. Qi, J., Yang, L., Gao, Y., Li, S. and Gao, Z.\Integrated multi-track station layout design and trainscheduling models on railway corridors", Transporta-tion Research Part C: Emerging Technologies, 69, pp.91-119 (2016).

Biographies

Masoud Shakibayifar received his PhD degree inIndustrial Engineering from Iran University of Science& Technology in 2017. He received BSc (1997-2001)and MSc (2004-2006) degrees in Civil Engineering atSharif University of Technology, Tehran, Iran. Hehas managed more than 15 transportation planningprojects in the Iranian Railway Company and theMinistry of Roads and Urban Development so far.Recently, he has managed a research project relatedto the design of railway tra�c simulation softwarefor the Iranian Railway Company. His research in-terests are railway electri�cation, railway schedulingand rescheduling, and optimization of transportationsystems under uncertainty.

Erfan Hassannayebi is an Assistant Professor ofIndustrial Engineering at Department of IndustrialEngineering, Faculty of Engineering, Central TehranBranch, Islamic Azad University, Tehran, Iran. Hereceived his PhD degree in Industrial Engineering fromTarbiat Modares University in 2017. His researchinterests are in the area of applied operational research,simulation-based optimization, and metaheuristic algo-rithms. He has several publications in internationaljournals.

Hamid Mirzahossein received his BSc degree in2009, MSc degree in 2011, both from Imam KhomeiniInternational University (IKIU), and PhD degree in2017 from Iran University of Science and Technology(IUST). At present he is Assistant Professor at ImamKhomeini International University (IKIU). His researchinterests are mainly in the areas of land-use and trans-portation interaction with special focus on accessibilityand mathematical models and optimization techniquesfor congestion pricing and tra�c assignment, andmore recently, on mathematical optimization of railwaysystems.

Shaghayegh Zohrabnia received her MSc degreein Industrial Management from Allameh TabatabeeUniversity of Tehran, Iran. Her professional interestsfocus on multi-objective optimization, meta-heuristicmethods in solving NP-hard problems{such as TabuSearch, Simulated Annealing and Genetic Algorithm{target costing and value engineering, balanced score-card, management information system, queuing systemoptimization, nonparametric methods in operationsresearch such as Data Envelopment Analysis (DEA).Her current project includes timetabling optimizationof mixed double and single tracked railway network.

Ali Shahabi is a PhD candidate at the Islamic AzadUniversity, Tehran Branch, in the �eld of IndustrialEngineering. His research interests include simulation,reliability engineering, supply chain management andlogistics, optimization methods, and advance qualitycontrol. He has also several publications in interna-tional journals.

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