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The sugarcane transport system plays a critical role in the overall performance of Australia’s sugarcane industry. An inefficient sugarcane transport system interrupts the raw sugarcane harvesting process, delays the delivery of sugarcane to the mill, deteriorates the sugar quality, increases the usage of empty bins, and leads to the additional sugarcane production costs. Due to these negative effects, there is an urgent need for an efficient sugarcane transport schedule that should be developed by the rail schedulers. In this study, a multi-objective model using mixed integer programming (MIP) is developed to produce an industry-oriented scheduling optimiser for sugarcane rail transport system. The exact MIP solver (IBM ILOG-CPLEX) is applied to minimise the makespan and the total operating time as multi-objective functions. Moreover, the so-called Siding neighbourhood search (SNS) algorithm is developed and integrated with Sidings Satisfaction Priorities (SSP) and Rail Conflict Elimination (RCE) algorithms to solve the problem in a more efficient way. In implementation, the sugarcane transport system of Kalamia Sugar Mill that is a coastal locality about 1050 km northwest of Brisbane city is investigated as a real case study. Computational experiments indicate that high-quality solutions are obtainable in industry-scale applications.

With around $2.0 billion in export earnings, Australia is the world’s third largest exporter of raw sugar. In Australia, there are about 380,000 hectares, 24 mills and 4400 sugarcane farming entities growing sugarcane. Moreover, around 85% of exported raw sugar production is from Queensland (a northeast state of Australia). According to Australian Sugar Milling Council [

The sugarcane transport system is a complex industrial management system, as it needs to schedule a large set of locomotives, bins, train runs, railway sections with satisfaction of specific demands from harvesters and the mills. A typical sugarcane railway network comprises single-track sections and multiple-track sections; and performs two main tasks: delivering the empty bins from the mills to the harvesters at farms; and collecting the full bins of sugarcane to the mills. Moreover, integration of several different sub-modules such as harvesting, delivering, unloading and milling is a requirement in the whole supply chain of the Australian sugar industry. The implementation of more efficient schedules is essential to reduce the overall cost and remove the negative effects on the sugar production system. For example, optimising the delivery and collection times can result in significant improvements on the throughput of the harvesters and the mills.

A short literature review related to sugarcane train scheduling is given as follows. Abel et al. [

As most of publications in train scheduling are theoretic, one main contribution of this paper is to develop a real-time optimiser to produce an automatic scheduler for a sugarcane rail transport system, which is adapted as an extended parallel-machine job shop scheduling systems with blocking constraints [

The outline of this paper is as follows. In Section 2, a sugarcane rail transport scheduling system is described and its main problem properties are analysed. In Section 3, a MIP model is developed to formulate the sugarcane rail transport scheduling problem. In Section 4, some heuristic solution approaches are presented to solve this complicated optimisation problem in an efficient way. Computational experiments and sensitivity analysis are reported in Section 5. We conclude this paper in the last section.

The sugarcane rail transport system applies a daily schedule to satisfy the requirements of the mills and the harvesters. Due to the potential negative effects such as interruptions to the raw sugar production process; delaying the supply of sugarcane to the mills and deteriorating the sugar quality, the sugarcane rail transport system needs to deal with many challenges by developing a mathematical model to optimise the real system. The railway system can generally operate for 24 hours a day, while the harvesting period is limited to about 12 hours each day. A train run consist of a series of operations, which involve activities such as traversing a track section, collecting bins, loading and unloading. In a crossing section, a conflict may occur when one operation may be in the outbound direction and the other may be in the inbound direction.

_{2,1}, s_{5,1} and s_{7,1} contain sidings (for storing empty and full bins for the harvesters). In addition, terminal and intermediate segments are defined in

To clarify these issues, assume that the train k_{1} run includes the path, Mill-s_{1,1}-s_{2,1}-s_{3,1}-s_{6,1}-s_{7,1}-s_{7,1}-s_{6,1}-s_{3,1}-s_{2,1}- s_{1,1}-Mill, where outbound operations O_{1}-O_{2}-O_{3} are implemented on the intermediate segment. Outbound operations 4 - 5 and inbound operations O_{6}-O_{7} are implemented on terminal segment 3 continuously. Inbound operations O_{8}-O_{9}-O_{10} are implemented on the intermediate segment. Blocking the intermediate segment during use of k_{1}, to satisfy the safety conditions, means this segment is blocked during the time period of implementing the operationsO_{1}-O_{2}-O_{3}-O_{8}-O_{9}-O_{10}. This period includes the time of operations O_{4}-O_{5}-O_{6}-O_{7} since the operations of each segment should be implemented and conducted continuously. As a result, if the train k_{2} requires the intermediate segment, the waiting time of the train k_{2} to use the intermediate segment equals the time period of implementing the operations O_{1}-O_{2}-O_{3}-O_{4}-O_{5}-O_{6}-O_{7}-O_{8}-O_{9}-O_{10} by train k_{1} which affect the utilisation efficiency of that segment.

The proposed model increases the utilisation efficiency of segments by assuming that intermediate segments have been given separate segment numbers for the outbound and inbound directions (segments 1 and 4 in _{1}-O_{2}-O_{3} and segment 4 includes the inbound operations O_{8}-O_{9}-O_{10}.

In the outbound and inbound directions of train k_{1}, segment 1 and segment 4 are blocked respectively. As a

result, the waiting time of train k_{2} is reduced to equal the time period of implementing the outbound operations O_{1}-O_{2}-O_{3} on segment 1 by train k_{1}. If k_{1} is in the inbound direction, the waiting time of k_{2} to catch segment 4 is equal to the time period of the inbound operations O_{8}-O_{9}-O_{10} of train k_{1}. Blocking segment 1 does not automatically mean that the intermediate segment is blocked completely, since segment 4 can be used by another train k_{2} while train k_{1} is using segment 1. This conflict is addressed by the proposed algorithms of the solution approach in section 3 distinguishing between the segment types to prevent using one physical segment by more than one train at the same time.

The efficiency of the blocking segment constraints can be increased further in the proposed models by considering the passing loops in each rail branch (a long segment). Any blocking for any segment which includes a passing point can increase the waiting time of the system and then increase the operating cost and decrease the efficiency of rail section utilisation. Passing points can be passing loops (no activities; no delivering and no collecting) or a long siding (delivering or collecting) with passing loop and can allow for more than one train to pass at the same time.

Each branch which includes a passing loop can be divided into two segments to increase the utilisation of this branch and reduce the waiting time of any train at this branch. As a result, the blocking segment is applied to each part that does not include a passing loop. For example in _{1} includes a passing loop, so two segments (A_{1} and A_{2}) are included in it where each segment includes some sections. The passing loop has two parallel tracks (C_{1} and C_{2}) without storage. Branch B_{2} has no passing loop so the whole branch is considered as one segment.

Siding types in sugarcane rail system are divided into big sidings that can allow for more than one train to pass and small sidings which do not allow for more than one train to pass at the same time. Small sidings can have a double track section, where one of them is used for sugarcane storage and another for a passing train (only one train at a time). The big sidings can have more than two tracks where one is used for sugarcane storage and other tracks for more than one train passing at a time (parallel machines). Each track in this siding can be considered as one segment that includes one section as shown in

_{3,1}, s_{4,1,}s_{5,1} respectively, implying that blocking segments in this case includes blocking sections.

The sugarcane rail transport system was formulated as a multi-objective optimisation model considering three main operations: harvesting, transporting and milling. The model involves integration between these operations with a large number of constraints to produce an optimal automated scheduler for the sugarcane rail transport system satisfying many objectives at the same time. The transporting operation is the important link between milling and harvesting in an integrated framework. The integrated framework was developed by constructing meaningful relationships between these operations to build an integrated system. The sugarcane rail scheduling problem is mathematically formulated by MIP. The proposed MIP models’ objective functions deal with minimising the makespan objective and the total waiting time together. The models’ constraints include rail operation constraints and sugarcane system constraints. Rail operation constraints are related to trains passing on the rail network and include precedence, order of rail segments, train runs, passing priority, and blocking constraints. The sugarcane transport system constraints include train capacity, siding capacity, mill capacity, empty and full bin requirements, harvester rates, and harvesting times.

Parameters:

K Number of locomotives

E Number of segments

e Index of a segment;

S Total number of sections for all segments

R Number of locomotives runs

Variables:

Objective Functions:

Equations ((1) and (2)) are defined together to minimise the makespan and the total operating time (TOT) for all train runs in the system.

Constraints:

Equation (3) ensures operation o of locomotive k should be after operation o + 1 of locomotive k on section s of segment e.

Equations (4) and (5) define the scheduling relationship of locomotives k and k' on section s of segment e.

Equation (6) defines the blocking constraints in the whole railway system.

Equations (7) and (8) ensure the deliveries and collections of empty and full bins equal the allotment at each siding.

Equation (9) satisfies the siding capacity.

Equation (10) requires the release of empty bin delivery conditions in the outbound direction.

Equation (11) ensures the collection of full bins in the inbound direction.

Equation (12) ensures no delay time in the first run.

Equation (13) ensures no delay time in delivering to the harvesters. .

Equations ((14) and (15)) ensure that the number of full bins collected is no more than the produced number of full bins at each siding at each run.

Some previous solution techniques developed to solve the single objective function model are extended and adapted to solve the multi-objective model.

The SNS algorithm was developed to build different paths and routes for each train from any visited point using the idea of neighbourhood change. Active siding (with harvester) neighbourhoods are considered to create new paths for the trains through the sugarcane rail network. This algorithm includes the following main steps:

Begin

Step 1. Construct the locomotive runs by assigning the first active siding to visit by the train that has the most urgent need for empty bins considering blocked paths by bins or trains.

Step 2. Construct neighbours list for the visited siding using the three main criteria:

Set the shortest distance from the current siding, to help in reducing the total operating time of each trip.

Set the urgent need for delivering empty bins, to reduce the harvesting delays.

Set the urgent need for collecting full bins because of siding capacity is filled.

Step 3. Select the siding that will be visited by the train from the neighbours list.

Step 4. Update the neighbours list for each siding by removing the sidings that finished their daily allotment.

Step 5. Repeat the second step until the daily total allotments of all sidings are completed.

End

This algorithm was developed to integrate with Siding Neighbourhood Search to produce a global list of all visit priorities for all active sidings in the system. A global list includes all neighbour lists that will be visited by trains in the SNS algorithm to and remove any conflicts between sidings by the filtering operation for the different neighbour lists. The filtering operation takes account of the sugarcane rail objectives and constraints. For instance, two trains visiting one active siding at the same time is not allowed. This list is always updated to provide the traffic office any information about the train trips or the expected paths for each train while processing the trip. The SSP algorithm consists of the following main steps:

Begin

Step 1. Construct a global list including all neighbours for all active sidings in SNS algorithm.

Step 2. Set the active sidings list that has high priority to visit.

Step 3. Eliminate any conflicts for the siding visits that will be selected from the high priority list.

Step 4. Update the high priority list and remove visited sidings from the list.

Step 5. Update the global list.

End

As a train conflict through the single rail track is a serious issue, the Rail Conflict Elimination (RCE) Algorithm is developed to resolve complex situations related to the conflicts through the rail network. Such a conflict will affect the safety and the efficiency of the system when two trains wish to pass through the same section at the same time. In this case, the potential conflicts are resolved by the RCE algorithm, as illustrated in

The main procedure of the RCE algorithm is described below.

Begin

Step 1. Select section s.

Step 2. Set trains k and k' require section s_{.}

Step 3. Set the finish times of trains k and k' on same section s.

Step 4. Get the conflict point (s, t) on section s during time t.

Step 5. If the finish time of train k is less than the finish time of train k', thentrain k will be selected to be scheduled first on section s;

Step 7. Else, train k’ is selected first.

Step 8. Backtrack choosing another section.

End

Five trains on a part of a rail network consisting of 22 rail sections including single, double and triple tracks are shown in

locations where one train has to wait for another to pass and the length of waiting time.

As analysed in

The sugarcane transport system is very complicated as the mathematical formulation model has a large set of constraints and variables even when the problem size is small. In the proposed MIP model, the system constraints are classified into two main categories: 1) constraints related to the rail operations’ feasibility due to passing of trains without accidents; 2) constraints related to the capacities of sidings and empty/full bins. To efficiently find the near-optimal schedule, Siding Neighbourhood Search (SNS) and Sidings Satisfaction Priorities (SSP) algorithms are developed and integrated in the solution procedure. A Rail Conflict Elimination (RCE) Algorithm is also adapted to resolve the train conflicts through the single rail track with the consideration of train passing constraints. Computational experiments show that the outputs are satisfactory to optimise the performance of the sugarcane transport systems system. Regarding the future research directions, more dynamic and stochastic elements will be considered and incorporated in a reactive sugarcane railway scheduling problem. Moreover, the proposed model in this paper will be extended to investigate an integrated train-track transportation dynamics [

The authors acknowledge the funding support of the Sugar Research and Development Corporation, MSF Sugar Limited, Sucrogen Limited, Proserpine Co-operative Sugar Milling Associated Limited, Mackay Sugar Limited, Bundaberg Sugar Limited and Isis Central Sugar Mill Co. Ltd.

Mahmoud Masoud,Geoff Kent,Erhan Kozan,Shi Qiang Liu, (2016) A New Multi-Objective Model to Optimise Rail Transport Scheduler. Journal of Transportation Technologies,06,86-98. doi: 10.4236/jtts.2016.62008