The datasets gives a problem of 220,000 variables and 380,000 constraints. With available constraints and variables, the paper uses all possibilities to solve the problems using the algorithms.
To arrive at the solution to the problem, the study uses the new traffic management concepts and other potential solving methods.
3-Part: Structure of the Model;
The paper uses the Ilog Cplex tool to solve the problem. The linear programming as follows:
The algorithms check all constraints and simplify the problem as much as possible using the mathematical point-of-view. Using the system, the study attempts to find the first solution and refine it in order to find the best solution as being revealed in Fig 1.
Fig 1: Linear Programming Algorithms
Based on the linear programming algorithms, the study uses the pre-solve phase to reduce problem from the 220,000 variables and 380,000 constraints to approximately 64.000 variables and 300.000 constraints. The Ilog Cyplex uses the branch and cut algorithm to derive the optimal solution. The calculation time is improved to meet real time processing and large scale dataset.
The algorithms rescheduling module allows this study to perform traffic management with real world data and the experiment is carried out using SISYFE train simulator where the software stimulates the train running and the details reveals how the system would evolves in real life situation. The operation is carried out using the algorithms which take into account the train's dynamic performances, the tracks layout, and distances to be covered.
The rescheduling module is a large traffic control stimulator named LIPARI which contains three different modules:
The paper first seeks to detect the abnormal situation and compare the original timetable produced by the train simulator with the real world life situation. When the study detects the incident, the study sends the data to the re-scheduling module. The solution provided is to minimize delays by providing new speed and a new routing, which assists in enhancing traffic management.
This study uses linear programming to arrive at the optimal solution to the problems.
Using network flows & linear programming operations research techniques, the paper uses a two-stage decomposition process:
Train schedule without time
Train routes
Block-train assignment
Locomotive assignment
Crew assignment
Train schedule with time
Train routes
Block-train assignment
Locomotive assignment
Crew assignment
Using the train route optimization, the paper determines the train schedule without time and day of operation. The construction is as follows:
Enumeration of all potential train routes
Determination of the goodness of each route
Selection of the best route
Continue to repeat until all blocks are routed
Based on the train route optimization, Amtrak Train will enjoy the following benefits:
There would be routes improvement using neighborhood search
There would be routes improvement using VLSN search
Details Optimization of the train is as follows:
Train Time Train Operating Block-to-Train
Optimization Operating Optimization
The paper uses a neighborhood search approach to optimize each set of decision variables as well as assessing the impact each alternative with respect to: railcars, locomotives, and crews. Thus, Amtrak rail will enjoy the costs reduction if implementing this technique.
Train Cost Savings
Average Train Starts
1.49%
Average Train Miles
1.02%
Average Trains Work Events
1.15%
Crew Cost Savings
Average Crew Wage
1.23%
Average Deadhead Crews
0.23%
With regard to blocking problem facing Amtrak Train, the company will record saving in clean-slate blocking and, incremental blocking. Based on the result of the integer programming:
Minimize "k" K ?(i, j)?Acij + xkij + ?i-N ?(i, j) ?O (i) hiyij"
Amtrak Train will enjoy saving as follows:
Results of Clean-Slate Blocking
% of Savings in Car Miles
% of Savings in Intermediate
Handling
Railroad 1
1.3%
14%
Railroad 2
0.6%
17.7%
Railroad 3
0.6%
20.5%
Results of Incremental Blocking
% New Blocks
% of Savings in Car Miles
% of Savings in Intermediate
Handlings
0.7%
0.6%
7.3%
0.9%
0.5%
7.9%
1.4%
0.5%
9.5%
1.9%
0.5%
10.5%
3.8%
0.5%
14.1%
9.5%
0.6%
19.1%
Integer programming based on the microscopic model, Amtrak Train will be able to manage the energy consumption to the company advantages.
Conclusion
The paper attempts to solve the problem facing Amtrak Train using various mathematical tools such as integer programming, optimization technique and network analysis. The integer programming results reveal that the company will be able achieve a significant saving in the costs of operations because the company will be able to address the blocking problem and reschedule its operations to its best advantages.
Works Cited
Gely, L. Dessagne, G. And Lerin, C. Train Re-scheduling Modeling with Operational Research and Optimization Techniques: Results and Applications at SNCF. SNCF Innovation and Research Department. 2008.
Semet, Y. Schoenauer, M. "An Efficient Memetic, Permutation-Based Evolutionary Algorithm for Real-World Train Timetabling," the Journal, Volume, pp. 110-120, (2005).
PRESOLVE
First Solution
Best Solution
Decision is made on train' times departure and arrival at each stop node on the route
Decision is made on the operating days of trains
Decision is made on block-to-train assignments
Train Route
Optimization
Train Route
Optimization
Optimizes Objectives
Train Schedule
Optimizer
Honor Constraints
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