scholarly journals A Fuzzy Programming Method for Modeling Demand Uncertainty in the Capacitated Road–Rail Multimodal Routing Problem with Time Windows

Symmetry ◽  
2019 ◽  
Vol 11 (1) ◽  
pp. 91 ◽  
Author(s):  
Yan Sun ◽  
Xia Liang ◽  
Xinya Li ◽  
Chen Zhang
Keyword(s):  
Demand Uncertainty ◽  
Transportation Network ◽  
Time Windows ◽  
Mixed Integer ◽  
Credibility Measure ◽  
Chance Constrained Programming ◽  
Road Transportation ◽  
Routing Problem ◽  
Operational Level ◽  
Fuzzy Expected Value

Demand uncertainty is an important issue that influences the strategic, tactical, and operational-level decision making in the transportation/logistics/supply chain planning. In this study, we explore the effect of demand uncertainty on the operational-level freight routing problem in the capacitated multimodal transportation network that consists of schedule-based rail transportation and time-flexible road transportation. Considering the imprecise characteristic of the demand, we adopt fuzzy set theory to model its uncertainty and use trapezoidal fuzzy numbers to represent the fuzzy demands. We set multiple transportation orders as the optimization object and employ soft time windows to reflect the customer requirement on on-time transportation. Under the above situation, we establish a fuzzy mixed integer nonlinear programming (FMINLP) model to formulate the capacitated road–rail multimodal routing problem with demand uncertainty and time windows. We first use the fuzzy expected value model and credibility measure based fuzzy chance-constrained programming to realize the defuzziness of the model and then adopt linearization technique to reformulate the crisp model to finally generate an equivalent mixed integer linear programming (MILP) model that can be solved by standard mathematical programming software. Finally, a numerical case is presented to demonstrate the feasibility of the proposed method. Sensitivity analysis and fuzzy simulation are combined to quantify the effect of demand uncertainty on the routing problem and also reveal some helpful insights and managerial implications.

scholarly journals Green and Reliable Freight Routing Problem in the Road-Rail Intermodal Transportation Network with Uncertain Parameters: A Fuzzy Goal Programming Approach

2020 ◽  
Vol 2020 ◽  
pp. 1-21 ◽  
Author(s):  
Yan Sun
Keyword(s):  
Transportation Network ◽  
Mixed Integer ◽  
Programming Approach ◽  
Uncertain Parameters ◽  
Intermodal Transportation ◽  
Road Transportation ◽  
Routing Problem ◽  
The Road ◽  
Green Routing ◽  
Freight Routing

In this study, the author focuses on modeling and optimizing a freight routing problem in a road-rail intermodal transportation network that combines the hub-and-spoke and point-to-point structures. The operations of road transportation are time flexible, while rail transportation has fixed departure times. The reliability of the routing is improved by modeling the uncertainty of the road-rail intermodal transportation network. Parameters that are influenced by the real-time status of the network, including capacities, travel times, loading and unloading times, and container trains’ fixed departure times, are considered uncertain in the routing decision-making. Based on fuzzy set theory, triangular fuzzy numbers are employed to formulate the uncertain parameters as well as resulting uncertain variables. Green routing is also discussed by treating the minimization of carbon dioxide emissions as an objective. First of all, a multiobjective fuzzy mixed integer nonlinear programming model is established for the specific reliable and green routing problem. Then, defuzzification, linearization, and weighted sum method are implemented to present a crisp linear model whose global optimum solutions can be effectively obtained by the exact solution algorithm run by mathematical programming software. Finally, a numerical case is given to demonstrate how the proposed methods work. In the case, sensitivity analysis is adopted to reveal the effects of uncertainty on the routing optimization. Fuzzy simulation is then performed to help decision makers to select the best crisp route plan by determining the best confidence level shown in the fuzzy chance constraints.

scholarly journals Fuzzy Programming Approaches for Modeling a Customer-Centred Freight Routing Problem in the Road-Rail Intermodal Hub-and-Spoke Network with Fuzzy Soft Time Windows and Multiple Sources of Time Uncertainty

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 739 ◽  
Author(s):  
Sun ◽  
Li
Keyword(s):  
Time Windows ◽  
Fuzzy Programming ◽  
Service Level ◽  
Mixed Integer ◽  
Chance Constrained Programming ◽  
Multiple Sources ◽  
Routing Problem ◽  
Hub And Spoke ◽  
Soft Time Windows ◽  
Time Uncertainty

In this study, we systematically investigate a road-rail intermodal routing problem the optimization of which is oriented on the customer demands on transportation economy, timeliness and reliability. The road-rail intermodal transportation system is modelled as a hub-and-spoke network that contains time-flexible container truck services and scheduled container train services. The transportation timeliness is optimized by using fuzzy soft time windows associated with the service level of the transportation. Reliability is enhanced by considering multiple sources of time uncertainty, including road travel time and loading/unloading time. Such uncertainty is modelled by using fuzzy set theory. Triangular fuzzy numbers are adopted to represent the uncertain time. Under the above consideration, we first establish a fuzzy mixed integer nonlinear programming model with a weighted objective that includes minimizing the costs and maximizing the service level for accomplishing transportation orders. Then we use the fuzzy expected value model and fuzzy chance-constrained programming separately to realize the defuzzification of the fuzzy objective and use fuzzy chance-constrained programming to deal with the fuzzy constraint. After defuzzification and linearization, an equivalent mixed integer linear programming (MILP) model is generated to enable the problem to be solved by mathematical programming software. Finally, a numerical case modified from our previous study is presented to demonstrate the feasibility of the proposed fuzzy programming approaches. Sensitivity analysis and fuzzy simulation are comprehensively utilized to discuss the effects of the fuzzy soft time windows and time uncertainty on the routing optimization and help decision makers to better design a crisp transportation plan that can effectively make tradeoffs among economy, timeliness and reliability.

scholarly journals New general mixed-integer linear programming model for mobile workforce management

2021 ◽  
Author(s):  
András Éles ◽  
István Heckl ◽  
Heriberto Cabezas
Keyword(s):  
Programming Model ◽  
Time Windows ◽  
Mutual Exclusion ◽  
Parallel Execution ◽  
Mixed Integer ◽  
Management Problem ◽  
Routing Problem ◽  
Workforce Management ◽  
Computational Performance ◽  
Wide Range

AbstractA mathematical model is introduced to solve a mobile workforce management problem. In such a problem there are a number of tasks to be executed at different locations by various teams. For example, when an electricity utility company has to deal with planned system upgrades and damages caused by storms. The aim is to determine the schedule of the teams in such a way that the overall cost is minimal. The mobile workforce management problem involves scheduling. The following questions should be answered: when to perform a task, how to route vehicles—the vehicle routing problem—and the order the sites should be visited and by which teams. These problems are already complex in themselves. This paper proposes an integrated mathematical programming model formulation, which, by the assignment of its binary variables, can be easily included in heuristic algorithmic frameworks. In the problem specification, a wide range of parameters can be set. This includes absolute and expected time windows for tasks, packing and unpacking in case of team movement, resource utilization, relations between tasks such as precedence, mutual exclusion or parallel execution, and team-dependent travelling and execution times and costs. To make the model able to solve larger problems, an algorithmic framework is also implemented which can be used to find heuristic solutions in acceptable time. This latter solution method can be used as an alternative. Computational performance is examined through a series of test cases in which the most important factors are scaled.

scholarly journals Location Routing Problem with Consideration of CO2 Emissions Cost: A Case Study

2020 ◽  
Vol 21 (2) ◽  
pp. 225-234
Author(s):  
Ananda Noor Sholichah ◽  
Y Yuniaristanto ◽  
I Wayan Suletra
Keyword(s):  
Co2 Emissions ◽  
Time Windows ◽  
Optimal Solution ◽  
Mixed Integer ◽  
Distribution Centers ◽  
Location Routing Problem ◽  
Routing Problem ◽  
Location Routing ◽  
Study Results

Location and routing are the main critical problems investigated in a logistic. Location-Routing Problem (LRP) involves determining the location of facilities and vehicle routes to supply customer's demands. Determination of depots as distribution centers is one of the problems in LRP.  In LRP, carbon emissions need to be considered because these problems cause global warming and climate change. In this paper, a new mathematical model for LRP considering CO2 emissions minimization is proposed. This study developed a new  Mixed Integer Linear Programming (MILP)  model for LRP with time windows and considered the environmental impacts.  Finally, a case study was conducted in the province of Central Java, Indonesia. In this case study, there are three depot candidates. The study results indicated that using this method in existing conditions and constraints provides a more optimal solution than the company's actual route. A sensitivity analysis was also carried out in this case study.

scholarly journals Modeling the Multicommodity Multimodal Routing Problem with Schedule-Based Services and Carbon Dioxide Emission Costs

2015 ◽  
Vol 2015 ◽  
pp. 1-21 ◽  
Author(s):  
Yan Sun ◽  
Maoxiang Lang
Keyword(s):  
Carbon Dioxide ◽  
Carbon Dioxide Emissions ◽  
Transportation Network ◽  
Linearization Method ◽  
Mixed Integer ◽  
Multicommodity Flow ◽  
Routing Problem ◽  
Multimodal Transportation ◽  
Proposed Model ◽  
Freight Routing

We explore a freight routing problem wherein the aim is to assign optimal routes to move commodities through a multimodal transportation network. This problem belongs to the operational level of service network planning. The following formulation characteristics will be comprehensively considered: (1) multicommodity flow routing; (2) a capacitated multimodal transportation network with schedule-based rail services and time-flexible road services; (3) carbon dioxide emissions consideration; and (4) a generalized costs optimum oriented to customer demands. The specific planning of freight routing is thus defined as a capacitated time-sensitive multicommodity multimodal generalized shortest path problem. To solve this problem systematically, we first establish a node-arc-based mixed integer nonlinear programming model that combines the above formulation characteristics in a comprehensive manner. Then, we develop a linearization method to transform the proposed model into a linear one. Finally, a computational experiment from the Chinese inland container export business is presented to demonstrate the feasibility of the model and linearization method. The computational results indicate that implementing the proposed model and linearization method in the mathematical programming software Lingo can effectively solve the large-scale practical multicommodity multimodal transportation routing problem.

scholarly journals Matheuristics and Column Generation for a Basic Technician Routing Problem

Algorithms ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 313
Author(s):  
Nicolas Dupin ◽  
Rémi Parize ◽  
El-Ghazali Talbi
Keyword(s):  
Machine Learning ◽  
Column Generation ◽  
Time Window ◽  
Time Windows ◽  
Machine Learning Techniques ◽  
Mixed Integer ◽  
Routing Problems ◽  
Routing Problem ◽  
Feasible Solutions ◽  
Time Window Constraints

This paper considers a variant of the Vehicle Routing Problem with Time Windows, with site dependencies, multiple depots and outsourcing costs. This problem is the basis for many technician routing problems. Having both site-dependency and time window constraints lresults in difficulties in finding feasible solutions and induces highly constrained instances. Matheuristics based on Mixed Integer Linear Programming compact formulations are firstly designed. Column Generation matheuristics are then described by using previous matheuristics and machine learning techniques to stabilize and speed up the convergence of the Column Generation algorithm. The computational experiments are analyzed on public instances with graduated difficulties in order to analyze the accuracy of algorithms for ensuring feasibility and the quality of solutions for weakly to highly constrained instances. The results emphasize the interest of the multiple types of hybridization between mathematical programming, machine learning and heuristics inside the Column Generation framework. This work offers perspectives for many extensions of technician routing problems.

scholarly journals Optimal vehicle route schedules in picking up and delivering cargo containers considering time windows in logistics distribution networks: A case study

2020 ◽  
Vol 26 (4) ◽  
pp. 174-184
Author(s):  
Thi Diem Chau Le ◽  
Duy Duc Nguyen ◽  
Judit Oláh ◽  
Miklós Pakurár
Keyword(s):  
Mathematical Model ◽  
Simulated Annealing ◽  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Time Windows ◽  
Distribution Networks ◽  
Mixed Integer ◽  
Vehicle Group ◽  
Real Problem ◽  
Routing Problem

AbstractThis study describes a pickup and delivery vehicle routing problem, considering time windows in reality. The problem of tractor truck routes is formulated by a mixed integer programming model. Besides this, three algorithms - a guided local search, a tabu search, and simulated annealing - are proposed as solutions. The aims of our study are to optimize the number of internal tractor trucks used, and create optimal routes in order to minimize total logistics costs, including the fixed and variable costs of an internal vehicle group and the renting cost of external vehicles. Besides, our study also evaluates both the quality of solutions and the time to find optimal solutions to select the best suitable algorithm for the real problem mentioned above. A novel mathematical model is formulated by OR tools for Python. Compared to the current solution, our results reduced total costs by 18%, increased the proportion of orders completed by internal vehicles (84%), and the proportion of orders delivered on time (100%). Our study provides a mathematical model with time constraints and large job volumes for a complex distribution network in reality. The proposed mathematical model provides effective solutions for making decisions at logistics companies. Furthermore, our study emphasizes that simulated annealing is a more suitable algorithm than the two others for this vehicle routing problem.

scholarly journals Urban Transportation Network Design for Fresh Fruit and Vegetables Using GIS–The Case of Bangkok

2019 ◽  
Vol 9 (23) ◽  
pp. 5048 ◽  
Author(s):  
Suraraksa ◽  
Shin
Keyword(s):  
Urban Areas ◽  
Transportation Network ◽  
Time Windows ◽  
Operating Cost ◽  
Distribution Networks ◽  
Cold Chain ◽  
Problem Analysis ◽  
Distribution Centers ◽  
Routing Problem ◽  
Fresh Products

A cold chain for perishable fresh products aims to preserve the quality of the products under the control of a predefined temperature range. To satisfy the delivery conditions within appropriate time windows, the most critical operations in cold chain management is the transportation and distribution of fresh products. Due to rapid population growth and increasing demand for high-quality fresh foods, it becomes critical to develop advanced transportation and distribution networks for fresh products, particularly in urban areas. This research aims to design different scenarios based on mathematical models for fresh products transportation and distribution network in the Bangkok metropolitan area using Geographic Information system (GIS). The proposed methodology integrates location–allocation and vehicle routing problem analysis. The performance of all possible scenarios is evaluated and compared by considering the number of required distribution centers and trucks, total travel time, total travel distance, as well as fairness among drivers. The results of the scenario analysis highlight that the alternative scenarios show a better performance as compared to the current network. In addition, the administrator can make a different decision among several alternatives by considering different aspects, such as investment cost, operating cost, and balance of using available resources. Therefore, it may help a public officer to design the fresh products logistics network considering actual demand and traffic conditions in Bangkok.

scholarly journals Time-Dependent Electric Vehicle Routing Problem with Time Windows and Path Flexibility

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Li Wang ◽  
Shuai Gao ◽  
Kai Wang ◽  
Tong Li ◽  
Lin Li ◽  
...  
Keyword(s):  
Vehicle Routing ◽  
Electric Vehicle ◽  
Vehicle Routing Problem ◽  
Time Windows ◽  
Optimal Path ◽  
Travel Speed ◽  
Path Selection ◽  
Time Dependent ◽  
Mixed Integer ◽  
Routing Problem

With energy and environmental issues becoming increasingly prominent, electric vehicles (EVs) have become the important transportation means in the logistics distribution. In the real-world urban road network, there often exist multiple paths between any two locations (depot, customer, and charging station) since the time-dependent travel times. That is, the travel speed of an EV on each path may be different during different time periods, and thus, this paper explicitly considers path selection between two locations in the time-dependent electric vehicle routing problem with time windows, denoted as path flexibility. Therefore, the integrated decision-making should include not only the routing plan but also the path selection, and the interested problem of this paper is a time-dependent electric vehicle routing problem with time windows and path flexibility (TDEVRP-PF). In order to determine the optimal path between any two locations, an optimization model is established with the goal of minimizing the distance and the battery energy consumption associated with travel speed and cargo load. On the basis of the optimal path model, a 0-1 mixed-integer programming model is then formulated to minimize the total travel distance. Hereinafter, an improved version of the variable neighborhood search (VNS) algorithm is utilized to solve the proposed models, in which multithreading technique is adopted to improve the solution efficiency significantly. Ultimately, several numerical experiments are carried out to test the performance of VNS with a view to the conclusion that the improved VNS is effective in finding high-quality distribution schemes consisted of the distribution routes, traveling paths, and charging plans, which are of practical significance to select and arrange EVs for logistics enterprises.

Variable Fixing for Two-Arc Sequences in Branch-Price-and-Cut Algorithms on Path-Based Models

2020 ◽  
Vol 54 (5) ◽  
pp. 1170-1188 ◽  
Author(s):  
Guy Desaulniers ◽  
Timo Gschwind ◽  
Stefan Irnich
Keyword(s):  
Vehicle Routing ◽  
Time Windows ◽  
Solution Process ◽  
Mixed Integer ◽  
Linear Programs ◽  
Vehicle Routing Problems ◽  
Routing Problems ◽  
Routing Problem ◽  
Benchmark Instances ◽  
Variable Fixing

Variable fixing by reduced costs is a popular technique for accelerating the solution process of mixed-integer linear programs. For vehicle-routing problems solved by branch-price-and-cut algorithms, it is possible to fix to zero the variables associated with all routes containing at least one arc from a subset of arcs determined according to the dual solution of a linear relaxation. This is equivalent to removing these arcs from the network used to generate the routes. In this paper, we extend this technique to routes containing sequences of two arcs. Such sequences or their arcs cannot be removed directly from the network because routes traversing only one arc of a sequence might still be allowed. For some of the most common vehicle-routing problems, we show how this issue can be overcome by modifying the route-generation labeling algorithm in order to remove indirectly these sequences from the network. The proposed acceleration strategy is tested on benchmark instances of the vehicle-routing problem with time windows (VRPTW) and four variants of the electric VRPTW. The computational results show that it yields a significant speedup, especially for the most difficult instances.

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