Metro Timetabling for Time-Varying Passenger Demand and Congestion at Stations

For the train timetabling problem (TTP) in a metro system, the operator-oriented and passenger-oriented objectives are both important but partly conflicting. This paper aims to minimize both objectives by considering frequency (in the line planning stage) and train cost (in the vehicle scheduling stage). Time-varying passenger demand and train capacity are considered in a nonsmooth, nonconvex programming model, which is transformed into a mixed integer programming model with a discrete time-space graph (DTSG). A novel dwell time determining process considering congestion at stations is proposed, which turns the dwell times into dependent variables. In the solution approach, we decompose the TTP into a subproblem for optimizing segment travel times (OST) and a subproblem for optimizing departure headways from the shunting yard (OH). Branch-and-bound and frequency determining algorithms are designed to solve OST. A novel rolling optimization algorithm is designed to solve OH. The numerical experiments include case studies on a short metro line and Beijing Metro Line 4, as well as sensitivity analyses. The results demonstrate the predictive ability of the model, verify the effectiveness and efficiency of the proposed approach, and provide practical insights for different scenarios, which can be used for decision-making support in daily operations.

Download Full-text

Soft Computing Methodology to Optimize the Integrated Dynamic Models of Cellular Manufacturing Systems in a Robust Environment

Mathematical Problems in Engineering ◽

10.1155/2021/3040391 ◽

2021 ◽

Vol 2021 ◽

pp. 1-13

Author(s):

Amir-Mohammad Golmohammadi ◽

Hasan Rasay ◽

Zaynab Akhoundpour Amiri ◽

Maryam Solgi ◽

Negar Balajeh

Keyword(s):

Machine Learning ◽

Programming Model ◽

Facility Layout ◽

Cell Formation ◽

Layout Design ◽

Metaheuristic Algorithms ◽

Sensitivity Analyses ◽

Mixed Integer ◽

Facility Layout Design ◽

Proposed Model

Machine learning, neural networks, and metaheuristic algorithms are relatively new subjects, closely related to each other: learning is somehow an intrinsic part of all of them. On the other hand, cell formation (CF) and facility layout design are the two fundamental steps in the CMS implementation. To get a successful CMS design, addressing the interrelated decisions simultaneously is important. In this article, a new nonlinear mixed-integer programming model is presented which comprehensively considers solving the integrated dynamic cell formation and inter/intracell layouts in continuous space. In the proposed model, cells are configured in flexible shapes during the planning horizon considering cell capacity in each period. This study considers the exact information about facility layout design and material handling cost. The proposed model is an NP-hard mixed-integer nonlinear programming model. To optimize the proposed problem, first, three metaheuristic algorithms, that is, Genetic Algorithm (GA), Keshtel Algorithm (KA), and Red Deer Algorithm (RDA), are employed. Then, to further improve the quality of the solutions, using machine learning approaches and combining the results of the aforementioned algorithms, a new metaheuristic algorithm is proposed. Numerical examples, sensitivity analyses, and comparisons of the performances of the algorithms are conducted.

Download Full-text

Highway Passenger Transport Based Express Parcel Service Network Design: Model and Algorithm

Journal of Advanced Transportation ◽

10.1155/2017/1712325 ◽

2017 ◽

Vol 2017 ◽

pp. 1-17 ◽

Cited By ~ 3

Author(s):

Yuan Jiang ◽

Baofeng Sun ◽

Gendao Li ◽

Zhibin Lin ◽

Changxu Zheng ◽

...

Keyword(s):

Network Design ◽

Network Flow ◽

Programming Model ◽

Real Data ◽

Path Selection ◽

Network Design Problem ◽

Mixed Integer ◽

Passenger Transport ◽

Service Network ◽

Time Space

Highway passenger transport based express parcel service (HPTB-EPS) is an emerging business that uses unutilised room of coach trunk to ship parcels between major cities. While it is reaping more and more express market, the managers are facing difficult decisions to design the service network. This paper investigates the HPTB-EPS network design problem and analyses the time-space characteristics of such network. A mixed-integer programming model is formulated integrating the service decision, frequency, and network flow distribution. To solve the model, a decomposition-based heuristic algorithm is designed by decomposing the problem as three steps: construction of service network, service path selection, and distribution of network flow. Numerical experiment using real data from our partner company demonstrates the effectiveness of our model and algorithm. We found that our solution could reduce the total cost by up to 16.3% compared to the carrier’s solution. The sensitivity analysis demonstrates the robustness and flexibility of the solutions of the model.

Download Full-text

A mixed procurement model for humanitarian relief chains

Journal of Humanitarian Logistics and Supply Chain Management ◽

10.1108/jhlscm-10-2018-0067 ◽

2019 ◽

Vol 10 (1) ◽

pp. 45-74 ◽

Cited By ~ 2

Author(s):

Mojtaba Aghajani ◽

S. Ali Torabi

Keyword(s):

Programming Model ◽

Dynamic Environment ◽

Sensitivity Analyses ◽

Mixed Integer ◽

Critical Parameters ◽

Content Type ◽

Procurement Process ◽

Non Linear Programming ◽

Supply Policy ◽

Post Disaster

Purpose The purpose of this paper is to improve the relief procurement process as one of the most important elements of humanitarian logistics. For doing so, a novel two-round decision model is developed to capture the dynamic nature of the relief procurement process by allowing demand updating. The model accounts for the supply priority of items at response phase as well. Design/methodology/approach A mixed procurement/supply policy is developed through a mathematical model, which includes spot market procurement and a novel procurement auction mechanism combining the concepts of multi-attribute and combinatorial reverse auctions. The model is of bi-objective mixed-integer non-linear programming type, which is solved through the weighted augmented e-constraint method. A case study is also provided to illustrate the applicability of the model. Findings This study demonstrates the ability of proposed approach to model post-disaster procurement which considers the dynamic environment of the relief logistics. The sensitivity analyses provide useful managerial insights for decision makers by studying the impacts of critical parameters on the solutions. Originality/value This paper proposes a novel reverse auction framework for relief procurement in the form of a multi-attribute combinatorial auction. Also, to deal with dynamic environment in the post-disaster procurement, a novel two-period programming model with demand updating is proposed. Finally, by considering the priority of relief items and model’s applicability in the setting of relief logistics, post-disaster horizon is divided into three periods and a mixed procurement strategy is developed to determine an appropriate supply policy for each period.

Download Full-text

A Path-Based Selection Solution Approach for the Low Carbon Vehicle Routing Problem with a Time-Window Constraint

Applied Sciences ◽

10.3390/app10041489 ◽

2020 ◽

Vol 10 (4) ◽

pp. 1489 ◽

Cited By ~ 2

Author(s):

Xianlong Ge ◽

Xiaobo Ge ◽

Weixin Wang

Keyword(s):

Time Window ◽

Programming Model ◽

Model Simulation ◽

Path Selection ◽

Urban Traffic ◽

Mixed Integer ◽

Low Carbon ◽

Gradual Improvement ◽

Solution Approach ◽

Urban Distribution

Due to the gradual improvement of urban traffic network construction and the increasing number of optional paths between any two points, how to optimize a vehicle travel path in a multi-path road network and then improve the efficiency of urban distribution has become a difficult problem for logistics companies. For this purpose, a mixed-integer mathematical programming model with a time window based on multiple paths for urban distribution in a multi-path environment is established and its exact solution solved using software CPLEX. Additionally, in order to test the application and feasibility of the model, simulation experiments were performed on the four parameters of time, distance, cost, and fuel consumption. Furthermore, using Jingdong (JD), the main urban area in Chongqing, as an example, the experimental results reveal that an algorithm that considers the path selection can significantly improve the efficiency of urban distribution in metropolitan areas with complex road structures.

Download Full-text

A Multistage Solution Approach for Dynamic Reactive Power Optimization Based on Interval Uncertainty

Mathematical Problems in Engineering ◽

10.1155/2018/3854812 ◽

2018 ◽

Vol 2018 ◽

pp. 1-10 ◽

Cited By ~ 1

Author(s):

Xiaodong Shen ◽

Yang Liu ◽

Yan Liu

Keyword(s):

Large Scale ◽

Reactive Power ◽

Power Optimization ◽

Programming Model ◽

Nonconvex Programming ◽

Interval Uncertainty ◽

Mixed Integer ◽

Reactive Power Optimization ◽

Renewable Energy Resources ◽

Integer Quadratic Programming

In order to solve the uncertainty and randomness of the output of the renewable energy resources and the load fluctuations in the reactive power optimization, this paper presents a novel approach focusing on dealing with the issues aforementioned in dynamic reactive power optimization (DRPO). The DRPO with large amounts of renewable resources can be presented by two determinate large-scale mixed integer nonlinear nonconvex programming problems using the theory of direct interval matching and the selection of the extreme value intervals. However, it has been admitted that the large-scale mixed integer nonlinear nonconvex programming is quite difficult to solve. Therefore, in order to simplify the solution, the heuristic search and variable correction approaches are employed to relax the nonconvex power flow equations to obtain a mixed integer quadratic programming model which can be solved using software packages such as CPLEX and GUROBI. The ultimate solution and the performance of the presented approach are compared to the traditional methods based on the evaluations using IEEE 14-, 118-, and 300-bus systems. The experimental results show the effectiveness of the presented approach, which potentially can be a significant tool in DRPO research.

Download Full-text

Application of Two-Phase Fuzzy Optimization Approach to Multiproduct Multistage Integrated Production Planning with Linguistic Preference under Uncertainty

Mathematical Problems in Engineering ◽

10.1155/2015/780830 ◽

2015 ◽

Vol 2015 ◽

pp. 1-20 ◽

Cited By ~ 1

Author(s):

Shan Lu ◽

Hongye Su ◽

Lian Xiao ◽

Li Zhu

Keyword(s):

Production Planning ◽

Programming Model ◽

Fuzzy Optimization ◽

Service Level ◽

Mixed Integer ◽

Planning Problem ◽

Optimization Approach ◽

Two Phase ◽

Steel Rolling ◽

Solution Approach

This paper tackles the challenges for a production planning problem with linguistic preference on the objectives in an uncertain multiproduct multistage manufacturing environment. The uncertain sources are modelled by fuzzy sets and involve those induced by both the epistemic factors of process and external factors from customers and suppliers. A fuzzy multiobjective mixed integer programming model with different objective priorities is proposed to address the problem which attempts to simultaneously minimize the relevant operations cost and maximize the average safety stock holding level and the average service level. The epistemic and external uncertainty is simultaneously considered and formulated as flexible constraints. By defining the priority levels, a two-phase fuzzy optimization approach is used to manage the preference extent and convert the original model into an auxiliary crisp one. Then a novel interactive solution approach is proposed to solve this problem. An industrial case originating from a steel rolling plant is applied to implement the proposed approach. The numerical results demonstrate the efficiency and feasibility to handle the linguistic preference and provide a compromised solution in an uncertain environment.

Download Full-text

Modelling and Optimizing an Open-Pit Truck Scheduling Problem

Discrete Dynamics in Nature and Society ◽

10.1155/2015/745378 ◽

2015 ◽

Vol 2015 ◽

pp. 1-8 ◽

Cited By ~ 8

Author(s):

Yonggang Chang ◽

Huizhi Ren ◽

Shijie Wang

Keyword(s):

Programming Model ◽

Valid Inequalities ◽

Upper Bounds ◽

Open Pit ◽

Mixed Integer ◽

Scheduling Problem ◽

Heuristic Solution ◽

Solution Approach ◽

Truck Scheduling ◽

Improvement Strategies

This paper addresses a special truck scheduling problem in the open-pit mine with different transport revenue consideration. A mixed integer programming model is formulated to define the problem clearly and a few valid inequalities are deduced to strengthen the model. Some properties and two upper bounds of the problem are proposed. Based on these inequalities, properties, and upper bounds, a heuristic solution approach with two improvement strategies is proposed to resolve the problem and the numerical experiment demonstrates that the proposed solution approach is effective and efficient.

Download Full-text

An Improved Differential Evolution Algorithm for a Multicommodity Location-Inventory Problem with False Failure Returns

Complexity ◽

10.1155/2018/1967398 ◽

2018 ◽

Vol 2018 ◽

pp. 1-13 ◽

Cited By ~ 1

Author(s):

Congdong Li ◽

Hao Guo ◽

Ying Zhang ◽

Shuai Deng ◽

Yu Wang

Keyword(s):

Reverse Logistics ◽

Programming Model ◽

Large Body ◽

Differential Evolution Algorithm ◽

Mixed Integer ◽

Inventory Problem ◽

Solution Approach ◽

Nonlinear Programming Model ◽

Customer Returns ◽

Improved Differential Evolution Algorithm

Customer returns are a common phenomenon in many industries, and they have a significant impact on business organizations and their supply chains. False failure returns are returned products that have no functional or cosmetic defects, and they represent a large body of customer returns in practice. In this paper, we develop a mixed-integer nonlinear programming model to study a multicommodity location-inventory problem in a forward-reverse logistics network. This model minimizes the total cost in this network by considering false failure returns, and it also considers many real-world business scenarios in forward and reverse logistics flows. Moreover, we design a new heuristic approach to solve the model efficiently. Finally, numerical experiments are conducted to validate our solution approach and provide meaningful managerial insights.

Download Full-text

Designing a clothing supply chain network considering pricing and demand sensitivity to discounts and advertisement

RAIRO - Operations Research ◽

10.1051/ro/2020118 ◽

2020 ◽

Author(s):

Mohammad Mahdi Paydar ◽

Marjan Olfati ◽

chefi Triki

Keyword(s):

Supply Chain ◽

Programming Model ◽

Rapid Development ◽

Supply And Demand ◽

Clothing Industry ◽

Sensitivity Analyses ◽

Mixed Integer ◽

Supply Chain Network ◽

Total Profit ◽

Demand Sensitivity

These days, clothing companies are becoming more and more developed around the world. Due to the rapid development of these companies, designing an efficient clothing supply chain network can be highly beneficial, especially with the remarkable increase in demand and uncertainties in both supply and demand. In this study, a bi-objective stochastic mixed-integer linear programming model is proposed for designing the supply chain of the clothing industry. The first objective function maximizes total profit and the second one minimizes downside risk. In the presented network, the initial demand and price are uncertain and are incorporated into the model through a set of scenarios. To solve the bi-objective model, weighted normalized goal programming is applied. Besides, a real case study for the clothing industry in Iran is proposed to validate the presented model and developed method. The obtained results showed the validity and efficiency of the current study. Also, sensitivity analyses are conducted to evaluate the effect of several important parameters, such as discount and advertisement, on the supply chain . The results indicate that considering the optimal amount for discount parameter can conceivably enhance total profit by about 20% compared to the time without this discount scheme. When we take the optimized parameter into account for advertisement, 12% is obtained for the total profit. Based on our findings, the more the expected profit value, the higher the total amount of total profit and risk. The results of this research also provide some interesting managerial insights for managers.

Download Full-text

A flexible mathematical model for crew pairing optimization to generate n-day pairings considering the risk of COVID-19: a real case study

Kybernetes ◽

10.1108/k-02-2021-0127 ◽

2021 ◽

Vol ahead-of-print (ahead-of-print) ◽

Author(s):

Bahareh Shafipour-Omrani ◽

Alireza Rashidi Komijan ◽

Seyed Jafar Sadjadi ◽

Kaveh Khalili-Damghani ◽

Vahidreza Ghezavati

Keyword(s):

Genetic Algorithm ◽

Programming Model ◽

Cost Minimization ◽

Crew Scheduling ◽

Mixed Integer ◽

Medium Size ◽

Content Type ◽

Solution Approach ◽

Proposed Model ◽

Crew Pairing

PurposeOne of the main advantages of the proposed model is that it is flexible to generate n-day pairings simultaneously. It means that, despite previous researches, one-day to n-day pairings can be generated in a single model. The flexibility in generating parings causes that the proposed model leads to better solutions compared to existing models. Another advantage of the model is minimizing the risk of COVID-19 by limitation of daily flights as well as elapsed time minimization. As airports are among high risk places in COVID-19 pandemic, minimization of infection risk is considered in this model for the first time. Genetic algorithm is used as the solution approach, and its efficiency is compared to GAMS in small and medium-size problems.Design/methodology/approachOne of the most complex issues in airlines is crew scheduling problem which is divided into two subproblems: crew pairing problem (CPP) and crew rostering problem (CRP). Generating crew pairings is a tremendous and exhausting task as millions of pairings may be generated for an airline. Moreover, crew cost has the largest share in total cost of airlines after fuel cost. As a result, crew scheduling with the aim of cost minimization is one of the most important issues in airlines. In this paper, a new bi-objective mixed integer programming model is proposed to generate pairings in such a way that deadhead cost, crew cost and the risk of COVID-19 are minimized.FindingsThe proposed model is applied for domestic flights of Iran Air airline. The results of the study indicate that genetic algorithm solutions have only 0.414 and 0.380 gap on average to optimum values of the first and the second objective functions, respectively. Due to the flexibility of the proposed model, it improves solutions resulted from existing models with fixed-duty pairings. Crew cost is decreased by 12.82, 24.72, 4.05 and 14.86% compared to one-duty to four-duty models. In detail, crew salary is improved by 12.85, 24.64, 4.07 and 14.91% and deadhead cost is decreased by 11.87, 26.98, 3.27, and 13.35% compared to one-duty to four-duty models, respectively.Originality/valueThe authors confirm that it is an original paper, has not been published elsewhere and is not currently under consideration of any other journal.

Download Full-text