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Advanced Planning, Scheduling and Routing Problems—Models, Methods, and Applications

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A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Transportation and Future Mobility".

Deadline for manuscript submissions: 20 December 2026 | Viewed by 7797

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Prof. Dr. Paweł Sitek

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Department of Applied Computer Sciences, Kielce University of Technology, 25-314 Kielce, Poland
Interests: constraint programming; operation research; optimization; decision support; logistics; manufacturing; supply chain management
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Special Issue Information

Dear Colleagues,

Advanced planning, scheduling and routing problems are key to efficient distribution, transportation, manufacturing, and supply chain coordination. They assign transportation tasks to a transport fleet and sequence stops/points. The development of transportation methods has expanded the definition of a vehicle (AVG, UAV, FPV, EV, etc.). These problems have many real-life applications and come in many variants, depending on the type of task, the objective, the time frames, and the types of constraints that must be met. Outside of transportation, logistics, and supply chains, routing problems have less intuitive but still important applications, e.g., robotics and manufacturing. Planning, scheduling and routing problems are computationally challenging discrete optimization issues. Therefore, modern methods and tools for modeling and solving these problems are necessary, including hybrid algorithms, machine learning, constraint programming, adaptive large neighborhood search, data-driven optimization, AI-driven methods, etc.

This Special Issue, titled “Advanced Planning, Scheduling and Routing Problems—Models, Methods, and Applications”, invites authors to submit articles discussing and presenting solutions regarding models, methods, applications, and new challenges pertaining to planning, scheduling and routing problems.

Prof. Dr. Paweł Sitek
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-anonymized peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Applied Sciences is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

planning and scheduling
optimization and algorithms
supply chains
urban logistics
last-mile delivery
autonomous vehicles
UAV fleet routing and scheduling
drone delivery systems
computer network routing
dynamic routing and scheduling
manufacturing
E-commerce logistics
AI-driven approach to modeling and solving
data-driven and robust optimization

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Published Papers (6 papers)

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Research

28 pages, 22641 KB

Open AccessArticle

Social Spider Optimization for Preliminary Earthwork-Balanced Highway Alignment Design

by Kadir Akgol and Fatmanur Pervan Sen

Appl. Sci. 2026, 16(15), 7434; https://doi.org/10.3390/app16157434 - 24 Jul 2026

Viewed by 302

Abstract

This study proposes a metaheuristic-based route optimization framework that balances earthworks in highway design by referencing a constant-slope “zero polygon.” The aim is to distribute excavation and embankment volumes evenly between fixed endpoints. The positions of Point of Intersection nodes and curve radii are optimized using the Social Spider Optimization (SSO) algorithm, guided by an objective function that minimizes the weighted signed distances between the route and the zero polygon while enforcing geometric constraints such as minimum curve radius, tangent length, and alignment continuity through penalty terms. Applications on two terrains with varying slopes demonstrate that the calibrated model substantially improves the cut–fill balance compared with both manual and pre-calibration solutions: the absolute difference between excavation and embankment volumes decreased from thousands to hundreds of cubic meters, and the cut–fill ratio fell below 0.1 in representative cases. Coupling a swarm-intelligence search with an interpretable geometric reference line, the framework offers a reproducible decision-support tool for preliminary corridor design. It enhances transparency and reduces reliance on trial-and-error practice. It targets preliminary, open-terrain corridor selection under a constant longitudinal slope without vertical curves, and does not yet incorporate land-use, environmental, or geotechnical constraints. Full article

(This article belongs to the Special Issue Advanced Planning, Scheduling and Routing Problems—Models, Methods, and Applications)

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29 pages, 1715 KB

Open AccessArticle

Static Pre-Scheduling for ICD Drayage Operations via Task Pooling and Enhanced Adaptive Large Neighborhood Search

by Shucheng Fan and Shaochuan Fu

Appl. Sci. 2026, 16(12), 5824; https://doi.org/10.3390/app16125824 - 9 Jun 2026

Viewed by 240

Abstract

Static pre-scheduling in inland container depot (ICD)-centered drayage must coordinate tractors, detachable load units, factory loading, and port deadlines before next-day execution. Conventional order-based routing is too rigid for mixed direct haulage, drop-and-pull, relay pickup, street-turn, and buffering operations. This study proposes a task-pooling framework that decomposes logistics orders into atomic tasks and recombines them across tractors in a unified static planning space. A compact route-based MILP is used for reduced-scale calibration, and an enhanced adaptive large neighborhood search (E-ALNS) is developed around ICD-oriented relay recombination and temporal-slack shifting. On a realistic synthetic benchmark with 100 generated order records (90 active executable orders), 60 available tractors, and 330 executable tasks, the proposed method reduces the internal search-ledger value from 42,213.29 to 34,421.22 and the compact ex post blueprint value from 53,802.28 to 47,717.99 relative to the greedy construction baseline. The resulting blueprint preserves an average inter-task slack of 89.86 min and a 5th-percentile slack of 61.73 min. A generic adaptive-neighborhood baseline reaches a slightly lower ex post value of 46,722.48 only with a longer runtime and much lower temporal reserve. The results support a cost–reserve–runtime tradeoff interpretation rather than unconditional cost dominance. Full article

(This article belongs to the Special Issue Advanced Planning, Scheduling and Routing Problems—Models, Methods, and Applications)

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25 pages, 2770 KB

Open AccessArticle

Analysis of the Travelling Time According to Weather Conditions Using Machine Learning Algorithms

by Gülçin Canbulut

Appl. Sci. 2026, 16(1), 6; https://doi.org/10.3390/app16010006 - 19 Dec 2025

Viewed by 1188

Abstract

A large share of the global population now lives in urban areas, which creates growing challenges for city life. Local authorities are seeking ways to enhance urban livability, with transportation emerging as a major focus. Developing smart public transit systems is therefore a key priority. Accurately estimating travel times is essential for managing transport operations and supporting strategic decisions. Previous studies have used statistical, mathematical, or machine learning models to predict travel time, but most examined these approaches separately. This study introduces a hybrid framework that combines statistical regression models and machine learning algorithms to predict public bus travel times. The analysis is based on 1410 bus trips recorded between November 2021 and July 2022 in Kayseri, Turkey, including detailed meteorological and operational data. A distinctive aspect of this research is the inclusion of weather variables—temperature, humidity, precipitation, air pressure, and wind speed—which are often neglected in the literature. Additionally, sensitivity analyses are conducted by varying k values in the K-nearest neighbors (KNN) algorithm and threshold values for outlier detection to test model robustness. Among the tested models, CatBoost achieved the best performance with a mean squared error (MSE) of approximately 18.4, outperforming random forest (MSE = 25.3) and XGBoost (MSE = 23.9). The empirical results show that the CatBoost algorithm consistently achieves the lowest mean squared error across different preprocessing and parameter settings. Overall, this study presents a comprehensive and environmentally aware approach to travel time prediction, contributing to the advancement of intelligent and adaptive urban transportation systems. Full article

(This article belongs to the Special Issue Advanced Planning, Scheduling and Routing Problems—Models, Methods, and Applications)

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38 pages, 7101 KB

Open AccessFeature PaperArticle

Assessing Feasibility in Service Teams Transport Scheduling with Dedicated and Flexible Dispatch Approaches

by Grzegorz Radzki, Grzegorz Bocewicz, Jarosław Rudy, Radosław Idzikowski and Zbigniew Banaszak

Appl. Sci. 2025, 15(23), 12727; https://doi.org/10.3390/app152312727 - 1 Dec 2025

Viewed by 919

Abstract

The research problem addressed in this paper concerns the formulation of feasibility conditions for planned service missions in networks where fulfilling customer orders requires the coordinated participation of multiple resources—referred to as the Service Teams Transport Scheduling (STTS) problem. The study examines feasibility conditions (sufficient and necessary) for routing and scheduling mobile service teams, taking into account constraints arising from service time windows arrangement, vehicle and team availability, and the applied vehicle dispatching strategies. Due to the NP-hard nature of the problem, which limits the possibility of determining service distribution plans in real time, it becomes essential to develop necessary feasibility conditions that can be used in preliminary tests prior to the final search for a feasible service mission plan. By introducing a graph-based representation of time-window arrangement, the study establishes necessary feasibility conditions derived from chromatic number analysis of the corresponding graphs. The feasibility verification approach, based on these conditions, was validated through a series of experiments. The approach combines discrete optimization and declarative modeling to support algorithmic decision-making in real-world service logistics. Full article

(This article belongs to the Special Issue Advanced Planning, Scheduling and Routing Problems—Models, Methods, and Applications)

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25 pages, 5186 KB

Open AccessArticle

Real-Time Global Velocity Profile Calculation for Eco-Driving on Long-Distance Highways Using Variable-Step Spatial Segmentation

by Jaeyeon Yoo, Yunchul Ha, Seongjoon Moon, Jeesu Kim and Jinwoo Yoo

Appl. Sci. 2025, 15(19), 10811; https://doi.org/10.3390/app151910811 - 8 Oct 2025

Viewed by 1329

Abstract

This study introduces a real-time optimization framework for eco-driving of heavy-duty vehicles over long-distance routes. A longitudinal dynamic model incorporating powertrain performance and fuel consumption is formulated, and the eco-driving scenario is expressed as a quadratic programming (QP) problem. To improve computational efficiency, a novel variable-step spatial segmentation method is introduced, which ensures a balance between modeling accuracy and computational cost. Simulations involving mixed-terrain scenarios verify the effectiveness of the proposed approach. The results show that the QP-based method achieves fuel savings comparable to those offered by dynamic programming while significantly reducing computation time to sub-second levels; thus, the proposed strategy offers real-time applicability. These findings demonstrate the feasibility of global optimal velocity profile generation in practical eco-driving scenarios. Full article

(This article belongs to the Special Issue Advanced Planning, Scheduling and Routing Problems—Models, Methods, and Applications)

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19 pages, 15300 KB

Open AccessArticle

Proactive Scheduling and Routing of MRP-Based Production with Constrained Resources

by Jarosław Wikarek and Paweł Sitek

Appl. Sci. 2025, 15(15), 8522; https://doi.org/10.3390/app15158522 - 31 Jul 2025

Viewed by 2586

Abstract

This research addresses the challenges of proactive scheduling and routing in manufacturing systems governed by the Material Requirement Planning (MRP) method. Such systems often face capacity constraints, difficulties in resource balancing, and limited traceability of component requirements. The lack of seamless integration between customer orders and production tasks, combined with the manual and time-consuming nature of schedule adjustments, highlights the need for an automated and optimized scheduling method. We propose a novel optimization-based approach that leverages mixed-integer linear programming (MILP) combined with a proprietary procedure for reducing the size of the modeled problem to generate feasible and/or optimal production schedules. The model incorporates dynamic routing, partial resource utilization, limited additional resources (e.g., tools, workers), technological breaks, and time quantization. Key results include determining order feasibility, identifying unfulfilled order components, minimizing costs, shortening deadlines, and assessing feasibility in the absence of available resources. By automating the generation of data from MRP/ERP systems, constructing an optimization model, and exporting the results back to the MRP/ERP structure, this method improves decision-making and competes with expensive Advanced Planning and Scheduling (APS) systems. The proposed innovation solution—the integration of MILP-based optimization with the proprietary PT (data transformation) and PR (model-size reduction) procedures—not only increases operational efficiency but also enables demand source tracking and offers a scalable and economical alternative for modern production environments. Experimental results demonstrate significant reductions in production costs (up to 25%) and lead times (more than 50%). Full article

(This article belongs to the Special Issue Advanced Planning, Scheduling and Routing Problems—Models, Methods, and Applications)

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