Minimum Transportation Cost Research Articles

Evaluation of the Minimum Transportation Cost of Asymmetric/Symmetric Triangular Fuzzy Numbers with -Cut by the Row-Column Minima Method

في هذه المقالة، الفكرة الرئيسية هي الحصول على الحد الأدنى من التكلفة الإجمالية الغامضة للنقل لمشكلة النقل الثلاثي باستخدام طريقة الحد الأدنى للصف والعمود (RCM) هنا، فإن سعة العرض ووجهة الطلب وتكلفة النقل كلها أرقام غامضة مثلثية بالكامل مع غير متماثلة أو متماثلة ولكن ليس مع الرقم الغامض الثلاثي السلبي (TFN) يلعب الغموض دورًا نشطًا في العديد من المجالات، مثل العلوم والهندسة والطب والإدارة وما إلى ذلك. في هذه الفكرة، تتحلل مشكلة TFN إلى مسألتين لنقل الأعداد الصحيحة الفاصلة IITP) ) باستخدام طريقة α-cut، وذلك بوضع α= 0.5 و α=0 للحصول على مشكلة النقل الفاصل الزمني العلوي ومشكلة النقل الفاصل الزمني الأدنى. يتم تقسيم هاتين المسألتين الفاصلتين مرة أخرى إلى مشكلتين: مشكلة النقل إلى اليمين RBTP ومشكلة النقل إلى اليسار LBTP) ) . أولاً، قم بحساب الحل الأساسي الأولي الممكن لـ RBTP، ثم احصل أيضًا على الحل الأمثل بالطريقة الحالية؛ ليست هناك حاجة لحل LBTP مباشرة لأن حل RBTP هو الحل الأولي لـ LBTP . قم بتطبيق طريقة RCM على LBTP، للحصول على حلول الفاصل الزمني لمشكلتي النقل الفاصل. ثم تم دمج وحساب الحد الأدنى لتكلفة النقل الثلاثي الغامض، حيث لا يتم تغيير مشكلة النقل الغامض الثلاثي غير المتماثل أو المتماثل TFTP إلى TP الكلاسيكية دون استخدام طرق التصنيف، وتم الحصول على نفس النتيجة باستخدام الطريقة الحالية. وقد تم توضيح بعض الأمثلة العددية، وهي مناسبة جدًا لتوضيح فكرة هذا المفهوم. هذه الفكرة هي طريقة سهلة لفهم حالة عدم اليقين التي تحدث في مواقف الحياة الواقعية.

Optimization of Truck–Cargo Matching for the LTL Logistics Hub Based on Three-Dimensional Pallet Loading

This study investigates the truck–cargo matching problem in less-than-truckload (LTL) logistics hubs, focusing on optimizing the three-dimensional loading of goods onto standardized pallets and assigning these loaded pallets to a fleet of heterogeneous vehicles. A two-stage hybrid heuristic algorithm is proposed to solve this complex logistics challenge. In the first stage, a tree search algorithm based on residual space is developed to determine the optimal layout for the 3D loading of cargo onto pallets. In the second stage, a heuristic online truck–cargo matching algorithm is introduced to allocate loaded pallets to trucks while optimizing the number of trucks used and minimizing transportation costs. The algorithm operates within a rolling time horizon, allowing it to dynamically handle real-time order arrivals and time window constraints. Numerical experiments demonstrate that the proposed method achieves high pallet loading efficiency (close to 90%), near-optimal truck utilization (nearly 95%), and significant cost reductions, making it a practical solution for real-world LTL logistics operations.

Automated construction site layout design system for prefabricated buildings using transformer based conditional GAN

Construction site layout plans (CSLP) are crucial for efficient prefabricated construction project management. Traditional manual design process is costly and time-consuming, while optimization methods heavily depend on expert knowledge. Recent advancements in deep generative models present promising alternatives. However, their application to the generation of prefabricated construction site layouts is hindered by several challenges, including limited datasets, significant overlap between facilities, and the necessity to generate layouts based on fixed facilities with specific attributes such as minimal transportation costs. These challenges constrain the efficacy and applicability of the generated layouts. To address these issues, this study introduces an innovative automated generative design system for prefabricated construction site layouts, leveraging a novel Transformer-based conditional generative adversarial network (GAN). The data preparation module of the system collects and augments layout data for training. The CSLGAN module is designed to generate layouts that conform to spatial constraints and desired attributes, with minimal facility overlap. Furthermore, this study establishes benchmarks in terms of model capacity and specialized performance metrics. Extensive experiments demonstrate the effectiveness of the proposed system in automated construction site layout generation.

Generalized multi-manufacturer multi-retailer production-delivery supply chain model and its minimum cost solution policy

Production of a product at multiple sources and its deliveries to multiple destinations are a common practice in business. Minimization of the integrated total cost of performing operations and transportation considering the relevant factors such as the minimum order quantity contract, capacities of transport vehicles, and times of transportation in this supply chain is essential, in supplying products to customers at reasonable lesser prices. However, such a supply chain has received little attention in terms of minimizing the integrated total cost taking into account these related factors explicitly. So, there lies a research scope on this topic to fulfill the growing need of minimizing the cost of production-deliveries of products to meet customers’ demands fruitfully. Here we develop such a generalized mathematical model to minimize the integrated total cost of carrying out operations at manufacturers and retailers, and transporting batches (sub-lots) of lots from sources to destinations considering the mentioned realistic constraints. The integrated production-delivery flow is synchronized by delivering lots with batches of equal and/or unequal sizes. First without considering transportation costs, we obtain optimal batches to minimize the total cost of the model. Each of these optimal batches is proportionally distributed at manufacturers as supplies and at retailers as demands. Then the minimum transportation cost solution from manufacturers to retailers is incorporated to the earlier solution to obtain the final result. We illustrate this solution policy with numerical example problems. Sensitivity analyses are performed to see the effect of increasing values of parameters on the minimum total cost.

From biogas to biomethane: Comparison of sustainable scenarios for upgrading plant location based on greenhouse gas emissions and cost assessments

Addressing the global energy crisis and achieving sustainable development goals (SDGs) necessitates shifting towards renewable energy sources, with biomethane emerging as a viable alternative. This study evaluated three scenarios for biomethane production from biogas: localized upgrading for biofuel use, district upgrading for biofuel use, and district upgrading with grid injection. By utilizing economic assessments and spatial and network analysis, the optimal locations for upgrading plants were identified to minimize transportation costs and GHG emissions (CO2 equivalents). Results indicate that Scenario 1 achieves the lowest emissions and operating costs (41 MEUR), while Scenarios 2 and 3, despite higher initial investments (152–173 MEUR), offer significant economies of scale (1187–1321 MEUR) and substantial annual production capacities (8.8 × 106 Sm³ of biomethane). Comparative and sensitivity analyses show renewable energy sources reduce GHG emissions by up to 83.7% and significantly lower operating costs. This research underscores the critical role of strategic planning and renewable energy integration in optimizing the biomethane value chain for environmental sustainability and economic viability while also emphasizing the need for further research to refine these findings.

Comparative view of the modified Vogel’s approximation methods in transportation problem

Recently, the whole world is experiencing economic hardship and one fast road to ply is to cut out some expenses. Xlife group is equally affected and so the study proposes a means to minimize its transportation cost if effected. A comparative surgery on Vogel’s approximation with its modified versions were conducted on minimizing the cost of transporting manufactured goods from (Xlife group’s) points of supply to certain destinations was undertaken. The Vogel's Approximation Method (VAM) and the Modified Vogel's Approximation Method based on standard deviation, distribution indicators and average cost were applied to determine an initial basic feasible solution and optimal solution for certain transportation problems. All methods yield identical minimum transportation cost except at an instance.

A quadratically constrained mixed-integer non-linear programming model for multiple sink distributions

Rising traffic congestion and fuel costs pose significant challenges for supply chains with numerous retailers. This paper addresses these challenges by optimizing transportation routes for processed tomatoes within a long-haul and intercity distribution network. We use the heterogeneous capacitated vehicle routing problem framework to create a new quadratically constrained mixed-integer non-linear programming model that aims to meet demand at multiple destinations while minimizing transportation costs. Our model incorporates real-time data and route optimization strategies that consider traffic conditions based on freight time and route diversions for expedited deliveries. It aims to devise an optimal transportation schedule that minimizes fuel, operational, and maintenance costs while ensuring efficient delivery of tomato paste. By applying this model to a real-world case study, we estimate a significant 27.59% reduction in transportation costs, dropping them from GH¢20,270 ($1,638.91) to GH¢14,676 ($1,186.61) on average. This highlights the effectiveness of our strategy in lowering costs while maintaining smooth and efficient deliveries.

A two-stage location model covering COVID-19 sampling, transport and DNA diagnosis: design of a national scheme for infection control.

During the COVID-19 pandemic, a system was established in China that required testing of all residents for COVID-19. It consisted of sampling stations, laboratories capable of carrying out DNA investigations and vehicles carrying out immediate transfer of all samples from the former to the latter. Using Beilin District, Xi'an City, Shaanxi Province, China as example, we designed a genetic algorithm based on a two-stage location coverage model for the location of the sampling stations with regard to existing residencies as well as the transfer between the sampling stations and the laboratories. The aim was to estimate the minimum transportation costs between these units. In the first stage, the model considered demands for testing in residential areas, with the objective of minimizing the costs related to travel between residencies and sampling stations. In the second stage, this approach was extended to cover the location of the laboratories doing the DNAinvestigation, with the aim of minimizing the transportation costs between them and the sampling stations as well as the estimating the number of laboratories needed. Solutions were based on sampling stations and laboratories existing in 2022, with the results visualized by geographic information systems (GIS). The results show that the genetic algorithm designed in this paper had a better solution speed than the Gurobi algorithm. The convergence was better and the larger the network size, the more efficient the genetic algorithm solution time.

Exact methods and a variable neighborhood search for the robust capacitated [formula omitted]-median problem

The capacitated p-median problem (CPMP) involves placing p identical facilities in a network and assigning customer nodes to these facilities to satisfy all customer demands with minimal transportation costs. In practical applications, demand and distance parameters are often uncertain during the planning process, leading to infeasible or excessively costly solutions if these uncertainties are disregarded. This paper addresses the robust CPMP (RCPMP), which incorporates demand uncertainty into the problem using the robust optimization paradigm. We propose a general framework to model and solve the RCPMP, considering different polyhedral uncertainty sets, namely the cardinality-constrained and the knapsack sets. We develop exact approaches encompassing compact models, different families of valid inequalities, and branch-and-cut and branch-and-price algorithms, exploring both implemented uncertainty sets and problem structure. Furthermore, we implement an efficient Variable Neighborhood Search (VNS) heuristic to solve these robust variants, which incorporates state-of-the-art algorithms, parallelization techniques, and optimized data structures. Computational experiments using adapted benchmark instances with up to 400 nodes indicate the effectiveness of the proposed approaches. The results show that using parallelization and hash tables within the VNS heuristic promotes significant performance improvements and yields near-optimal solutions for most instances, as well as outperforming the exact approaches in several instances where the optimal solution was not found. Moreover, these results highlight the benefits of using robust solutions in practical settings, especially when considering different uncertainty sets to generate solutions with advantageous trade-offs between cost and risk.

A novel framework for production planning and class-based storage location assignment: Multi-criteria classification approach

Efficient warehouse management is essential for optimizing inventory, minimizing transportation costs, and enhancing overall performance. This research introduces a novel Mixed-Integer Nonlinear Programming (MINLP) model to address the Storage Location Assignment Problem (SLAP) in warehouse management. Integrating multi-criteria decision-making with strategic production planning, our model advances warehouse operations by allocating storage locations to products strategically, focusing on reducing transportation distances and maximizing storage efficiency. The distinctive innovation of this study is the nuanced application of the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) results to strategic storage location assignments, enhancing the model's capability to consider a comprehensive evaluation of inventory attributes, including physical characteristics and perishability. This approach evolves TOPSIS's application in warehouse management, enabling it to consider both physical characteristics and perishability of products. The outcomes of TOPSIS, including product classifications and preferences, serve as vital inputs to the mathematical model, facilitating a comprehensive evaluation of storage locations that encompasses spatial, demand-related, and physical aspects of inventory. Additionally, our research introduces a versatile decision support system, adaptable to various operational requirements. This system enhances practical decision-making in warehouse management, accommodating scenarios based on single or multiple criteria, including the cube-per-order index (COI). The research results highlight the significant impact of this innovative approach in enhancing warehouse management. By addressing the complexities of storage location assignment and integrating multiple criteria, we achieve more efficient and cost-effective warehouse operations. The approach has been shown to be adaptable and practical, making it a valuable contribution to the field of logistics and warehouse management.

Multi-objective Optimization-Based Algorithm for Selecting the Optimal Path of Rural Multi-temperature Zone Cold Chain Dynamic Logistics Intermodal Transportation

The road network in rural areas is complex and the infrastructure is relatively backward. The multi-temperature zone cold chain logistics involves agricultural products with different temperature requirements, which requires considering the transportation cost, carbon emission cost, refrigeration cost, and time cost of different temperature zones during path planning, thereby increasing the difficulty of path planning. Therefore, a multi-objective optimization-based algorithm for selecting the optimal path of rural multi-temperature zone cold chain dynamic logistics intermodal transportation is proposed. Based on the analysis of the multi-temperature cold chain collection and distribution model based on multimodal transportation, a multi-objective optimization model is constructed. This model aims to minimize transportation costs, carbon emission costs, refrigeration costs, time costs, and maximize logistics quality, while satisfying constraints such as transfer schedule times, the number of transport mode conversions, transport mode selection, and time continuity. To solve this model, an improved NSGA-II algorithm is adopted, which combines an improved mutation operator, congestion distance calculation, and the C-W saving algorithm to achieve the optimal transport path solution. Additionally, ArcGIS software is used to implement the shortest path planning based on real road networks. The experimental results show that by selecting the road-rail combined transport mode and adopting the D1–D6–D10 transport path, it is possible to transport fresh agricultural products from location A to the distribution center at location B, with the lowest Pareto fitness value. Furthermore, the algorithm's effectiveness is further verified by completing the end-of-life fresh agricultural product distribution task with four multi-temperature refrigerated vehicles. The study also finds that extending or shortening the latest service time window for customers, although it leads to a decrease or increase in the optimal value of the algorithm's objective function, has little impact on the average distribution time and transport vehicles. These findings provide new theoretical and practical guidance for the path selection of multimodal transportation in multi-temperature cold chain logistics, with significant theoretical and application value.

A GRASP algorithm for the concrete delivery problem

This paper addresses a novel variant of the Concrete Delivery Problem (CDP), which involves the efficient scheduling of ready-mixed concrete deliveries to construction sites while balancing the conflicting goals of minimizing transportation costs and maximizing customer satisfaction. In this study, we propose an exact formulation and a heuristic approach based on the Greedy Randomized Adaptive Search Procedure (GRASP) to tackle this challenging CDP variant. This variant introduces realistic side constraints, including driver working shifts, a minimum driver working time, and overtime penalties. Additionally, it considers the case where customers may request multiple types of concrete delivered within the same time window. We assess the performance of our heuristic using new instances generated for this problem and provide a comparative analysis with another CDP variant from the literature to demonstrate its effectiveness.

Application of Dijkstra Algorithm in Determining Transportation Costs for Tourist Attractions in Lombok Island Based on the Shortest Path

Purpose: Lombok Island is known as an attractive tourist destination with natural beauty and unique culture. The growth of the tourism sector is very important for regional economic development. Lombok Island often faces challenges in its transportation system, including complex routes, varying road conditions, and traffic problems. Method: In this research, the data used were 30 tourist attractions on the island of Lombok sourced from the Tourism Office. Tourist attractions in Lombok are represented by vertices in the graph. Then the edges represent roads connecting tourist attractions and the weights represent the cost of getting to each tourist attraction from a starting vertex. Then, to determine the minimum transportation cost for each tourist attraction based on this graph, we use Dijkstra algorithm based on the shortest path for each tourist attraction. Result: The minimum transportation costs for each tourist attraction are obtained based on the shortest route for each tourist attraction on Lombok Island. Contribution: The application of Dijkstra algorithm can be a solution to overcome some of these challenges by determining the shortest path and optimizing transportation costs.

A real-time on-site precision nutrient monitoring system for hydroponic cultivation utilizing LIBS

Indoor hydroponic farming is an advanced cultivation technique with diverse sustainability benefits, such as facilitating local produce, minimizing transportation costs and emissions, and enabling year-round crop cultivation. To optimize crop growth for enhanced yield, improved crop quality, and reduced environmental footprint, precise monitoring and replenishment of essential nutrients within hydroponic systems is crucial. Current methods employed in most commercial farms for online nutrient supply monitoring is limited to pH and conductivity measurements. These techniques can only offer an indication of the overall change in the complex nutrient mixture and lack the capability to precisely identify the specific nutrient or quantify the nutrient content. Most of the existing techniques for measuring individual nutrient levels are expensive and invasive, necessitating sample preparation, frequent recalibration, and skilled personnel for operation. In this context, we propose and demonstrate a real-time, on-site monitoring system for the precise analysis of hydroponic nutrient supply based on laser-induced breakdown spectroscopy (LIBS). We also discuss the system design considerations, parametric optimizations, limit of detection (LOD), and limit of quantitation (LOQ) of key nutrient components such as potassium (K), sodium (Na), calcium (Ca), and magnesium (Mg), using the proposed approach. The detection range of the developed LIBS-based monitoring system can encompass the typical concentration range observed in hydroponic nutrient solutions used at agricultural farms. This technique offers rapid online monitoring of individual nutrient components, providing precise, real-time analysis and the potential to enable comprehensive automation capabilities for current and future hydroponic farms.Graphical abstract

BDE-Jaya: A binary discrete enhanced Jaya algorithm for multiple automated guided vehicle scheduling problem in matrix manufacturing workshop

With the advent of "Industry 4.0", more matrix manufacturing workshops have adopted automated guided vehicle (AGV) for material handling. AGV transportation has become a key link in manufacturing production. Traditional AGVs scheduling problem (AGVSP) is studied in depth. However, most research overlooks an important problem, in production with limited resources, the number of AGVs is insufficient. Therefore, the wait time of workstations is longer than expected. The service time of the task is delayed and the cost is increased. To solve above problem, this paper proposes the binary discrete enhanced Jaya (BDE-Jaya) algorithm. The main goal is to minimize transportation cost, including AGV traveling cost, service early penalty, and total tardiness (TTD). A key-task shift method is proposed to reduce TTD and task service early penalty. Two heuristics based on the problem features are designed to generate the initial solution. In the evolutionary stage, three offspring generation methods are used to improve the algorithm exploitation capability and exploration capability. Then, an insertion-based repair method is designed to prevent the exploitation process falling into local optimum. Furthermore, three parameters are proposed to improve the performance of the algorithm. Finally, simulation experiment shows that the proposed BDE-Jaya algorithm has significant advantages compared with other algorithms.

Optimized transportation scheduling for precast concrete components considering heterogeneous vehicle-size matching

Recently, prefabricated construction has been vigorously promoted, resulting in high demand for precast concrete (PC) components. The transportation scheduling optimization problem of PC components with various kinds from multiple projects arises. Unlike conventional cargo, PC components are characterized by shape heterogeneity, large volume, and strict delivery time limits. Based on three characteristics, a heterogeneous fixed fleet vehicle routing problem (HFFVRP) for PC components is introduced, where heterogeneous vehicles, allocation of PC components to size-matching vehicles, and hybrid time windows are considered. Then a two-stage solution strategy based on the improved ant colony optimization (ACO) and Dijkstra algorithm is designed to obtain optimal vehicle routes under minimum transportation costs. The results indicate that the improved ACO-Dijkstra algorithm outperforms in obtaining optimal transportation plans for heterogeneous vehicles compared with manual decision-making and other heuristic algorithms. Sensitivity analysis denotes that utilizing heterogeneous vehicles contributes to reductions in transportation costs, and vehicle configuration should be adjusted along with demand scales. The proposed model and algorithm extend the theoretical basis of construction industrial applications.

The Logistics of Volkswagen Development Center Applies Operations Research to Optimize Transshipments

Volkswagen Technical Development (TE) is responsible for all prototype development and prototype production for the Volkswagen brand and has its own logistics department (TE-Logistics). In the logistics of prototype parts in the automotive industry, new versions of prototype parts (henceforth referred to as updating parts) are repeatedly assembled in finished prototype vehicles. These updating parts are stored in warehouses and provided to an assembly site to ensure a timely assembly of the associated prototype vehicles. As the internal warehouse on the company site is not large enough for the high variety of parts, an additional external warehouse in the logistics network is needed. However, since prototype parts are unique, the allocation of the parts in suitable warehouses is particularly important. Currently, the various warehouses and the short-term demands repeatedly lead to reactive transshipments between the warehouses. To this end, we developed an approach for proactive transshipments based on a machine learning forecast and a mixed-integer linear programming model for planning proactive transshipments of parts between the warehouses to minimize transport costs. The model is based on a probability estimation of future demands to anticipate the expected optimal warehouse. After the model had revealed high improvement potential through a case study with real-world data in terms of costs and availability time compared to the current reactive process, we derived decision rules and developed a rule-based heuristic algorithm that leads to the optimal solution for the industrial use case. We implemented the heuristic with a spreadsheet-based decision support system (DSS) for daily transshipment planning. After successful test implementation, TE-Logistics estimated the annual cost savings for transport to be approximately 10%.

An exact method for vehicle routing problem with backhaul discounts in urban express delivery network

The surge in e-commerce has led to an increased demand for urban express services, requiring the strategic development of delivery networks that are both efficient and cost-effective. This study addresses a practical vehicle routing problem (VRP) in an urban express delivery network to minimize transportation costs. Specifically, it considers the implementation of backhaul discounts, a factor disregarded in the existing literature. This VRP is further complicated by various realistic constraints, including pickup and delivery, time windows, multiple trips, heterogeneous fleets, and docking capacity limitations, which make most general VRP solvers inapplicable. This study proposes a trip-based formulation to overcome this challenge and develop a tailored branch-and-price algorithm. Feasible trips are classified into four types to simplify the computation of backhaul discounts, thereby enhancing solution efficiency. Validation with real-world data from SF Express substantiates the efficacy of our method and yields insights for sustainable city logistics management. Moreover, our simplified column generation algorithm exhibits competitive performance, achieving optimal solutions expeditiously for the tested instances.

Modelling and optimization for integrated scheduling problem considering spare parts production, batch transportation and equipment operation

Existing production scheduling research has made great effort to integrate multiple production-related actives to achieve efficient product supply, such as the integration of production and transportation, and the integration of production and equipment operation and maintenance (O&M). However, rare studies are executed to investigate the integration of production, transportation and O&M, which may lead to inefficient supply plans. Encouraged by this, we consider a novel integrated scheduling problem, in which two-stage hybrid flow shop scheduling for spare parts manufacturing, transportation scheduling of the third-party logistics (3PL) and operational strategies of complex equipment are considered simultaneously. To tackle it, a mixed-integer linear programming model is constructed to minimize total production costs, minimize transportation costs and maximize operational utility of the equipment. Furthermore, a two-stage memetic algorithm (TSMA) is designed for addressing the problem. It employs a five-layer encoding method for chromosome representation and three well-tailored initialization methods to generate a high-quality initial population. In the first optimization stage, some problem-specific operators, including three crossovers, two mutations, and an entity-oriented local search operator, are proposed to improve its search capability. Two cost-saving strategies devised in the second optimization stage are designed to further optimize the optimal Pareto solutions generated in the previous stage. Extensive experiments demonstrate the superiority of the proposed designs and TSMA in addressing the considered problem. In addition, the necessity of integrating production, transportation and equipment operation is verified through a set of comparison experiments. The study enriches integrated production scheduling theory, and provides methodological support for improving operational utility of complex equipment.

Transportation Model : Review of Its Practical Application in Kogi State, Nigeria

The transportation model is a linear programming model targeting at minimization of transportation cost for any firm. However, it is critical to examine how effective it can be applied to enable firms pursue its immediate and strategic objectives. This study on transportation model is carried out to examine the practical application of transportation model in Otebu Investment limited Idah, Kogi State. The study was induced by the curiosity to ascertain the extent in which the transportation model as a branch of linear programming model is being applied by the firm and how this model has been able to enhance the performance through cost minimization. The study empirically reached both the Management, senior and junior employees of the enterprise through field descriptive survey research and finding revealed that the application of transportation model of linear programming have been able to enhance the performance of the firm hence considering the fact that there is a link between cost minimization and revenue drive of the Firms this model should be consistently adopted so as to be able to continuously minimize transportation cost.