Mathematics

Research

18 pages, 382 KiB

Open AccessArticle

Fuzzy Multi-Item Newsvendor Problem: An Application to Inventory Management

by João M. C. Sousa, Rodrigo Luís, Rui Mirra Santos, Luís Mendonça and Susana M. Vieira

Mathematics 2024, 12(11), 1652; https://doi.org/10.3390/math12111652 - 24 May 2024

Viewed by 718

This paper proposes a novel approach to the fuzzy newsvendor problem for inventory management applications. The main contributions of the paper are the following: a new credibility estimation is proposed, to explore the neighborhood around the most impactful demand scenarios; a simulation procedure [...] Read more.

This paper proposes a novel approach to the fuzzy newsvendor problem for inventory management applications. The main contributions of the paper are the following: a new credibility estimation is proposed, to explore the neighborhood around the most impactful demand scenarios; a simulation procedure was designed for the different demand scenarios, which allows comparison of the proposed approach with classical and fuzzy multi-item newsvendor problems; a modified genetic algorithm (GA) is introduced to ameliorate previous genetic algorithms in both the generation and evaluation of solutions. The new formulation of the fuzzy newsvendor problem, together with the modified GA, were shown to improve the average profit by up to 55% in problems with low-budget scenarios. Full article

(This article belongs to the Special Issue Mathematical Methods and Operation Research in Logistics, Project Planning, and Scheduling, 2nd Edition)

► Show Figures

Figure 1

12 pages, 910 KiB

Open AccessArticle

Model and Algorithm for a Two-Machine Group Scheduling Problem with Setup and Transportation Time

by Yu Ni, Shufen Dai, Shuaipeng Yuan, Bailin Wang and Zhuolun Zhang

Mathematics 2024, 12(6), 888; https://doi.org/10.3390/math12060888 - 18 Mar 2024

Viewed by 795

Abstract

This paper investigates a two-machine group scheduling problem with sequence-independent setup times and round-trip transportation times, which is derived from the production management requirements of modern steel manufacturing enterprises. The objective is to minimize the makespan. Addressing limitations in prior studies, we consider [...] Read more.

This paper investigates a two-machine group scheduling problem with sequence-independent setup times and round-trip transportation times, which is derived from the production management requirements of modern steel manufacturing enterprises. The objective is to minimize the makespan. Addressing limitations in prior studies, we consider a critical but largely ignored transportation method, namely round-trip transportation, and restricted transporter capacity between machines. To solve this problem, a mixed-integer programming model is first developed. Then, the problem complexity is analyzed for situations with both single and unlimited transporters. For the NP-hard case of a single transporter, we design an efficient two-stage heuristic algorithm with proven acceptable solution quality bounds. Extensive computational experiments based on steel plant data demonstrate the effectiveness of our approach in providing near-optimal solutions, and the maximum deviation between our algorithm and the optimal solution is 1.38%. This research can provide an operable optimization method that is valuable for group scheduling and transportation scheduling. Full article

(This article belongs to the Special Issue Mathematical Methods and Operation Research in Logistics, Project Planning, and Scheduling, 2nd Edition)

► Show Figures

Figure 1

23 pages, 877 KiB

Open AccessArticle

REFS-A Risk Evaluation Framework on Supply Chain

by István Mihálcz and Zsolt T. Kosztyán

Mathematics 2024, 12(6), 841; https://doi.org/10.3390/math12060841 - 13 Mar 2024

Viewed by 960

Abstract

Large, powerful corporations were formerly solely and exclusively responsible for supplies, manufacturing, and distribution; however, the supply chain has undergone significant transformations over the last half-century. Almost all supply chain processes are currently outsourced, owing to the initiatives of cutting-edge, contemporary businesses. According [...] Read more.

Large, powerful corporations were formerly solely and exclusively responsible for supplies, manufacturing, and distribution; however, the supply chain has undergone significant transformations over the last half-century. Almost all supply chain processes are currently outsourced, owing to the initiatives of cutting-edge, contemporary businesses. According to a compilation of studies, analysts, and news sources, the level of risk associated with modern supply chains is considerably higher than the majority of supply chain managers believe. Supply chain vulnerabilities continue to pose a substantial obstacle for a great number of organizations. Neglecting to adequately address these risks—encompassing natural disasters, cyber assaults, acts of terrorism, the credit crisis, pandemic scenarios, and war—could result in substantial reductions in metrics such as profitability, productivity, revenue, and competitive advantage. Unresolved concerns persist with respect to the risk assessment of the supply chain. The purpose of this article is to propose a framework for risk evaluation that can be efficiently applied to the evaluation of hazards within the supply chain. This research study significantly enhances the existing knowledge base by offering supply chain managers a pragmatic tool to evaluate their processes, regardless of the mathematical foundations or the variety of variables utilized in risk assessment. The outcomes of multiple aggregation methods are compared using a case study from an automotive EMS production; the conclusions are validated by risk and FMEA specialists from the same factory. Full article

(This article belongs to the Special Issue Mathematical Methods and Operation Research in Logistics, Project Planning, and Scheduling, 2nd Edition)

► Show Figures

Figure 1

19 pages, 2021 KiB

Open AccessArticle

Simulation of Heuristics for Automated Guided Vehicle Task Sequencing with Resource Sharing and Dynamic Queues

by Jonas F. Leon, Mohammad Peyman, Xabier A. Martin and Angel A. Juan

Mathematics 2024, 12(2), 271; https://doi.org/10.3390/math12020271 - 14 Jan 2024

Viewed by 1376

Abstract

Automated guided vehicles (AGVs) stand out as a paradigmatic application of Industry 4.0, requiring the seamless integration of new concepts and technologies to enhance productivity while reducing labor costs, energy consumption, and emissions. In this context, specific industrial use cases can present a [...] Read more.

Automated guided vehicles (AGVs) stand out as a paradigmatic application of Industry 4.0, requiring the seamless integration of new concepts and technologies to enhance productivity while reducing labor costs, energy consumption, and emissions. In this context, specific industrial use cases can present a significant technological and scientific challenge. This study was inspired by a real industrial application for which the existing AGV literature did not contain an already well-studied solution. The problem is related to the sequencing of assigned tasks, where the queue formation dynamics and the resource sharing define the scheduling. The combinatorial nature of the problem requires the use of advanced mathematical tools such as heuristics, simulations, or a combination of both. A heuristic procedure was developed that generates candidate task sequences, which are, in turn, evaluated in a discrete-event simulation model developed in Simul8. This combined approach allows high-quality solutions to be generated and realistically evaluated, even graphically, by stakeholders and decision makers. A number of computational experiments were developed to validate the proposed method, which opens up some future lines of research, especially when considering stochastic settings. Full article

(This article belongs to the Special Issue Mathematical Methods and Operation Research in Logistics, Project Planning, and Scheduling, 2nd Edition)

► Show Figures

Figure 1

21 pages, 2256 KiB

Open AccessArticle

Multiple Control Policy in Unreliable Two-Phase Bulk Queueing System with Active Bernoulli Feedback and Vacation

by S. P. Niranjan, S. Devi Latha, Miroslav Mahdal and Krishnasamy Karthik

Mathematics 2024, 12(1), 75; https://doi.org/10.3390/math12010075 - 25 Dec 2023

Cited by 1 | Viewed by 1016

Abstract

In this paper, a bulk arrival and two-phase bulk service with active Bernoulli feedback, vacation, and breakdown is considered. The server provides service in two phases as mandatory according to the general bulk service rule, with minimum bulk size

^{'} a^{'}

and [...] Read more.

In this paper, a bulk arrival and two-phase bulk service with active Bernoulli feedback, vacation, and breakdown is considered. The server provides service in two phases as mandatory according to the general bulk service rule, with minimum bulk size

^{'} a^{'}

and maximum bulk size

^{'} b^{'}

. In the first essential service (FES) completion epoch, if the server fails, with probability

^{'} δ^{'}

, then the renewal of the service station is considered. On the other hand, if there is no server failure, with a probability

^{'} 1 - δ^{'}

, then the server switches to a second essential service (SES) in succession. A customer who requires further service as feedback is given priority, and they join the head of the queue with probability

β

. On the contrary, a customer who does not require feedback leaves the system with a probability

^{'} 1 - β^{'}

. If the queue length is less than

^{'} a^{'}

after SES, the server may leave for a single vacation with probability

^{'} 1 - β^{'}

. When the server finds an inadequate number of customers in the queue after vacation completion, the server becomes dormant. After vacation completion, the server requires some time to start service, which is attained by including setup time. The setup time is initiated only when the queue length is at least

^{'} a^{'}

. Even after setup time completion, the service process begins only with a queue length ‘N’ (N > b). The novelty of this paper is that it introduces an essential two-phase bulk service, immediate Bernoulli feedback for customers, and renewal service time of the first essential service for the bulk arrival and bulk service queueing model. We aim to develop a model that investigates the probability-generating function of the queue size at any time. Additionally, we analyzed various performance characteristics using numerical examples to demonstrate the model’s effectiveness. An optimum cost analysis was also carried out to minimize the total average cost with appropriate practical applications in existing data transmission and data processing in LTE-A networks using the DRX mechanism. Full article

(This article belongs to the Special Issue Mathematical Methods and Operation Research in Logistics, Project Planning, and Scheduling, 2nd Edition)

► Show Figures

Figure 1

18 pages, 3975 KiB

Open AccessEditor’s ChoiceArticle

Demand Prediction of Shared Bicycles Based on Graph Convolutional Network-Gated Recurrent Unit-Attention Mechanism

by Jian-You Xu, Yan Qian, Shuo Zhang and Chin-Chia Wu

Mathematics 2023, 11(24), 4994; https://doi.org/10.3390/math11244994 - 18 Dec 2023

Cited by 3 | Viewed by 1143

Abstract

Shared bicycles provide a green, environmentally friendly, and healthy mode of transportation that effectively addresses the “final mile” problem in urban travel. However, the uneven distribution of bicycles and the imbalance of user demand can significantly impact user experience and bicycle usage efficiency, [...] Read more.

Shared bicycles provide a green, environmentally friendly, and healthy mode of transportation that effectively addresses the “final mile” problem in urban travel. However, the uneven distribution of bicycles and the imbalance of user demand can significantly impact user experience and bicycle usage efficiency, which makes it necessary to predict bicycle demand. In this paper, we propose a novel shared-bicycle demand prediction method based on station clustering. First, to address the challenge of capturing patterns in station-level bicycle demand, which exhibits significant fluctuations, we employ a clustering method that combines graph information from the bicycle transfer graph and potential energy. This method aggregates closely related stations into corresponding prediction regions. Second, we use the GCN-CRU-AM (Graph Convolutional Network-Gated Recurrent Unit-Attention Mechanism) model to predict bicycle demand in each region. This model extracts the spatial information and correlation between regions, integrates time feature data and local weather data, and assigns weights to the input features. Finally, experimental results based on the data from Citi Bike System in New York City demonstrate that the proposed model achieves a more accurate demand prediction. Full article

(This article belongs to the Special Issue Mathematical Methods and Operation Research in Logistics, Project Planning, and Scheduling, 2nd Edition)

► Show Figures

Figure 1

25 pages, 3065 KiB

Open AccessArticle

Multi-Objective Q-Learning-Based Brain Storm Optimization for Integrated Distributed Flow Shop and Distribution Scheduling Problems

by Shuo Zhang, Jianyou Xu and Yingli Qiao

Mathematics 2023, 11(20), 4306; https://doi.org/10.3390/math11204306 - 16 Oct 2023

Cited by 1 | Viewed by 1262

Abstract

In recent years, integrated production and distribution scheduling (IPDS) has become an important subject in supply chain management. However, IPDS considering distributed manufacturing environments is rarely researched. Moreover, reinforcement learning is seldom combined with metaheuristics to deal with IPDS problems. In this work, [...] Read more.

In recent years, integrated production and distribution scheduling (IPDS) has become an important subject in supply chain management. However, IPDS considering distributed manufacturing environments is rarely researched. Moreover, reinforcement learning is seldom combined with metaheuristics to deal with IPDS problems. In this work, an integrated distributed flow shop and distribution scheduling problem is studied, and a mathematical model is provided. Owing to the problem’s NP-hard nature, a multi-objective Q-learning-based brain storm optimization is designed to minimize makespan and total weighted earliness and tardiness. In the presented approach, a double-string representation method is utilized, and a dynamic clustering method is developed in the clustering phase. In the generating phase, a global search strategy, a local search strategy, and a simulated annealing strategy are introduced. A Q-learning process is performed to dynamically choose the generation strategy. It consists of four actions defined as the combinations of these strategies, four states described by convergence and uniformity metrics, a reward function, and an improved ε-greedy method. In the selecting phase, a newly defined selection method is adopted. To assess the effectiveness of the proposed approach, a comparison pool consisting of four prevalent metaheuristics and a CPLEX optimizer is applied to conduct numerical experiments and statistical tests. The results suggest that the designed approach outperforms its competitors in acquiring promising solutions when handling the considered problem. Full article

(This article belongs to the Special Issue Mathematical Methods and Operation Research in Logistics, Project Planning, and Scheduling, 2nd Edition)

► Show Figures

Figure 1

22 pages, 2218 KiB

Open AccessArticle

Resilient Supply Chain Optimization Considering Alternative Supplier Selection and Temporary Distribution Center Location

by Na Wang, Jingze Chen and Hongfeng Wang

Mathematics 2023, 11(18), 3955; https://doi.org/10.3390/math11183955 - 18 Sep 2023

Cited by 2 | Viewed by 2828

Abstract

The global supply chain is facing huge uncertainties due to potential emergencies, and the disruption of any link may threaten the security of the supply chain. This paper considers a disruption scenario in which supply disruption and distribution center failure occur simultaneously from [...] Read more.

The global supply chain is facing huge uncertainties due to potential emergencies, and the disruption of any link may threaten the security of the supply chain. This paper considers a disruption scenario in which supply disruption and distribution center failure occur simultaneously from the point of view of the manufacturer. A resilient supply chain optimization model is developed based on a combination of proactive and reactive defense strategies, including manufacturer’s raw material mitigation inventory, preference for temporary distribution center locations, and product design changes, with the objective of obtaining maximum expected profit. The proposed stochastic planning model with demand uncertainty is approximated as a mixed integer linear programming model using Latin hypercube sampling (LHS), sample average approximation (SAA), and scenario reduction (SR) methods. In addition, an improved genetic algorithm (GA) is also developed to determine the approximate optimal solution. The algorithm ensures the feasibility of the solution and improves the solving efficiency through specific heuristic repair strategies. Numerical experiments are conducted to verify the application and advantages of the proposed disruption recovery model and approach. The experimental results show that the proposed resilient supply chain optimization model can effectively reduce the recovery cost of manufacturers after disruption, and the proposed approach performs well in dealing with related problems. Full article

(This article belongs to the Special Issue Mathematical Methods and Operation Research in Logistics, Project Planning, and Scheduling, 2nd Edition)

► Show Figures