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Mathematics
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Mathematical Approaches Applied in Operations Research, Logistics, and Inventory
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Mathematical Approaches Applied in Operations Research, Logistics, and Inventory

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Computational and Applied Mathematics".

Deadline for manuscript submissions: 10 April 2025 | Viewed by 6520

Special Issue Editors

Dr. Pei-Fang Tsai

E-Mail Website
Guest Editor
Department of Industrial Engineering and Management, National Taipei University of Technology, Taipei 10608, Taiwan
Interests: optimization; operations research; operations management; inventory; scheduling; simulation
Prof. Dr. Ming-Feng Yang

E-Mail Website
Guest Editor
Department of Transportation Science, National Taiwan Ocean University, Keelung 20224, Taiwan
Interests: supply chain management; inventory management; operations management

Special Issue Information

Dear Colleagues,

With the advances in sensors and automation technologies, data collection has become cheaper and ubiquitous. The availability of huge data opens up opportunities in efficient design in possible operation strategies by correcting prediction in system behaviors with uncertainty. To deal with practical difficulties in digital transformation and intelligent data analytics, innovative mathematical approaches are required to help manufacturers as well as service providers make better decisions. Another drive in utilizing mathematical models also lies in how to operate business functions to fulfil the competing needs in customer satisfaction, cost, and quality requirement while considering corporate resilience and various goals related to environmental, social, and governance (ESG) factors.

This Special Issue aims to demonstrate the latest research findings and scientific articles of the latest mathematical applications in operations research, logistics, and inventory. High-quality research in the innovative adoption or mix use of mathematical approaches with potential in real-world applications are particularly welcome.

Dr. Pei-Fang Tsai
Prof. Dr. Ming-Feng Yang
Guest Editors

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 100 words) can be sent to the Editorial Office for announcement on this website.

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-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics 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 2600 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

  • operations research
  • logistics management
  • inventory management
  • mathematical models
  • mathematical methods
  • optimization
  • decision making
  • planning under carbon footprint constraints
  • green manufacturing
  • resilience and flexibility in planning and scheduling
  • risk evaluation and analysis modelling
  • operations management
  • uncertainty
  • Internet of Things
  • Industry 5.0

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Further information on MDPI's Special Issue polices can be found here.

Published Papers (5 papers)

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Research

16 pages, 2126 KiB  
Article
Optimizing Supply Chain Design under Demand Uncertainty with Quantity Discount Policy
by Jung-Fa Tsai, Peng-Nan Tan, Nguyen-Thao Truong, Dinh-Hieu Tran and Ming-Hua Lin
Mathematics 2024, 12(20), 3228; https://doi.org/10.3390/math12203228 - 15 Oct 2024
Viewed by 633
Abstract
In typical business situations, sellers usually offer discount schemes to buyers to increase overall profitability. This study aims to design a supply chain network under uncertainty of demand by integrating an all-unit quantity discount policy. The objective is to maximize the profit of [...] Read more.
In typical business situations, sellers usually offer discount schemes to buyers to increase overall profitability. This study aims to design a supply chain network under uncertainty of demand by integrating an all-unit quantity discount policy. The objective is to maximize the profit of the entire supply chain. The proposed model is formulated as a mixed integer nonlinear programming model, which is subsequently linearized into a mixed integer linear programming model and hence able to obtain a global solution. Numerical examples in the manufacturing supply chain where customer demand follows normal distributions are used to assess the effect of quantity discount policies. Key findings demonstrate that the integration of quantity discount policies significantly reduces total supply chain costs and improves inventory management under demand uncertainty, and decision makers need to decide a balance level between service levels and profits. Full article
(This article belongs to the Special Issue Mathematical Approaches Applied in Operations Research, Logistics, and Inventory)
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27 pages, 1446 KiB  
Article
A Graph-Refinement Algorithm to Minimize Squared Delivery Delays Using Parcel Robots
by Fabian Gnegel, Stefan Schaudt, Uwe Clausen and Armin Fügenschuh
Mathematics 2024, 12(20), 3201; https://doi.org/10.3390/math12203201 - 12 Oct 2024
Viewed by 701
Abstract
In recent years, parcel volumes have reached record highs, prompting the logistics industry to explore innovative solutions to meet growing demand. In densely populated areas, delivery robots offer a promising alternative to traditional truck-based delivery systems. These autonomous electric robots operate on sidewalks [...] Read more.
In recent years, parcel volumes have reached record highs, prompting the logistics industry to explore innovative solutions to meet growing demand. In densely populated areas, delivery robots offer a promising alternative to traditional truck-based delivery systems. These autonomous electric robots operate on sidewalks and deliver time-sensitive goods, such as express parcels, medicine and meals. However, their limited cargo capacity and battery life require a return to a depot after each delivery. This challenge can be modeled as an electric vehicle-routing problem with soft time windows and single-unit capacity constraints. The objective is to serve all customers while minimizing the quadratic sum of delivery delays and ensuring each vehicle operates within its battery limitations. To address this problem, we propose a mixed-integer quadratic programming model and introduce an enhanced formulation using a layered graph structure. For this layered graph, we present two solution approaches based on relaxations that reduce the number of nodes and arcs compared to the expanded formulation. The first approach, Iterative Refinement, solves the current relaxation to optimality and refines the graph when the solution is infeasible for the expanded formulation. This process continues until a proven optimal solution is obtained. The second approach, Branch and Refine, integrates graph refinement into a branch-and-bound framework, eliminating the need for restarts. Computational experiments on modified Solomon instances demonstrate the effectiveness of our solution approaches, with Branch and Refine consistently outperforming Iterative Refinement across all tested parameter configurations. Full article
(This article belongs to the Special Issue Mathematical Approaches Applied in Operations Research, Logistics, and Inventory)
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22 pages, 409 KiB  
Article
On the Number of Customer Classes in a Single-Period Inventory System
by Mónica López-Campos, Pablo Escalona, Alejandro Angulo, Francisca Recabarren and Raúl Stegmaier
Mathematics 2024, 12(10), 1509; https://doi.org/10.3390/math12101509 - 12 May 2024
Viewed by 912
Abstract
A common practice in inventory systems with several customers requiring differentiated service levels is to group them into two or three classes, where a customer class is a group of customers with the same preset service level in terms of product availability. However, [...] Read more.
A common practice in inventory systems with several customers requiring differentiated service levels is to group them into two or three classes, where a customer class is a group of customers with the same preset service level in terms of product availability. However, there is no evidence that grouping customers into two or three classes is optimal in terms of the ordering policy parameters. This paper studies the effect of the number of customer classes on the inventory level of a single-period inventory system with stochastic demand and individual service-level requirements from multiple customer classes. Using a Sample Average Approximation approach, we formulate computationally tractable multi-class service level models, under responsive and anticipative priority policies in cases of shortage, as mixed integer linear problems (MIPs). The effect of the number of classes on the inventory level is determined using a round-up aggregation scheme; i.e., given a sufficiently large initial number of classes, it is reduced by adding the lower service level classes to the next higher class. We analytically characterize the optimal inventory level under responsive and anticipative priority policies as a function of the initial number of classes and the number of classes grouped based on the round-up aggregation scheme. Under a responsive priority policy, we show that there is an optimal number of classes, while under an anticipative priority policy, the optimal number of classes is equal to the initial number of classes. The effect of free-riders resulting from the round-up aggregation scheme on the optimal inventory level is studied through numerical experiments. Full article
(This article belongs to the Special Issue Mathematical Approaches Applied in Operations Research, Logistics, and Inventory)
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15 pages, 2654 KiB  
Article
An EOQ Model for Temperature-Sensitive Deteriorating Items in Cold Chain Operations
by Ming-Fang Yang, Pei-Fang Tsai, Meng-Ru Tu and Yu-Fang Yuan
Mathematics 2024, 12(5), 775; https://doi.org/10.3390/math12050775 - 5 Mar 2024
Cited by 1 | Viewed by 1258
Abstract
To improve the inventory management of cold chain logistics, we propose an economic order quantity (EOQ) inventory model for temperature-sensitive deteriorating products. Considering that the products are temperature-sensitive, the deterioration rate of the proposed model is a function of the temperature. In addition, [...] Read more.
To improve the inventory management of cold chain logistics, we propose an economic order quantity (EOQ) inventory model for temperature-sensitive deteriorating products. Considering that the products are temperature-sensitive, the deterioration rate of the proposed model is a function of the temperature. In addition, the transportation cost, which is a function of the quantity ordered, is considered in this study. This article aims to find the optimal value of the total profit, selling price, and the length of the ordering cycle. Numerical examples are provided; the sensitivity analysis shows that the total profit is much more sensitive to transportation costs, compared with ordering and holding costs. Full article
(This article belongs to the Special Issue Mathematical Approaches Applied in Operations Research, Logistics, and Inventory)
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16 pages, 3626 KiB  
Article
An Optimization Approach to Berth Allocation Problems
by Shu-Chuan Chang, Ming-Hua Lin and Jung-Fa Tsai
Mathematics 2024, 12(5), 753; https://doi.org/10.3390/math12050753 - 2 Mar 2024
Cited by 4 | Viewed by 2100
Abstract
The berth allocation problem determining the berthing time and position for incoming vessels in port operations has garnered increased attention within the global transportation network. This study focuses on the berth allocation problem with a continuous quay and dynamic vessel arrivals. With the [...] Read more.
The berth allocation problem determining the berthing time and position for incoming vessels in port operations has garnered increased attention within the global transportation network. This study focuses on the berth allocation problem with a continuous quay and dynamic vessel arrivals. With the overarching goal of enhancing service quality and optimizing berth utilization rates, this article proposes a mathematical programming model that minimizes the total waiting time of vessels and the overall completion time of vessel service. The formulated model is a mixed-integer linear programming problem that deterministic optimization techniques can globally solve. For large-scale problems, this study develops a genetic algorithm optimization approach to improve computational efficiency in reaching a near-optimal solution. Several numerical experiments are conducted to demonstrate the effectiveness and efficiency of the proposed approach. Full article
(This article belongs to the Special Issue Mathematical Approaches Applied in Operations Research, Logistics, and Inventory)
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