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Applied Mathematics in Supply Chain and Logistics
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Applied Mathematics in Supply Chain and Logistics

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E5: Financial Mathematics".

Deadline for manuscript submissions: 30 September 2025 | Viewed by 16650

Special Issue Editor

Prof. Dr. Chunqiao Tan

E-Mail Website
Guest Editor
School of Business, Nanjing Audit University, Nanjing 211815, China
Interests: game theory and application; decision analysis; supply chain and logistics management; business big data analysis
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The function of supply chain management is to design and manage the processes, assets, and flows of material and information required to satisfy customers’ demands. The globalization of the economy and electronic commerce has heightened the strategic importance of supply chain management. E-logistics has created new distribution channels for consumers. The last decade has seen rapid growth in business models built around digital platforms that bring together buyers and sellers to interact and trade in new and innovative ways. These business models, referred to as the sharing economy, on-demand economy, and platform economy, bring new challenges to supply chain management and logistics. The COVID-19 pandemic has profoundly affected the stability of global logistics and supply chains. Rapid advances and complexity in digital technology, such as big data, cloud computing, blockchain, and artificial intelligence (AI), as well as the growing uncertainty in the global business environment, have had a profound impact on the development of supply chain management and logistics. The global economy and advanced digital technologies have also generated unprecedented opportunities for innovative methodologies and technologies for designing, operating, and managing supply chains and logistics.

This Special Issue aims to collate original research papers that offer the latest developments and applications of supply chain management and logistics in a broad range of fields.

  • sustainable supply chain;
  • green supply chain;
  • low-carbon supply chain;
  • closed-loop supply chain;
  • omni-channel supply chain;
  • low-carbon logistics;
  • supply chain agility;
  • supply chain adaptability;
  • dynamic supply chain alignment;
  • supply chain resilience;
  • mathematical logistics;
  • game theory;
  • contract design;
  • information economy;
  • marketing;
  • big data;
  • blockchain;
  • artificial intelligence;
  • platform economy;
  • on-demand economy;
  • sharing economy;
  • digital economy;
  • multiple-criteria decision-making.

Prof. Dr. Chunqiao Tan
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 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.

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Published Papers (12 papers)

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Research

20 pages, 2230 KiB  
Article
Coordinating the Reverse Factoring System: Buying Back and Bargaining
by Shengying Zhao and Huan Zhou
Mathematics 2024, 12(23), 3850; https://doi.org/10.3390/math12233850 - 6 Dec 2024
Viewed by 1117
Abstract
Reverse factoring is a retailer-led supply chain financing system that can enhance liquidity of suppliers and reduce factoring fraud. This paper proposes a bargaining game theory model to analyze the profit distribution in reverse factoring for a two-echelon supply chain system that comprises [...] Read more.
Reverse factoring is a retailer-led supply chain financing system that can enhance liquidity of suppliers and reduce factoring fraud. This paper proposes a bargaining game theory model to analyze the profit distribution in reverse factoring for a two-echelon supply chain system that comprises a core retailer and a capital-constrained supplier. By taking into account the retailer’s credit loss risk, the impact of buying back and bargaining is investigated. Our study shows that in reverse factoring without buying back, the supplier would rather not bargain but the retailer would like to negotiate the wholesale price if the supplier’s bargaining power is low. If buying back exists and the supplier’s bargaining power is low, the retailer is also willing to negotiate the wholesale price. If there is no bargaining but the supplier takes a large portion of the supply chain’s profit, buying back is preferred. Furthermore, when there is bargaining on the wholesale price, both supplier and retailer can benefit from buying back. In addition, bargaining on the buy-back price in reverse factoring is bargaining-proof. Our study first contributes to the growing body of literature on reverse factoring and bargaining game theory. Two managerial implications for reverse factoring also emerge from the study. We find that bargaining should be considered if the supplier tends to coordinate the supply chain financing system by buying back the retailer’s unsold products. In addition, both supplier and retailer should negotiate the wholesale price as they cannot benefit from bargaining on the buy-back price. Full article
(This article belongs to the Special Issue Applied Mathematics in Supply Chain and Logistics)
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26 pages, 2654 KiB  
Article
Decision Making by Trade-In Programs in the E-Commerce Supply Chain, Considering Cash Rebate Strategies and Platform Services
by Zhaoqing Yu, Yuyan Wang, Liang Shen and Xue Ji
Mathematics 2024, 12(23), 3792; https://doi.org/10.3390/math12233792 - 30 Nov 2024
Cited by 1 | Viewed by 773
Abstract
As the consumer market becomes more saturated, the e-commerce supply chain (E-SC) has introduced the trade-in program in an attempt to drive consumption. This paper considers the strategy of the E-SC to provide cash rebates for consumers participating in the trade-in program and [...] Read more.
As the consumer market becomes more saturated, the e-commerce supply chain (E-SC) has introduced the trade-in program in an attempt to drive consumption. This paper considers the strategy of the E-SC to provide cash rebates for consumers participating in the trade-in program and incorporates the e-commerce platform’s trade-in service efforts into the E-SC’s decision-making system. Depending on who provides the cash rebate, we construct four decision-making models of the E-SC, i.e., the no-cash-rebate model, the manufacturer model, the platform model, and the cooperative model, where both the manufacturer and the platform jointly provide the cash rebate. We show that the platform model reduces the trade-in service level, but the manufacturer model increases the trade-in service level. In addition, since the cash rebate increases operation costs, the sale price of products is inevitably improved. Furthermore, the platform model raises product demand, but the manufacturer model lowers product demand. The cooperative model proves effective in enhancing demand only when the manufacturer contributes a minor share of the cash rebate and the trade-in service is less efficient. Cash rebates can increase the E-SC’s profits, but the degree of this increase becomes smaller as the cash rebates increase. The manufacturer and the platform always want to exploit each other’s cash rebate strategies. Consumer surplus and social welfare are highest in the platform model and lowest in the manufacturer model. Taking into account the profits, consumer surplus, and social welfare, the platform model is the most conducive to E-SC system operations. Full article
(This article belongs to the Special Issue Applied Mathematics in Supply Chain and Logistics)
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27 pages, 3723 KiB  
Article
Industry 5.0 Drivers Analysis Using Grey-DEMATEL: A Logistics Case in Emerging Economies
by Chih-Hung Hsu, Shu-Jin Chen, Ming-Qiang Huang and Qi Le
Mathematics 2024, 12(22), 3588; https://doi.org/10.3390/math12223588 - 16 Nov 2024
Viewed by 1282
Abstract
The terms “Industry 5.0” and “smart logistics” have recently emerged as key concepts within the field of logistics. Nevertheless, the interconnection between these two concepts has been less extensively examined in academic literature, particularly in the context of emerging economies. In the contemporary [...] Read more.
The terms “Industry 5.0” and “smart logistics” have recently emerged as key concepts within the field of logistics. Nevertheless, the interconnection between these two concepts has been less extensively examined in academic literature, particularly in the context of emerging economies. In the contemporary business context, the logistics industry is seeking to advance sustainable development through the implementation of Industry 5.0. However, the industry is still in its nascent stages of realizing the transformation of smart logistics. Accordingly, the objective of this study is to identify the key drivers of Industry 5.0 in relation to the advancement of smart logistics in the logistics industry in emerging economies. In this study, the initial screening and identification of 15 core drivers was conducted using the fuzzy Delphi method. This involved the collation of the relevant literature and the collection of opinions from experts in the field. The identified drivers were then classified into three groups: sustainability, people-centricity, and resilience. Subsequently, the study adopted the Grey-DEMATEL method, which combines grey system theory with the decision making trial and evaluation laboratory (DEMATEL) technology. This approach enables the effective resolution of complex system issues characterized by uncertainty and incomplete information, facilitating the identification of causal relationships between the drivers and the construction of a centrality–causality outcome diagram. The study identified two key drivers: “government support policies” and “logistics standardization and infrastructure development”. This study represents a preliminary investigation into the ways managers, practitioners and policy makers can leverage Industry 5.0 to advance the field of smart logistics within the logistics industry. Full article
(This article belongs to the Special Issue Applied Mathematics in Supply Chain and Logistics)
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23 pages, 1457 KiB  
Article
Tripartite Evolutionary Game Analysis of Product Quality Supervision in Live-Streaming E-Commerce
by Yang Song and Yijun Kong
Mathematics 2024, 12(16), 2446; https://doi.org/10.3390/math12162446 - 6 Aug 2024
Cited by 2 | Viewed by 1400
Abstract
With the rapid development of information technology, live-streaming e-commerce has risen rapidly as a new business model. However, product quality problems that exist in the development of live-streaming e-commerce continue to emerge. The influence of strategic interactions between social media influencers, live-streaming e-commerce [...] Read more.
With the rapid development of information technology, live-streaming e-commerce has risen rapidly as a new business model. However, product quality problems that exist in the development of live-streaming e-commerce continue to emerge. The influence of strategic interactions between social media influencers, live-streaming e-commerce platforms, and consumers on product quality deserves to be studied. Therefore, this paper constructs a tripartite game model of “social media influencers–the live-streaming e-commerce platform–consumers” and analyzes the dynamic evolution process of the strategy selection among subjects and influencing factors by using evolutionary game theory. This study shows that products with high functional value are more likely to stimulate consumer rights protection behavior, prompting social media influencers to shift from lax to strict quality control. But when the emotional value is high, consumers are more inclined to give up on defending their rights, which leads to the maintenance of lax quality control, and the platform supervision will be weakened accordingly. Moreover, less quality differences motivate social media influencers to choose lax quality control. An increase in quality differences will promote a shift from an equilibrium strategy to strict quality control. However, if the penalty of the platforms is not strong enough, this strategic shift will not happen. In addition, a high percentage of platform commissions can encourage influencers to implement strict quality control, while platforms can maintain weak supervision. This study’s findings provide valuable guidance for understanding and managing product quality issues in live-streaming e-commerce. In the future, the government will be considered a new player in the game in studying the impact of its policies on product quality in live-streaming e-commerce. Full article
(This article belongs to the Special Issue Applied Mathematics in Supply Chain and Logistics)
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19 pages, 2594 KiB  
Article
Recycling Models of Waste Electrical and Electronic Equipment under Market-Driven Deposit-Refund System: A Stackelberg Game Analysis
by Yi Liu, Weihua Liu and Chunsheng Li
Mathematics 2024, 12(14), 2187; https://doi.org/10.3390/math12142187 - 12 Jul 2024
Viewed by 1387
Abstract
Recycling waste electrical and electronic equipment (WEEE) has garnered considerable societal attention. To incentivize WEEE recycling within a closed-loop supply chain (CLSC), a deposit-refund system (DRS) has been implemented. This study delves into the implications of a market-driven DRS on WEEE recycling under [...] Read more.
Recycling waste electrical and electronic equipment (WEEE) has garnered considerable societal attention. To incentivize WEEE recycling within a closed-loop supply chain (CLSC), a deposit-refund system (DRS) has been implemented. This study delves into the implications of a market-driven DRS on WEEE recycling under different recycling models. A Stackelberg game analysis is employed, where an electronics manufacturer (leader) has sufficient channel power over an electronics retailer and a third-party recycler (followers). The results indicate that the market-driven DRS significantly incentivizes consumer recycling efforts, ultimately elevating the economic efficiency of the supply chain. When the electronics manufacturer assumes responsibility for WEEE recycling, it streamlines the recycling process, thereby enhancing operational efficiency and profitability. Conversely, when the electronics retailer handles WEEE recycling, it reduces retail prices and simplifies the recycling process, positively influencing consumer purchasing behavior. However, when a third-party recycler undertakes WEEE recycling, the recycling volume tends to be minimal, resulting in the lowest level of supply chain profits. This paper provides theoretical and practical implications for improving the recycling effectiveness and operational efficiency of the CLSC. Full article
(This article belongs to the Special Issue Applied Mathematics in Supply Chain and Logistics)
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12 pages, 1086 KiB  
Article
Rightful Rewards: Refining Equity in Team Resource Allocation through a Data-Driven Optimization Approach
by Bo Jiang, Xuecheng Tian, King-Wah Pang, Qixiu Cheng, Yong Jin and Shuaian Wang
Mathematics 2024, 12(13), 2095; https://doi.org/10.3390/math12132095 - 3 Jul 2024
Viewed by 1108
Abstract
In group management, accurate assessment of individual performance is crucial for the fair allocation of resources such as bonuses. This paper explores the complexities of gauging each participant’s contribution in multi-participant projects, particularly through the lens of self-reporting—a method fraught with the challenges [...] Read more.
In group management, accurate assessment of individual performance is crucial for the fair allocation of resources such as bonuses. This paper explores the complexities of gauging each participant’s contribution in multi-participant projects, particularly through the lens of self-reporting—a method fraught with the challenges of under-reporting and over-reporting, which can skew resource allocation and undermine fairness. Addressing the limitations of current assessment methods, which often rely solely on self-reported data, this study proposes a novel equitable allocation policy that accounts for inherent biases in self-reporting. By developing a data-driven mathematical optimization model, we aim to more accurately align resource allocation with actual contributions, thus enhancing team efficiency and cohesion. Our computational experiments validate the proposed model’s effectiveness in achieving a more equitable allocation of resources, suggesting significant implications for management practices in team settings. Full article
(This article belongs to the Special Issue Applied Mathematics in Supply Chain and Logistics)
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13 pages, 5661 KiB  
Article
Mixed-Integer Optimization for Ship Retrofitting in Green Logistics
by Tianfang Ma, Xuecheng Tian, Yan Liu, Yong Jin and Shuaian Wang
Mathematics 2024, 12(12), 1831; https://doi.org/10.3390/math12121831 - 12 Jun 2024
Cited by 1 | Viewed by 1065
Abstract
Maritime transportation plays a pivotal role in global trade and international supply chains. However, the sector is also a significant source of emissions. One of the most promising technologies for reducing these emissions is air lubrication, which involves installing bubbles along the hull [...] Read more.
Maritime transportation plays a pivotal role in global trade and international supply chains. However, the sector is also a significant source of emissions. One of the most promising technologies for reducing these emissions is air lubrication, which involves installing bubbles along the hull of a ship. Despite its potential, the design of cost-effective bubble-installation plans for ship fleets over the planning horizon remains unexplored in the literature. This paper addresses this gap by proposing a mathematical programming model designed to optimize the installation of bubble-based systems. We present several propositions concerning the model’s properties, supported by rigorous proofs. To validate the model’s effectiveness, we conduct a series of computational experiments. The findings demonstrate that our optimization model enables shipping companies to devise bubble-installation plans that are cost-effective. This contribution not only extends the current understanding of emission reduction technologies in maritime transportation, but also offers practical insights for their implementation. Full article
(This article belongs to the Special Issue Applied Mathematics in Supply Chain and Logistics)
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23 pages, 903 KiB  
Article
Optimal Routing and Scheduling of Flag State Control Officers in Maritime Transportation
by Xizi Qiao, Ying Yang, Yu Guo, Yong Jin and Shuaian Wang
Mathematics 2024, 12(11), 1647; https://doi.org/10.3390/math12111647 - 24 May 2024
Cited by 2 | Viewed by 1151
Abstract
Maritime transportation plays a pivotal role in the global merchandise trade. To improve maritime safety and protect the environment, every state must effectively control ships flying its flag, which is called flag state control (FSC). However, the existing FSC system is so inefficient [...] Read more.
Maritime transportation plays a pivotal role in the global merchandise trade. To improve maritime safety and protect the environment, every state must effectively control ships flying its flag, which is called flag state control (FSC). However, the existing FSC system is so inefficient that it cannot perform its intended function. In this study, we adopt an optimization method to tackle this problem by constructing an integer programming (IP) model to solve the FSC officer routing and scheduling problem, which aims to maximize the total weight of inspected ships with limited budget and human resources. Then we prove that the IP model can be reformulated into a partially relaxed IP model with the guarantee of the result optimality. Finally, we perform a case study using the Hong Kong port as an example. The results show that our model can be solved to optimality within one second at different scales of the problem, with the ship number ranging from 20 to 1000. Furthermore, our study can be extended by considering the arrangement of working timetables with finer granularity and the fatigue level of personnel. Full article
(This article belongs to the Special Issue Applied Mathematics in Supply Chain and Logistics)
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21 pages, 6223 KiB  
Article
Research on Dynamic Takeout Delivery Vehicle Routing Problem under Time-Varying Subdivision Road Network
by Fengjie Xie, Zhiting Chen and Zhuan Zhang
Mathematics 2024, 12(7), 962; https://doi.org/10.3390/math12070962 - 24 Mar 2024
Cited by 4 | Viewed by 1555
Abstract
For the dynamic takeout delivery vehicle routing problem, which faces fluctuating order demand and time-varying speeds, this study presents a novel approach. We analyze the time distribution of takeout orders and apply a Receding Horizon Control (RHC) strategy to convert the dynamic challenge [...] Read more.
For the dynamic takeout delivery vehicle routing problem, which faces fluctuating order demand and time-varying speeds, this study presents a novel approach. We analyze the time distribution of takeout orders and apply a Receding Horizon Control (RHC) strategy to convert the dynamic challenge into a static one. The driving speed of delivery vehicles on different roads at different times is determined based on the subdivision criteria of the urban road network and a traffic congestion measurement method. We propose a dynamic takeout delivery vehicle routing optimization model and a time-varying subdivision road network is established to minimize the total delivery cost. We validated the model through simulation examples. The optimization results show that the total distribution cost is reduced after considering the time-varying subdivision road network, with the penalty cost decreasing by 39%. It is evident that considering the subdivision of the road network can enhance order delivery efficiency and optimize the overall dining experience. The sensitivity analysis of various parameters reveals that the delivery platform must appropriately determine the time domain and allocate the number of delivery personnel based on order scale to avoid escalating delivery costs. These findings provide theoretical guidance for vehicle routing planning in the context of delivery platforms. Full article
(This article belongs to the Special Issue Applied Mathematics in Supply Chain and Logistics)
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23 pages, 6000 KiB  
Article
Usefulness of the Ordinal Logistic Biplot: Analysis of the Path Taken towards a Circular Primary Sector in Spain
by Saudi-Yulieth Enciso-Alfaro, Víctor Amor-Esteban, Davi-Jônatas Cunha-Araújo and Isabel-María García-Sánchez
Mathematics 2024, 12(2), 322; https://doi.org/10.3390/math12020322 - 18 Jan 2024
Cited by 1 | Viewed by 1521
Abstract
Population growth and greater global interconnection require a profound transformation in how we produce, consume, and manage natural resources. In this sense, the circular transition of the agricultural and livestock sectors is vital to guarantee adequate production without compromising the availability of resources [...] Read more.
Population growth and greater global interconnection require a profound transformation in how we produce, consume, and manage natural resources. In this sense, the circular transition of the agricultural and livestock sectors is vital to guarantee adequate production without compromising the availability of resources for future generations. In this work, we analyze the level of circular development of the primary sector in Spain using a sample of the 84 largest companies. We utilize the biplot analysis, multivariate graphic models that represent the joint distribution of four scores (constructed with sixteen ecological initiatives), and three financial and geographic variables. These techniques allow for visualization of the status and the relationships between all of them. We evidence an important degree of progress in initiatives associated with the use of non-polluting energy, eco-design, eco-innovation, management, and care of ecosystems. We also observe that the current transition towards a circular primary sector is strongly associated with firms’ capital investments and long-term innovations. On the other hand, the actions aimed at protecting water resources are in an intermediate state of progress, being necessary to invest in additional friendly water initiatives. In this vein, it is advisable to promote public policies focused on promoting the ecological transition of this sector and the research that advances efficient water management. Full article
(This article belongs to the Special Issue Applied Mathematics in Supply Chain and Logistics)
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20 pages, 1972 KiB  
Article
Recycling Pricing and Government Subsidy Strategy for End-of-Life Vehicles in a Reverse Supply Chain under Consumer Recycling Channel Preferences
by Zhiguo Wang
Mathematics 2024, 12(1), 35; https://doi.org/10.3390/math12010035 - 22 Dec 2023
Cited by 2 | Viewed by 1590
Abstract
In the existing recycling system for end-of-life vehicles (ELVs), online recycling based on the Internet platform is a useful supplement. In this paper, a Stackelberg game pricing model, which is dominated by ELV part remanufacturers and composed of remanufacturers, recyclers, and consumers, is [...] Read more.
In the existing recycling system for end-of-life vehicles (ELVs), online recycling based on the Internet platform is a useful supplement. In this paper, a Stackelberg game pricing model, which is dominated by ELV part remanufacturers and composed of remanufacturers, recyclers, and consumers, is constructed considering consumer preferences for recycling channels. The influence of different subsidy strategies on the optimal pricing, profit, and recycling volume of the reverse supply chain (RSC) of ELVs is discussed, and the effects of factors such as subsidy amount and consumer preferences on the RSC of ELVs are analyzed using numerical simulation. The results show that the increase in consumers’ online recycling preferences has a positive effect on the recycling volume and profit of the RSC of ELVs. Considering the recycling volume of the RSC, when fewer subsidies are given, more recycling volume can be generated by subsidizing remanufacturers, and, on the contrary, recycling volume will be generated by subsidizing consumers. Considering the profit of the RSC, when subsidies are given at the lower-middle level, higher profits can be earned by subsidizing remanufacturers, and, on the contrary, higher profits can be earned by subsidizing consumers. Full article
(This article belongs to the Special Issue Applied Mathematics in Supply Chain and Logistics)
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15 pages, 4026 KiB  
Article
On the Fundamental Diagram for Freeway Traffic: Exploring the Lower Bound of the Fitting Error and Correcting the Generalized Linear Regression Models
by Yidan Shangguan, Xuecheng Tian, Sheng Jin, Kun Gao, Xiaosong Hu, Wen Yi, Yu Guo and Shuaian Wang
Mathematics 2023, 11(16), 3460; https://doi.org/10.3390/math11163460 - 9 Aug 2023
Viewed by 1472
Abstract
In traffic flow, the relationship between speed and density exhibits decreasing monotonicity and continuity, which is characterized by various models such as the Greenshields and Greenberg models. However, some existing models, i.e., the Underwood and Northwestern models, introduce bias by incorrectly utilizing linear [...] Read more.
In traffic flow, the relationship between speed and density exhibits decreasing monotonicity and continuity, which is characterized by various models such as the Greenshields and Greenberg models. However, some existing models, i.e., the Underwood and Northwestern models, introduce bias by incorrectly utilizing linear regression for parameter calibration. Furthermore, the lower bound of the fitting errors for all these models remains unknown. To address above issues, this study first proves the bias associated with using linear regression in handling the Underwood and Northwestern models and corrects it, resulting in a significantly lower mean squared error (MSE). Second, a quadratic programming model is developed to obtain the lower bound of the MSE for these existing models. The relative gaps between the MSEs of existing models and the lower bound indicate that the existing models still have a lot of potential for improvement. Full article
(This article belongs to the Special Issue Applied Mathematics in Supply Chain and Logistics)
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