Mathematics

Research

15 pages, 3158 KiB

Open AccessArticle

Inferencing Space Travel Pricing from Mathematics of General Relativity Theory, Accounting Equation, and Economic Functions

by Kang-Lin Peng, Xunyue Xue, Liqiong Yu and Yixin Ren

Mathematics 2024, 12(5), 757; https://doi.org/10.3390/math12050757 - 03 Mar 2024

Viewed by 681

Abstract

This study derives space travel pricing by Walrasian Equilibrium, which is logical reasoning from the general relativity theory (GRT), the accounting equation, and economic supply and demand functions. The Cobb–Douglas functions embed the endogenous space factor as new capital to form the space [...] Read more.

This study derives space travel pricing by Walrasian Equilibrium, which is logical reasoning from the general relativity theory (GRT), the accounting equation, and economic supply and demand functions. The Cobb–Douglas functions embed the endogenous space factor as new capital to form the space travel firm’s production function, which is also transformed into the consumer’s utility function. Thus, the market equilibrium occurs at the equivalence of supply and demand functions, like the GRT, which presents the equivalence between the spatial geometric tensor and the energy–momentum tensor, explaining the principles of gravity and the motion of space matter in the spacetime framework. The mathematical axiomatic set theory of the accounting equation explains the equity premium effect that causes a short-term accounting equation inequality, then reaches the equivalence by suppliers’ incremental equity through the closing accounts process of the accounting cycle. On the demand side, the consumption of space travel can be assumed as a value at risk (VaR) investment to attain the specific spacetime curvature in an expected orbit. Spacetime market equilibrium is then achieved to construct the space travel pricing model. The methodology of econophysics and the analogy method was applied to infer space travel pricing with the model of profit maximization, single-mindedness, and envy-free pricing in unit-demand markets. A case study with simulation was conducted for empirical verification of the mathematical models and algorithm. The results showed that space travel pricing remains associated with the principle of market equilibrium, but needs to be extended to the spacetime tensor of GRT. Full article

(This article belongs to the Special Issue Operations and Supply Chain Management with the Application of Mathematical Models)

► Show Figures

Figure 1

30 pages, 685 KiB

Open AccessArticle

Supply Chain Inventory Management from the Perspective of “Cloud Supply Chain”—A Data Driven Approach

by Yue Tan, Liyi Gu, Senyu Xu and Mingchao Li

Mathematics 2024, 12(4), 573; https://doi.org/10.3390/math12040573 - 14 Feb 2024

Viewed by 1040

Abstract

This study systematically investigates the pivotal role of inventory management within the framework of “cloud supply chain” operations, emphasizing the efficacy of leveraging machine learning methodologies for inventory allocation with the dual objectives of cost reduction and heightened customer satisfaction. Employing a rigorous [...] Read more.

This study systematically investigates the pivotal role of inventory management within the framework of “cloud supply chain” operations, emphasizing the efficacy of leveraging machine learning methodologies for inventory allocation with the dual objectives of cost reduction and heightened customer satisfaction. Employing a rigorous data-driven approach, the research endeavors to address inventory allocation challenges inherent in the complex dynamics of a “cloud supply chain” through the implementation of a two-stage model. Initially, machine learning is harnessed for demand forecasting, subsequently refined through the empirical distribution of forecast errors, culminating in the optimization of inventory allocation across various service levels.The empirical evaluation draws upon data derived from a reputable home appliance logistics company in China, revealing that, under conditions of ample data, the application of data-driven methods for inventory allocation surpasses the performance of traditional methods across diverse supply chain structures. Specifically, there is an improvement in accuracy by approximately 13% in an independent structure and about 16% in a dependent structure. This study transcends the constraints associated with examining a singular node, adopting an innovative research perspective that intricately explores the interplay among multiple nodes while elucidating the nuanced considerations germane to supply chain structure. Furthermore, it underscores the methodological significance of relying on extensive, large-scale data. The investigation brings to light the substantial impact of supply chain structure on safety stock allocation. In the context of a market characterized by highly uncertain demand, the strategic adaptation of the supply chain structure emerges as a proactive measure to avert potential disruptions in the supply chain. Full article

(This article belongs to the Special Issue Operations and Supply Chain Management with the Application of Mathematical Models)

► Show Figures

Figure 1

20 pages, 1779 KiB

Open AccessArticle

Optimizing Rack Locations in the Mobile-Rack Picking System: A Method of Integrating Rack Heat and Relevance

by Mengyue Zhai and Zheng Wang

Mathematics 2024, 12(3), 413; https://doi.org/10.3390/math12030413 - 26 Jan 2024

Viewed by 701

Abstract

The flexible movement of racks in the mobile-rack picking system (MRPS) significantly improves the picking efficiency of e-commerce orders with the characteristics of “one order multi–items” and creates a challenging problem of how to place racks in the warehouse. This is because the [...] Read more.

The flexible movement of racks in the mobile-rack picking system (MRPS) significantly improves the picking efficiency of e-commerce orders with the characteristics of “one order multi–items” and creates a challenging problem of how to place racks in the warehouse. This is because the placement of each rack in the MRPS directly influences the distance that racks need to be moved during order picking, which in turn affects the order picking efficiency. To handle the rack location optimization problem (RLOP), this work introduces a novel idea and methodology, taking into account the heat degree and the relevance degree of racks, to enhance the efficiency of rack placements in the MRPS. Specifically, a two-stage solution strategy is implemented. In stage 1, an integer programming model (Model 1) is developed to determine the heat and relevance degree of racks, and it can be solved quickly by the Gurobi. Stage 2 entails developing a bi-objective integer programming model (Model 2) with the objective to minimize the travel distances of robots in both heavy load and no-load conditions, using the rack heat and relevance degree as inputs. In light of the challenge of decision coupling and the vast solution space in stage 2, we innovatively propose two lower bounds by slacking off the distance between storage locations. A matheuristic algorithm based on Benders decomposition (MABBD) is designed, which utilizes Benders-related rules to reconstruct Model 2, introduces an enhanced cut and an improved optimal cut with RLOP characteristics, and designs the warm start strategy and the master variable fixed strategy. Given the substantial size of real-life problems, the Memetic algorithm (MA) is specifically devised to address them. Instances of varying sizes are also employed to validate the science and efficacy of the model and algorithm. Full article

(This article belongs to the Special Issue Operations and Supply Chain Management with the Application of Mathematical Models)

► Show Figures

Figure 1

11 pages, 5525 KiB

Open AccessArticle

Decomposition Is All You Need: Single-Objective to Multi-Objective Optimization towards Artificial General Intelligence

by Wendi Xu, Xianpeng Wang, Qingxin Guo, Xiangman Song, Ren Zhao, Guodong Zhao, Dakuo He, Te Xu, Ming Zhang and Yang Yang

Mathematics 2023, 11(20), 4390; https://doi.org/10.3390/math11204390 - 23 Oct 2023

Cited by 1 | Viewed by 1353

Abstract

As a new abstract computational model in evolutionary transfer optimization (ETO), single-objective to multi-objective optimization (SMO) is conducted at the macroscopic level rather than the intermediate level for specific algorithms or the microscopic level for specific operators; this method aims to develop systems [...] Read more.

As a new abstract computational model in evolutionary transfer optimization (ETO), single-objective to multi-objective optimization (SMO) is conducted at the macroscopic level rather than the intermediate level for specific algorithms or the microscopic level for specific operators; this method aims to develop systems with a profound grasp of evolutionary dynamic and learning mechanism similar to human intelligence via a “decomposition” style (in the abstract of the well-known “Transformer” article “Attention is All You Need”, they use “attention” instead). To the best of our knowledge, it is the first work of SMO for discrete cases because we extend our conference paper and inherit its originality status. In this paper, by implementing the abstract SMO in specialized memetic algorithms, key knowledge from single-objective problems/tasks to the multi-objective core problem/task can be transferred or “gathered” for permutation flow shop scheduling problems, which will reduce the notorious complexity in combinatorial spaces for multi-objective settings in a straight method; this is because single-objective tasks are easier to complete than their multi-objective versions. Extensive experimental studies and theoretical results on benchmarks (1) emphasize our decomposition root in mathematical programming, such as Lagrangian relaxation and column generation; (2) provide two “where to go” strategies for both SMO and ETO; and (3) contribute to the mission of building safe and beneficial artificial general intelligence for manufacturing via evolutionary computation. Full article

(This article belongs to the Special Issue Operations and Supply Chain Management with the Application of Mathematical Models)

► Show Figures

Figure 1

23 pages, 3230 KiB

Open AccessArticle

Cost of Ownership of Spare Parts under Uncertainty: Integrating Reliability and Costs

by Orlando Durán, Paulo Afonso, Víctor Jiménez and Katty Carvajal

Mathematics 2023, 11(15), 3316; https://doi.org/10.3390/math11153316 - 28 Jul 2023

Cited by 1 | Viewed by 1078

Abstract

In capital-intensive organizations, decisions regarding capital costs play an important role due to the significant amount of investment required and the expected return on investment. Spare parts management is crucial to those ends, as spare parts management can constitute a significant portion of [...] Read more.

In capital-intensive organizations, decisions regarding capital costs play an important role due to the significant amount of investment required and the expected return on investment. Spare parts management is crucial to those ends, as spare parts management can constitute a significant portion of OPEX. Companies must implement a trade-off analysis between stock levels and assets’ availability. Decision-making supports mechanisms such as the Level of Repair Analysis (LORA), Integrated Logistics Systems (ILS), and life-cycle costing (LCC) models have been developed to aid in equipment selection, implementation, and decommissioning. Nowadays, these mechanisms appear to be integrated with risk-management models and standards. This paper proposes a long-term costing model that integrates a capacity analysis, reliability functions, and risk considerations for the cost management of logistics activities, particularly in MRO structures. The model is built upon Time-Driven Activity-Based Costing (TD-ABC) and incorporates the volume of activities generated by MRO needs. It also addresses uncertainty through the integration of a cost-at-risk model. By integrating spare parts, activity-based cost models, and risk measurement through Monte Carlo simulation, this study offers powerful insights into optimizing spare parts logistics activities. The proposed model is a novel approach to include the risk of cost in spare parts management, and its matrix-activity-based structure makes possible the development of sophisticated mathematical models for costing and optimization purposes in different domains. Full article

(This article belongs to the Special Issue Operations and Supply Chain Management with the Application of Mathematical Models)

► Show Figures

Figure 1

22 pages, 892 KiB

Open AccessArticle

Optimization of a Two-Echelon Supply Chain Considering Consumer Low-Carbon Preference

by Ying Shi and Xin Li

Mathematics 2023, 11(15), 3264; https://doi.org/10.3390/math11153264 - 25 Jul 2023

Viewed by 647

Abstract

This paper considers a fresh food supply chain with a supplier who takes responsibility for the cold chain and a retailer who needs to reprocess the fresh food. Carbon emissions will be produced in the processes of production, transportation, processing, etc. We consider [...] Read more.

This paper considers a fresh food supply chain with a supplier who takes responsibility for the cold chain and a retailer who needs to reprocess the fresh food. Carbon emissions will be produced in the processes of production, transportation, processing, etc. We consider the four-stage game, obtain the function expressions of optimal market prices with respect to carbon emission reduction level (CERL), analyze the best responses of the supplier and the retailer regarding their CERLs, and obtain the 25 optimal CERLs under competitive equilibrium. In 24 of the 25 equilibrium cases, the supplier or the retailer either do nothing to reduce carbon emissions, or make the most effort to reduce carbon emissions. Excluding these special cases, we focused on a non-trivial case where the increasing consumer preferences for low-carbon products will encourage the supplier and the retailer to reduce carbon emissions. Interestingly, we find that when the consumer preference for low-carbon products is low, the retailer’s and supplier’s equilibrium carbon reduction levels are low, so that the potential market size is small such that the competition for two kinds of customers is fierce. Then, an increase in the sale cost will reduce the retail price. However, when the consumer preference for low-carbon products is high, the potential market size is large such that the competition is not fierce. Then, an increase in the sale cost will advance the retail price. Full article

(This article belongs to the Special Issue Operations and Supply Chain Management with the Application of Mathematical Models)

► Show Figures

Figure 1

16 pages, 1533 KiB

Open AccessArticle

A Study on the Choice of Online Marketplace Co-Opetition Strategy Considering the Promotional Behavior of a Store on an E-Commerce Platform

by Tao Wang

Mathematics 2023, 11(10), 2263; https://doi.org/10.3390/math11102263 - 11 May 2023

Cited by 1 | Viewed by 1725

Abstract

The huge traffic of e-commerce platforms provides a wide market for stores, but the fierce competition among stores for onsite traffic increases the cost of onsite promotion for stores, and it also reduces the effectiveness of promotion. Therefore, more and more stores on [...] Read more.

The huge traffic of e-commerce platforms provides a wide market for stores, but the fierce competition among stores for onsite traffic increases the cost of onsite promotion for stores, and it also reduces the effectiveness of promotion. Therefore, more and more stores on e-commerce platforms are using content platforms for offsite promotion. In the face of stores’ onsite and offsite promotion behaviors, the choice of competition and cooperation strategies among participants in the promotion process is the key to solving the problem of increasing traffic. Accordingly, this paper constructs an onsite and offsite promotion decision model consisting of an e-commerce platform, a store on the e-commerce platform, and a content platform, and it compares the results based on the decentralized decision situation, centralized decision situation, and promotion investment sharing situation. In addition, some results are presented in more detail in the form of numerical analysis. The results show that the promotion investment sharing does not change the level of onsite promotion investment, but the centralized decision makes the onsite promotion investment decrease; promotion investment sharing and centralized decision scenarios increase the promotion investment of the e-commerce platform and the content platform. When the sum of the parts of promotion investments shared by the store and the content platform for the e-commerce platform is relatively small, each participant will be willing to participate in the promotion investment sharing agreement. We believe that this study will provide important implications for the resolution of stores’ traffic dilemmas on e-commerce platforms. Full article

(This article belongs to the Special Issue Operations and Supply Chain Management with the Application of Mathematical Models)

► Show Figures

Figure 1

26 pages, 1017 KiB

Open AccessArticle

Government Subsidy Strategies Considering Greenness on Agricultural Product E-Commerce Supply Chain

by Fangfang Guo, Tao Zhang, Xiuquan Huang and Yaoguang Zhong

Mathematics 2023, 11(7), 1662; https://doi.org/10.3390/math11071662 - 30 Mar 2023

Cited by 4 | Viewed by 1418

Abstract

Based on the Stackelberg game theory, this paper explores the incentive effects of five government subsidy strategies on agricultural products in e-commerce. A two-tier e-commerce supply chain of one farmer and one e-commerce platform is constructed to examine the impact of five different [...] Read more.

Based on the Stackelberg game theory, this paper explores the incentive effects of five government subsidy strategies on agricultural products in e-commerce. A two-tier e-commerce supply chain of one farmer and one e-commerce platform is constructed to examine the impact of five different government subsidy strategies on the greenness of an agricultural product, the wholesale price, the selling price, and the profit of the supply chain. The results show that the effect of offering government subsidies is significant. Also, the direct subsidization from the government to a farmer has the maximum effect on the sales and greenness of the agricultural product. The results of this study provide policy implications for governments in establishing a sustainable mechanism through direct subsidization. Full article

(This article belongs to the Special Issue Operations and Supply Chain Management with the Application of Mathematical Models)

► Show Figures

Figure 1

Journal Menu

Journal Browser

Operations and Supply Chain Management with the Application of Mathematical Models

Share This Special Issue

Special Issue Editors

Special Issue Information

Keywords

Published Papers (8 papers)

Research

Further Information

Guidelines

MDPI Initiatives

Follow MDPI