Profit Maximization Problem Research Articles

The Application of Derivatives in Enhancing Economic Decision-Making

This paper explores the specific application of derivatives in economic analysis, aiming to provide an effective mathematical tool for economic analysis to improve decision-making efficiency and accuracy. Through two specific cases - the profit maximization problem of fast-moving consumer goods companies and the profit maximization problem of retail enterprises, it can be demonstrated how to use derivatives to solve and analyze economic models, and then propose corresponding optimization suggestions. In addition, through detailed mathematical derivation and data analysis, how derivatives can help enterprises optimize decision-making and improve economic efficiency was analyzed. Research has shown that derivatives, as an important tool in economic analysis, can effectively enhance the scientifically and accuracy of decision-making.

Research on Pricing and Dynamic Replenishment Planning Strategies for Perishable Vegetables Based on the RF-GWO Model

This paper addresses the challenges of automated pricing and replenishment strategies for perishable products with time-varying deterioration rates, aiming to assist wholesalers and retailers in optimizing their production, transportation, and sales processes to meet market demand while minimizing inventory backlog and losses. The study utilizes an improved convolutional neural network–long short-term memory (CNN-LSTM) hybrid model, autoregressive moving average (ARIMA) model, and random forest–grey wolf optimization (RF-GWO) algorithm. Using fresh vegetables as an example, the cost relationship is analyzed through linear regression, sales volume is predicted using the LSTM recurrent neural network, and pricing is forecasted with a time series analysis. The RF-GWO algorithm is then employed to solve the profit maximization problem, identifying the optimal replenishment quantity, type, and most effective pricing strategy, which involves dynamically adjusting prices based on predicted sales and market conditions. The experimental results indicate a 5.4% reduction in inventory losses and a 6.15% increase in sales profits, confirming the model’s effectiveness. The proposed mathematical model offers a novel approach to automated pricing and replenishment in managing perishable goods, providing valuable insights for dynamic inventory control and profit optimization.

A Profit Maximization Problem of Equipment Rental and Scheduling with Split Services

This study addresses a scheduling problem arising from the “Rent Instead of Buy” business model where rental service platforms rent equipment from suppliers to satisfy customer requests in exchange for a lump-sum payment. Suppliers often implement piecewise linear concave charging policies to encourage longer rental duration. This policy prompts the platform to consolidate service periods into longer rental agreements for lower rental rates, potentially necessitating the splitting of a customer request among multiple facilities. We establish an integer programming model to maximize the platform’s profit, which is equal to the total revenue from serving customers minus the total rental and scheduling costs. To solve the problem, we propose two Dantzig-Wolfe decomposition reformulations and design branch-and-price algorithms accordingly. Furthermore, by exploiting the property of the concave rental cost functions, we derive the optimal structure regarding the start and end times of services, significantly reducing the subproblem’s search space. Numerical experiments based on real-life data validate the efficiency of the designed algorithms compared to commercial solvers and highlight the benefits of split services. Sensitivity analysis reveals that as the rental cost function becomes more segmented, more requests are split-serviced, but the times for splitting a request are seldom more than once.

A comparative analysis of metaheuristic algorithms in interval-valued sustainable economic production quantity inventory models using center-radius optimization

The real-world production inventory systems involve uncertainties surrounding demand, production, defectiveness, and costs, which pose significant challenges. Various methodologies, including interval, fuzzy, stochastic, and fuzzy-stochastic approaches, have been developed to address these challenges. Among these, the interval approach offers a realistic representation of uncertainty. This study develops a green production model within an interval-based framework, incorporating interval-valued representations of defective rates and demand, which is also stochastic in nature. Differential equations governing inventory levels are formulated in an interval format and solved using advanced parametric techniques. The study extends to profit optimization within this interval-based framework, with the profit maximization problem transformed into a crisp form using interval order relations and center-radius optimization. The optimized solution is obtained through various metaheuristic algorithms. A numerical example validates the proposed model, and sensitivity analyses explore variations in different algorithms and inventory parameters. Additionally, statistical analysis using ANOVA tests is performed. This research contributes to production inventory management by providing a robust framework for handling uncertainty and optimizing performance in real-world scenarios.

A Cooperative Operation Strategy for Multi-Energy Systems Based on the Power Dispatch Meta-Universe Platform

To meet the challenges of renewable energy consumption and improve the efficiency of energy systems, we propose an intelligent distributed energy dispatch strategy for multi-energy systems based on Nash bargaining by utilizing the power dispatch meta-universe platform. First, the operational framework of the multi-energy system, including wind park (WP), photovoltaic power plant (PVPP), and energy storage (ES), is described. Using the power dispatch meta-universe platform, the models of WP, PVPP, and ES are constructed and analyzed. Then, a Nash bargaining model of the multi-energy system is built and transformed into a coalition profit maximization problem, which is solved using the alternating direction multiplier method (ADMM). Finally, the effectiveness of the proposed strategy is verified. The results show that the strategy greatly improves the consumption of renewable energy sources and the profit of the overall system.

Disclosing Delivery Performance Information When Consumers Are Sensitive to Promised Delivery Time, Delivery Reliability, and Price

Problem definition: We investigate how the characteristics of consumers and a service firm influence the firm’s optimal pricing and promised delivery-time decisions as well as the optimal investment in the quality of delivery reliability information available to consumers. Methodology/results: We use utility, queuing, and choice modeling theories to model consumers’ behavior and to find solutions to the firm’s profit maximization problem. Managerial implications: The optimal strategy is to disclose either error-free delivery reliability information or no information at all. We also delineate conditions for each of the two strategies to dominate. Funding: This research was supported by the General Research Fund (GRF) of the Hong Kong Research Grants Council under Research Project LU13500822. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2023.0223 .

Uncertain Maximum Benefit about Chinese Postman Problem

This research deals with the generalization of profit maximization of the Chinese postman with several vehicles under uncertainty, and then it is solved using the Lagrangian algorithm. Four different cases of the model are discussed. The first mode performs Chinese postman routing and assumes that the origin and destination are the same for each vehicle for each cycle and is provided by the user, which is the case of a typical postman. The second takes into account the assumption that the origin and destination of each vehicle should not be the same and allows users to choose the possible origin or destination of the vehicles. The third case takes the origin of each vehicle as input and generates a solution based on finding the best destination for each vehicle. The last parameter, which is very general, allows the optimization model to choose possibly different locations for the origin and destination of the vehicle during each cycle. Modeling these issues in the real world requires the use of uncertainty theory. Liu expressed the theory of uncertainty. Here, is a model of the Chinese postman’s multiple profit maximization problem. So far, there is no such uncertainty analysis of these models. After stating the uncertainty problem of the maximum profit problem of the Chinese postman, we will state the problem using the Lagrangian algorithm. We then compare the results.

Optimizing Cloud Broker Profitability through Advanced Cloud Computing Techniques

Cloud computing has gained significant traction as an efficient solution for delivering on-demand computing resources and services. For cloud service providers, ensuring profitability while maintaining service quality is crucial. However, the prevalent single long-term renting approach often results in compromised service quality and substantial resource wastage. To address this, our paper proposes a pioneering double resource renting scheme that integrates short-term and long-term renting. This innovative approach not only guarantees optimal service quality for all requests but also significantly minimizes resource wastage. We adopt an M/M/m+D queuing model to analyse the performance indicators affecting the profitability of our double renting scheme, including the average charge and the ratio of requests necessitating temporary servers. By formulating a profit maximization problem tailored to the double renting scheme, we derive an optimized cloud platform configuration. Comparative calculations between our proposed scheme and the traditional single renting scheme demonstrate that our approach not only ensures superior service quality for all requests but also yields increased profitability. Key Words- Cloud computing, Double resource renting, Service quality, M/M/m+D queuing model, Performance indicators, Profit maximization, Short-term renting, Long-term renting.

Teaching production theory through simulation

The authors present a Web application they designed in the R programming language as an experiential learning tool for teaching production theory. The app simulates production decisions where a manager is tasked to find the optimal mixture of inputs through experimentation. Users of the application are instructed to use calculations and intuitions from production theory to improve profitability quickly. The underlying parameters and starting points are randomized to allow for additional practice. Variations of the exercise correspond to cost-minimization and profit-maximization problems with and without market power in the output market. Also, the app provides dynamic, interactive visualizations in 3D in order to assist in a better understanding of standard production theory graphs. The app is located at https://bit.ly/387HsHL.

Формирование оптимального кредитного портфеля с использованием нечётко-множественного подхода

The problem of profit maximization from lending to a financial organization is considered. A set of loan con-tracts forms a loan portfolio, which makes it possible to use the portfolio theory in the study of the designated problem. We will consider the formation of a loan portfolio as the formation of an investment portfolio. The problem arises of redistributing the funds of the investment portfolio in order to minimize its possible risk and maximize profitability. This problem in classical formulation can be solved according to Markowitz risk diversification. Thus, the problem of risk minimization and profitability maximization from lending to a financial institu-tion can be represented as a fuzzy mathematical programming problem, and more specifically, as a fuzzy linear programming problem. The resulting problem is solved by considering discrete α-levels and is reduced to a set of linear programming problems constructed for each of them. A clear expected optimal solution can be obtained by applying the defuzzification method, which allows you to convert a fuzzy set into a crisp number.

DSO Market for Transactive Scheduling of Electric Vehicle Charging Stations in Constrained Hierarchical Power Distribution and Urban Transportation Networks

The trend toward the deployment of electric vehicle charging stations (EVCSs) equipped with on-site distributed energy resources indicates potential transactive energy market (TEM) operations among EVCSs. However, unlike regular prosumers, EVCS operations are influenced by both the power distribution network (PDN) and the urban transportation network. In this paper, we propose a three-stage approach for solving the hierarchical energy scheduling and trading problem of EVCSs. At the first stage, the day-ahead traffic assignment problem of the transportation system is solved to determine individual EVCSs’ charging load. At the second stage, EVCSs solve their profit maximization problem to determine their energy scheduling and market participation decisions. Lastly, at the third stage, TEM among EVCSs is cleared by the distribution system operator (DSO). With the DSO shouldering both grid operator and market operator functions, the DSO problem is formulated as an unbalanced three-phase optimal power flow (OPF) model integrating a double-sided auction mechanism. To further improve the PDN operation, grid features such as network reconfiguration and tap changers are introduced into the OPF model. The effectiveness of the proposed framework is proved through case studies.

A new demand function graph: Analysis of retailer-to-individual customer product supply strategies under a non-essential demand pattern.

The core objective of a successful product supply strategy is to determine the mechanism through which consumers' psychological effects influence customer demand. As stated in the theory of supply and demand, a higher level of dynamic equilibrium should be formed in which demand drives supply and supply creates demand. There is a lack of systematic research in the literature on the identification of consumer goods demand attributes and the formation of influencing factors in consumer goods supply chains. In this paper, we use the literature on demand functions and product pricing functions to establish three mathematical models to study the factors that influence retailers in designing and planning product supply strategies for different customers under nonessential demand patterns and to solve the profit maximization problem. The results of numerical examples validate the validity of the model. The research results can help retailers develop different supply strategies according to different types of customers and different demand patterns, thereby improving business performance. The theoretical contribution of this study is the construction of value ranges and a demand function diagram for identifying consumer product demand attributes.

A sustainable dynamic optimization model of pricing and advertising in the presence of green innovation investment

Due to the increasing greenhouse effect and global warming, ecological and environmental protection issues are growing tremendously. The Paris Agreement and other international agreements have been enacted to slow down the increase in carbon emissions to prevent it from degrading the ecosystem. With the increasing consumer awareness of environmental protection and environmental regulatory pressures, firms must integrate carbon emissions concerns into decision-making. This paper analyzes a joint dynamic pricing, green innovation investment, and advertising model under the cap-and-price mechanism. The demand rate is multiplicatively related to the selling price and goodwill. The profit-maximizing problem is considered over an infinite horizon. Specifically, we assume that the stock of goodwill grows with green innovation and advertising efforts but depreciates by a constant proportion each period. Numerous theoretical results have been established to expand our comprehension of the problem. Moreover, we present several explications corresponding to these structural properties, characterizing the effects of critical parameters on optimal decisions. Finally, some numerical illustrations and explanations of the concepts of sensitivity analysis are presented to obtain managerial insights, followed by concluding remarks and future research.

An Efficient Matching Game Approach to Association Formation in UAV-Enabled Hierarchical Distributed Learning.

Distributed machine learning has emerged as a promising data processing technology for next-generation communication systems. It leverages the computational capabilities of local nodes to efficiently handle large datasets, creating highly accurate data-driven models for analysis and prediction purposes. However, the performance of distributed machine learning can be significantly hampered by communication bottlenecks and node dropouts. In this article, a novel unmanned aerial vehicle (UAV)-enabled hierarchical distributed learning architecture is proposed to support machine learning applications, e.g., regional monitoring. Multiple UAV receivers (URs) are introduced as wireless relays to improve the communication between the UAV transmitters (UTs) and the cloud server. Our objective is to identify the optimal UT-UR association to maximize the social welfare of the network, which is distinctly different from the existing works that focus on the unilateral profit-maximizing problem. We formulate a two-side many-to-one matching game to model the UT-UR association problem, and a two-phase many-to-one matching algorithm is designed to identify the stable matching. The validity of our proposed scheme is verified through in-depth numerical simulations.

Joint Optimization of Distance-Based Fares and Headway for Fixed-Route Bus Operations

This paper proposes a profit maximization problem designed for fixed-route bus operations, optimizing two key variables: distance-based fares and headways. This study formulates a profit maximization problem while considering the dynamic nature of transit ridership influenced by various demand elasticities. The elasticity of demand is modeled using parameters such as onboard time, waiting time, and fare. Three primary constraints are considered: (1) a financial constraint ensuring the profit (including government subsidy) is non-negative, (2) a demand constraint that ensures actual demand is non-negative (i.e., elastic demand function value is between zero and one, and (3) a maximum headway constraint that limits passenger waiting times to half the headway duration, so that no passengers wait more than one bus. Notably, this research goes beyond the existing literature, which predominantly focuses on average fares, by exploring the implications of a distance-based (user-based) fare structure. A genetic algorithm is used to find solutions. The study employs numerical analyses to verify the solution method and conducts sensitivity analyses on critical input parameters. This study is suitable for one time block (e.g., multiple hours) for a steady demand, and can be extended into multiple time periods to reflect demand changes with the time of day.

An Efficient Method to Obtain Initial Basic Feasible Solution of a Transportation Problem

Transportation Problem (TP) is the study of strategy for shipping the product from the origin (supplier) to the destination (consumers) and the optimal shipment cost of the TP obtained from the initial basic feasible solution (IBFS). IBFS is the prime element of TP which helps to optimize the TP objective function. Existing methods for finding IBFS could not give the nearest value to minimal cost everywhere. Hence an innovative technique Known as TOCM-MT provides IBFS, which is the closest to an optimal solution. Many researchers have used this TOCM-MT technique through thousands of real-life TP problems, in every time got a better result than VAM, JHM, and TDM1 techniques. Hence, this technique is best for obtaining IBFS. This research is illustrated the TOCM-MT approach through time minimizing, transshipment, and profit maximization problems with some numerical examples.

A Dynamic Model of Profit Maximization for Carsharing Services: Astana, Republic of Kazakhstan

This study considers building a dynamic model of profit maximization for a carsharing system and its verification based on the case of implementing such a system in Astana, Republic of Kazakhstan. The region, bounded by the administrative boundaries of Astana, was divided into subregions that covered the region with regular hexagons placed side by side. A dataset was built with information on 1168 trips to Astana from January to March 2023. The Kepler visualization service constructed maps of the beginning and end of the trips to the region and a map of trips binding to the hexagonal grid cells. Each cell of the grid corresponds to a specific subregion, for which the quantitative parameters necessary for solving the profit maximization problem in the carsharing system are calculated. Stations with cars are placed in the cells of the grid, which are available to carsharing service customers. Based on the collected data, dynamic (four periods per day) and static profit maximization models in the carsharing system were built. Modeling was carried out based on the built models in the case of Astana. It was established that using a dynamic profit maximization model in the carsharing system increases profit by 3.7%. The obtained results are important for the development of the infrastructure of the capital of Kazakhstan and for finding a solution to the problems of urban science in this region.

A four-echelon supply chain inventory model for growing items with imperfect quality and errors in quality inspection

To safeguard the livelihood of consumers, food producers are required, either by law or regulatory bodies, to inspect their products for quality before selling the products to consumers. This is because food processing, as is the case with most production systems, is not perfect and there is a possibility that some of the processed products do not meet the required quality standard. Likewise, the inspection process is seldom perfect, meaning that it is subject to errors and thus, some of the processed products might be incorrectly classified. In light of this, an inventory model for a four-echelon food processing supply chain is developed. The supply chain has a farming echelon where live items are grown with the possibility that some of them might not survive; a processing echelon where the live items are transformed into processed inventory; an inspection echelon where the processed inventory is classified into good and poorer quality classes under the assumption that the inspection process is subject to type I and type II errors; and a retail echelon where the processed inventory of good quality is sold to consumers. The supply chain is modelled as a profit maximisation problem and a solution procedure for solving the model is proposed. The problem is studied under both centralised and decentralised supply chain structures and from the analysis, the centralised supply chain with a profit-sharing agreement performs better in terms of profit maximisation.

A robust optimization model for multiple electricity retailers based on electricity trading in the presence of demand response program

This paper focuses on the short-term cooperation between the electricity retailers at distribution network level and proposes an electricity trading based cooperative mechanism to manage the cooperation between retailers. Under the cooperative mechanism, the objective of the retailers who are engaged in cooperation is to maximize their overall profit through appropriate electricity trading. The profit maximization problem for the retailers is formulated as a robust optimization model and solved via heuristic algorithms. The profit increment brought by electricity trading is allocated according to the proposed profit allocation method. The simulation results demonstrate that the proposed mechanism can effectively increase the overall profit of the retailers. Compared with the non-cooperative case, the cooperative case can increase the overall profit of 427.34 $ at best. Moreover, the results demonstrate that the number of the retailers involved in electricity trading has a positive impact on overall profit increment. The results also reveal that each retailer can achieve profit growth even under the most unfavorable conditions by adopting the profit allocation method.

Platform Profit Maximization in D2D Collaboration Based Multi-Access Edge Computing

Multi-access edge computing (MEC) has been an important and promising paradigm for offering computing services to mobile users with computation-intensive and latency-critical tasks. In this paper, we study a D2D collaboration based MEC system, where the service platform purchases resources from resource-rich collaborative D2D devices when the task arrival rate exceeds the platform’s capability for providing satisfactory QoS. The design objective is to maximize the platform profit while maximally satisfying the delay requirements of tasks. We define delay based utility functions for different participants and accordingly formulate the platform profit maximization problem as a Mixed Integer Non-Linear Programming (MINLP) problem. For the online case where future task arrivals are unknown in advance, we propose a reverse auction based task assignment and urgency-value based transmission scheduling algorithm (RAGM). We present the detailed algorithm design and deduce its computation complexity. We prove that RAGM satisfies individual rationality of all participants. We conduct extensive simulations and the results show the high performance of RAGM as compared with benchmark algorithms.