Profit Function Research Articles

Customer segmentation, pricing, and lead time decisions: A stochastic-user-equilibrium perspective

Multiple price/lead time options are often used as a competitive tool in supply chain operations when customers have heterogeneous price and lead time preferences. We study a two-echelon supply chain network consisting of manufacturers and retailers facing customers that differ in their price- and time-sensitivity. We examine how many price/lead time options should be provided by manufacturers and retailers under decentralized and centralized supply chain management with time-cost tradeoffs. We adopt a stochastic-user-equilibrium (SUE) approach in a supply chain network by incorporating discrete choice theory and using a multinomial logit-based variational inequality to express equilibrium conditions. This is one of the first papers to study time-cost tradeoffs in a supply chain network by introducing an SUE approach. One critical part of our analysis is the establishment of concavity of profit functions, which allows for analytical derivation of the equilibrium strategies. Another critical part of our analysis is the development of SUE conditions in decentralized and centralized supply chain networks. We demonstrate that the variance of heterogeneous customers’ time-sensitivity distribution plays a crucial role in customer segmentations in a time-cost tradeoff supply chain. We find that under SUE conditions, there exists a unique equilibrium in the decentralized and centralized supply chain networks, respectively. We conduct comparative statics analyze to demonstrate the effect of SUE and UE conditions and the influence of decentralized versus centralized supply chain management paradigms. We show how the SUE approach can be applied to supply chain network management with time-cost tradeoffs. Our approach can be extended to other tradeoff decision problems in supply chain network management, especially those in which customers are heterogeneous.

Profit Analysis to an Industrial System Possessing Active Redundancy form Using Geometric Distribution

This paper elaborates on the approach towards reliability analysis for the active redundant system with a dual nature of repair strategy according to the kind of failure. The reliability characteristics using regenerative techniques are analyzed stochastically for the system, which includes two parallel units acting in an active redundancy form. A transition model has been designed for the working mechanism discussed in the paper and evaluated with the help of a geometric distribution possessing distinct repair. Regenerative techniques and geometric distribution were used to derive the numerical equations for reliability parameters such as availability, mean time to system failure, and repair mechanisms following down period of the system. A graphical analysis of the repair/failure rate with respect to the profit function has also been presented.

Using Carbon Tax to Reach the U.S.’s 2050 NDCs Goals—A CGE Model of Firms, Government, and Households

Our study shows how the United States government can achieve its goal of Nationally Determined Contribution (NDC) in 2025, 2030, and 2050 by reducing energy consumption through a pure carbon tax. To achieve its emissions reduction goals, it is necessary for the U.S. to impose a long-term carbon tax that balances taxes on labour, capital, energy, and carbon. Therefore, in this study, through the two-layer CGE Cobb–Douglas model, the carbon tax rate is set while balancing the production and profit functions of government, businesses, and households. This study concludes that the carbon price will increase from USD 0.4391/kg CO2 in 2020 to USD 2.5671/kg CO2 in 2050, when the CO2 emissions reduction target is increased from 17% reduction in 2020 to 83% reduction in 2050 for the U.S.

Device association and trajectory planning for UAV-assisted MEC in IoT: a matching theory-based approach

Unmanned aircraft vehicles (UAVs)-enabled mobile edge computing (MEC) can enable Internet of Things devices (IoTD) to offload computing tasks to them. Considering this, we study how multiple aerial service providers (ASPs) compete with each other to provide edge computing services to multiple ground network operators (GNOs). An ASP owning multiple UAVs aims to achieve the maximum profit from providing MEC service to the GNOs, while a GNO operating multiple IoTDs aims to seek the computing service of a certain ASP to meet its performance requirements. To this end, we first quantify the conflicting interests of the ASPs and GNOs by using different profit functions. Then, the UAV scheduling and resource allocation is formulated as a multi-objective optimization problem. To address this problem, we first solve the UAV trajectory planning and resource allocation problem between one ASP and one GNO by using the Lagrange relaxation and successive convex optimization (SCA) methods. Based on the obtained results, the GNOs and ASPs are then associated in the framework based on the matching theory, which results in a weak Pareto optimality. Simulation results show that the proposed method achieves the considerable performance.

Economic Aspects of Profit Maximization if Cost of Principal Raw Material Increases

In this study sensitivity analysis of various inputs is discussed, when per unit cost of principal raw materials is increased. The organization has its main target of achieving maximum profit through the adjustment of various inputs and outputs in future production. In this study Cobb-Douglas production function is considered as a profit function to investigate sensitivity analysis during profit maximization procedures. In this article the method of Lagrange multiplier is applied to represent higher dimensional unconstrained problem from the lower dimensional constrained problem. Moreover, the determinant of the 6×6 bordered Hessian matrix and 6×6 Jacobian are applied for the augmentation of the sensitivity analysis efficiently.

Contract Design for Return Products in a Cooperative Closed-Loop Supply Chain

The importance of considering the End-of-life product (EOL) in the closed-loop supply chain network has led it to model a two-echelon closed-loop supply chain network between the retailer and the manufacturer in this article, considering the redemption guarantee. Consumer products to be paid. Therefore, the model is considered in two modes, in which initially the members of the supply chain under a Stakelberg game are competing with each other for pricing on new products, product redemption and wholesale prices. In this (decentralized) scenario, members of the supply chain (retailer and manufacturer) are a percentage increase in their profit function. In this scenario, the producer, after determining the wholesale price as the leader of the game, maximizes the profit from the sale of its products, and then the retailer, as the leader in the game, determines the price of the products and the redemption price. In another (centralized) scenario, the main goal is to increase the profitability of the entire supply chain. This article also examines a contract related to the rate of purchase of returned products and the sale of new products, which encourages supply chain members to work together to increase their profits over a decentralized scenario. The stated materials lead to the design of models in a focused and decentralized scenario. The results of implementing the model on the sample problem show the high efficiency of this type of contract in increasing the profit of supply chain members compared to the decentralized scenario.

An Optimized Fed-Batch Culture Strategy Based on Multidimensional Time Series Aggregation

An optimized feeding strategy for the fed-batch fermentation of 2-keto-L-gulonic acid (2-KGA) is proposed to enhance the total profit of a workshop. Instead of assigning the same quantity of substrate to each batch in the empirical scheduling, the online feeding strategy offers a practical approach that allows for the precise management of substrate feeding to maximize economic performance. The forecasting of the profit function has been achieved through the proposed similarity measurement and multidimensional time series aggregation method. This method solves the problem of predicting the total economic benefit at the end of fermentation, in the absence of fermentation substrate measurement data. Pseudo-online simulation has been conducted, utilizing data derived from ninety industrial batches. A 6% increase in total profit is observed, which indicates that the optimized strategy utilizes the substrate and other related resources more efficiently and leads to a higher overall profit.

Determination of optimal warranty length for smart wearable device considering customer complaint

ABSTRACT This study investigates optimal warranty length for a new type of smart wearable device to maximize manufacturer’s profit in a competitive market. Most studies explore optimal warranty length based on product performance without considering customer complaints. In this study, unlike existing models, the optimal warranty length is obtained by maximizing an expected profit function comprising essential factors such as customer complaints, early and late warranty periods, product reliability, and reduced profit, using Bayesian analysis. Managers can effectively integrate these factors, and can be more confident about the accuracy of estimated optimal warranty length. This study’s contribution is to propose a methodology to develop new types of smart wearable devices considering their long-term commercial prospects. Sensitivity analyses indicate that in the early warranty period, managers should be more concerned about average reduced profit due to customer complaints and reduced profit percentage due to complaint handling costs. In the late warranty period, improved profit percentage due to good response to complaints is essential in smart wearable device sales. Consequently, managers should adequately deal with customer complaints about smart wearable devices, whether in the early or late warranty period.

Modeling the Efficiency of Operating Costs in Introducting Innovations in the Agrarian Sphere

The purpose of the work is to demonstrate the results of modeling the impact of innovation on the efficiency of operating costs for crop production by agricultural enterprises. Based on the dialectical method of cognition, abstract-logical, and graphic methods were used; nonlinear correlation-regression analysis and economic-mathematical modeling It is established that the innovations of technical and technological character contribute to the increase of the extremum of the yield function. At the same time, the impact of innovation on the profit function is twofold. In the case of free product innovation, an increase in output estimated at market prices generates an increase in the extremum of the profit function while increasing the profit optimum of costs. That is why the latter is approaching the technological optimum. In turn, the innovation payoff affects the profit curve, reducing the value of the cost optimum and the function extremum. However, a significant increase in the cost of an innovative product can lead to a decrease in profit below the achieved level.

Models of the dynamics of maximal and optimal profits of a manufacturing enterprise implementing technological innovations

The published article presents new mathematical models that describe the dynamics of the development of manufacturing enterprises using innovative technologies. It is shown that the level of use of innovative technologies in an enterprise depends on dimensionless coefficients that describe the diffusion process of introducing technological innovations and affect the increase in output and cost reduction. The dependence of the enterprise's profit on the levels of production and transaction costs has been studied. It has been established that the formation of transaction costs arising from the search and processing of economic information, financing of negotiation procedures, conclusion of contracts with partners, protection of property rights and payment for the opportunistic behavior of employees and management of the enterprise, force the management of the enterprise to maximize not only the profit function, but also the target a transactional utility function that takes into account the redistribution of profits in the interests of the enterprise's management and for the implementation of socially-oriented programs. Dimensionless redistribution coefficients are calculated, which determine the size of the part of the profit that is used for non-production purposes. It is shown that in the presence of transaction costs, the limiting value of the enterprise's profit is not its maximum possible value, but its lower optimal value.

Optimizing the Production rate of EV battery cell in an EPQ model with process-based cost method using Genetic Algorithm: A case study of NMC-622 cell

This research is motivated by a real-world industry problem. Environmental concerns caused by the increasing number of internal combustion engine vehicles are developing a growing interest in the study and development of electric vehicle (EV) batteries. The cost of EV batteries is critical for the market growth of electric vehicles. As cell is the most essential component in the EV battery, the cost-effective manufacturing of battery cells is a popular topic in industry and academics. Manufacturers invest billions of dollars in battery cell factories based on predicted EV growth rates. However, these manufacturers require information on total manufacturing costs, plant area, total capital equipment costs, and their cost drivers to achieve the goal of a profitable firm. Inspired by these concerns, an EPQ model with a process-based cost modeling technique is developed for the large-scale manufacturing of EV battery cells. The goal of this research is to provide the most precise framework for the manufacturer to maximize its profit in cell manufacturing. The data used in this model is collected from the BatPac model (version 4) developed by Argonne National Laboratory. This study considers two types of battery cells used in electric vehicles, and the firm produces 5 % of defective cells. A well-known cost estimation method (PBCM) and the EPQ model are combined to generate total profit function. The production rate and selling price for both cells are considered as decision variables. The profit function is maximized by using genetic algorithm and graphs are provided to show the relation between decision variables and profit function. According to the findings, the production rate of the cells has a significant impact on the overall profit, and in order to maximize the profit, the production rate and selling price of cell 1 must be lower than cell 2. A detailed cost analysis has been provided to identify which process steps and cost aspects significantly impact the total cost. Finally, managerial implications and conclusions are presented that support manufacturers in increasing the firm’s profit.

Different outcomes of alternative approaches to forest carbon accounting at the local level

In forest carbon accounting and policy assessment at the micro level, inconsistencies, and even confusion, abound regarding how timber and carbon are treated as joint products, whether the Paris Agreement principles of additionality and permanence are followed, and if the differentiated composition and duration of harvested wood products (HWPs) are captured. Here, we tackle these issues with two widely used alternative analytic frameworks. The first features a Hartman modification of the Faustmann model for forest growth and harvest without incorporating accounting principles and HWPs, whereas the second builds from a profit function of forest production incorporating accounting principles and measures of HWPs. Using the intensively managed pine plantations of the U.S. South as an empirical case, we show that the carbon outcomes of the two approaches vary greatly. The Hartman-Faustmann approach exaggerates carbon credits for a landowner by a factor of at least 2.76. Furthermore, while adding carbon to the valuation has limited impact on the optimal harvest age, it increases net revenue under the profit function approach by 45% at a price of $20 per ton of CO2. These distinctions are of broad importance as policymakers and forest economists in all regions of the world look for appropriately integrated assessments of forest sector solutions to climate change.

A Study on Nonlinear Budget Constraint of a Local Industrial Firm of Bangladesh: A Profit Maximization Investigation

Every local or global firm expects to achieve maximum profit for its survival in sustainable economic environment. This article considers that a local industrial firm of Bangladesh has achieved maximum profit during its total operation. So that this study directly tries to calculate maximum profit and also Lagrange multiplier for profit maximization investigation by the consideration of nonlinear budget constraint. In this study Cobb-Douglas production function is considered as profit function to operate mathematical procedures. Method of Lagrange multiplier is also applied here to obtain accurate results.

Is the online-offline buy-online-pickup-in-store retail strategy best among other product delivery strategies under variable lead time?

Every industry improves customer satisfaction by either preventing stockout situations or fulfilling the customer's demand by reducing lead time and variance of the lead time with several services offered. This study considers online selling, offline selling, and buy-online-pickup-in-store policies for selling products from retail stores. This study builds a characteristic relation between buy-online-pickup-in-store, backorder, and on-hand inventory by giving an exact total profit function instead of the expected profit function. The marginal values on lead time and variance of the lead time earn more exact outcomes for any retail strategy. The specific transportation cost for different retail strategies is considered and tested. This paper shows the analytical results which prove that the total profit of the sustainable supply chain is a convex function of both lead time and variance of the lead time. As different channel selling is crucial to any industry for increasing customer demand, the retailer sells their products by hybrid channel and advertises their products online to make them more famous. The model is solved through a classical optimization technique to get a semi-closed-form solution. In this method, it is possible to find out the optimum results for the decision variables separately by equating the first order partial derivative of the total profit with respect to the decision variables to zero and the global optimality by the Hessian matrix. A numerical experiment is conducted here, and the result shows that the supply chain system gives 14.48% more profit if advertisement policy is applied. The supply chain system gives 57.31% less profit and 72.72% less profit when only an online or offline channel is adopted, respectively. A sensitivity analysis is done for the managerial effects of cost parameters on the total profit.

Interplay of noise, memory and entangling operator in quantum Stackelberg-Bertrand duopoly game

In this work, we make an attempt to understand how noise, memory and entangling operators collectively decide the profit of the firms Here we have studied the quantum version of Stackelberg-Bertrand duopoly game using modified EWL scheme in both correlated and uncorrelated noise channels. When this game is analyzed for amplitude damping channels following interesting results are obtained: Firstly, decoherence in channel 2 effects the profit function of the firms more than that of channel 1. Secondly, in the case of correlated noise memory prevents the death of entanglement at maximum noise. Finally, the profit function of the firms depends upon noise, memory, strategies, and entangling operator in any given game setting.

Sustainable circular economy production system with emission control in LED bulb companies.

Mother Earth has a completely sustainable circular life cycle pattern. In its life cycle, there is no harm created to any living creature or to the environment. In this paper, a sustainable circular economic production and consumption system for a LED bulb firm that follows the same cycle pattern as our planet is developed. The circular economy concept, green technology, and carbon cap-and-trade policy are introduced in this model to control the carbon emission rate and resource depletion in LED firms. The profit function is maximized by Lagrange's multipliers method and Karush-Kuhn-Tucker (KKT) criteria. This paper determined the optimal production quantity and circularity index of the LED bulb for a wise manufacturing process. The concavity of the optimal profit function is proved by using the Hessian matrix method. Different linear and non-linear combinations of demand and profit functions were discussed. This article claims that the circularity level of LED bulbs has influenced their selling price, cost, and demand. Green technology and carbon cap-and-trade policies improved the sustainability of LED bulb companies. Numerical examples, results discussions, and an optimal solution table are provided to show the implication of this model for LED bulb companies. Sensitivity analysis is presented for key parameters. Managerial implication explained in terms of arrived results. Limitations and possible future extensions of this model are given in the conclusion section.

Farm households’ input demand and output supply response to price shocks in Nigeria

Panel data on farm household output for a full range of commodities are scarce, and as a consequence, only a few other studies have considered estimating farm household output supply and input demand response to price changes in Nigeria using panel data within the multiple inputs and multiple outputs frameworks. This study examined the extent to which farm households' respond to production inputs and output price changes using panel data covering the period 2010-2016. Specifically, to determine whether a commodity output's price positively affects its supply and other output categories; and whether an input price negatively affects its usage in Nigeria within the multiple input and multiple output (MI-MO) framework. The translog profit function was used to simultaneously examine the production response of farm households' in terms of the factor demand and produce supply. Seven output supply and four input demand equations were estimated. The results indicated that the response of output supply to own price ranged from 0.59 for animal products and 1.24 for cereals. The own-price demand elasticities of farm input range from -0.82 for mechanisation to -1.46 for intermediate inputs. Also, a substantial degree of farm households' response to input price shocks. Farm inputs and outputs were economic complements to price changes. Therefore, price policy issues aimed at improving the production response of farm households' to both input and output price shocks should be developed with a particular focus on farm inputs.

Decision making under service‐level contracts: The role of cost saliency

This study examines human ordering behavior in service‐level inventory contracts, a class of contracts important in practice. Studies of wholesale price contracts find that people tend to place orders that are suboptimal and biased toward mean demand. Unlike wholesale price contracts, service‐level contracts can be parameterized such that they have steep expected profit functions, making the expected profit‐maximizing order more salient, in the sense that deviations from optimal ordering are more costly. Utilizing an analytical model and results from existing literature, we hypothesize that people will order closer to optimality under service‐level contracts with steeper expected profit functions. In a laboratory experiment, we find that subjects achieve up to 97.2% supply chain efficiency under a steep service‐level contract, compared with 92.2% under a flat service‐level contract, and steep service contract ordering also exhibits lower variability. Our results suggest that managers can benefit by designing service‐level contracts with higher penalty costs and lower fill rates.

Economic optimization and predictive control for nonlinear systems using Lyapunov based nonlinear cost function design

Optimal control of physical processes depends on the formulation of objective functions and contemplation of appropriate predictive control. In this article, we propose a new framework, to blend the concepts of the Lyapunov-based economic model predictive control (Ly-EMPC) scheme with the novel cost-efficient profit function design. Furthermore, Lyapunov’s stability criteria is employed to verify the existence of duality and optimality for the designed economic stage costs. This method differs from the existing EMPC techniques by implementing Lagrange multipliers in the rotated cost function as a measure of stability. The closed-loop performance using the regularized Ly-EMPC is validated against a standard tracking objective-based nonlinear MPC for three benchmark examples through an econometrics gauge factor. Interestingly, in contrast to tracking NMPC, the proposed Ly-EMPC scheme excels in economic performance, while the formation of nonlinear economic stage cost is conceptually simpler, novel, and practically profitable.

The impact of information sharing and bullwhip effects on improving consumer services in dual-channel retailing

Data sharing among the supply chain players can be an exceptionally significant factor for the retailing industry. In this consideration, an improved retailing methodology for a dual-channel supply chain with a single retailer and manufacturer is built under the bullwhip effect and asymmetric data sharing. Retailer provides asymmetric information to the manufacturer regarding demand to increase their profit. In this scenario, measuring the bullwhip effect is essential in retailing strategy. By adopting an online-to-offline retailing strategy, industries can earn more profit and increase the satisfaction level of customers. The present study focuses on dual-channel retailing, where the demand for the product in both channels varies with the selling price. Keeping in mind the goal of sustainable development, an advanced transportation strategy is utilized in this study, along with some carbon emission costs. Autonomated inspection is utilized to identify defective products. Finally, centralized and decentralized profit functions are formulated for this study. Several cases and numerical examples are provided to validate this study. It is clear from the numerical findings that information sharing within the players provides 1.26% more profit compared to a decentralized case. Due to asymmetric information, which leads to the bullwhip effect, the retailing system faces loss. Thus, information sharing is 0.19% beneficial for dual-channel retailing. Sensitivity analysis for key parameters ensures the findings' applicability in the real world.