Profit Function Research Articles

Technical progress and induced innovation in China: a variable profit function approach

We propose a new methodology to estimate empirically the input price-induced technical change and total factor productivity (TFP) growth in China. Our primary goal is to test Hicks’ induced innovation hypothesis by examining whether technical change in China has been induced by sharp increase in input prices that have accompanied its rapid economic growth. Utilizing the idea of a firm’s two-stage optimization problem, we develop a new parametric form of the variable profit function wherein the derived input demand and output supply functions can be easily constrained to be regular, and the functional structure is parsimonious in the number of parameters. Applying this methodology to Chinese time series data for 1986–2017, we find that not only is wage-induced innovation significant and quantitatively important, but also that it substantially buffered a decline in TFP growth before 2006 that would otherwise be substantial. Overall, we conclude that China’s economic growth is predominantly driven by wage-induced innovation along with massive injection of heavily subsidized physical inputs in public works and huge investment in industrial sectors.

An EOQ Model with Carbon Emissions and Inflation for Deteriorating Imperfect Quality Items under Learning Effect

We developed an economic order quantity (EOQ) model with a learning effect and carbon emissions under inflationary conditions and inspection for retailers where the items deteriorate naturally. Finally, the total profit of the retailer is maximized with respect to cycle length. A sensitivity analysis was also performed to understand the robustness of the model. In the sensitivity analysis, we discuss the impact of learning rate, inflation rate, and deterioration rate on lot size and length of the cycle, as well as the retailer’s entire profit function. Observations and managerial insights are discussed. The effect of inventory parameters on the total profit is shown in the sensitivity section.

Profit Efficiency of Smallholder Vegetable Farms in Nepal: Implications for Improving Household Income

Enhancing profit efficiency in vegetable farming is important to increase income, livelihoods, and nutrition security, and to reduce poverty of smallholder farmers, particularly in developing countries. This study examined the profit efficiency and its determinants in smallholder vegetable farms in Nepal using the stochastic translog profit function with cross-section data collected in 2013. The results revealed a high level of inefficiency in vegetable farms because of the combined effects of technical, allocative, and scale inefficiencies. The profitability differential in vegetable farms is significantly explained by input variables, namely, labor, land, seeds, fertilizer, pesticides, and capital. The determinants of profit inefficiency in vegetable farming were the types of crop varieties, access to information and extension services, access to agricultural credit, distance of farms to markets, and sex of farm manager. The profit efficiency in vegetable farming can be enhanced by adopting improved seed varieties, improving effective information and extension programs, increasing accessibility of credit facilities to the farmers, developing market infrastructure, and empowering women farmers in vegetable farming that leads to improve household income and nutrition security.

Determinants of Profit Efficiency among Small Scale Rice Farmers in North Central, Nigeria: A Profit Function Approach

The study employed a stochastic frontier profit function to measure profit efficiency among rice farmers in North Central, Nigeria. A multi-stage sampling procedure was employed in selecting 218 rice farming household heads in six Local Government Areas of North Central, Nigeria. The results showed that rice production is highly profitable with an estimated net farm income and Gross margin of N67,808.31 and N 70,273.56 per hectare and the return on investment of N1.26 was realized as profit for every one naira invested in production of rice in North Central Nigeria. The gross ratio of 0.46 and the operating ratio of 0.44 are indicators that rice production was profitable in the study area. Furthermore, the result of tranlog stochastic function revealed that rice farmers in North Central were not all fully profit efficient and thus an average farmer in study area could potentially increase profit level if resources are more efficiently utilized. However, the results show that fertilizer, labour, agrochemical, farm size, age, household size, education, farming experience, awareness of climate change and access to climate information had significant effects on the profit efficiency of rice farmers in the study area. The study recommended that since the area has a great potential to increase rice production and farmers’ income, efforts should be made by encouraging rice farmers to intensify the use of improved varieties of rice in order to increase their output. Now that the present administration change agenda is geared towards agriculture, youths in the country could be encouraged by government at all levels and Non-Governmental Organizations (NGOs) to venture into rice farming agribusiness that will serve as potential employment source.

Distribution-Free Pricing

Problem definition: We study a monopolistic robust pricing problem in which the seller does not know the customers’ valuation distribution for a product but knows its mean and variance. Academic/practical relevance: This minimal requirement for information means that the pricing managers only need to be able to answer two questions: How much will your targeted customers pay on average? To measure your confidence in the previous answer, what is the standard deviation of customer valuations? Methodology: We focus on the maximin profit criterion and derive distribution-free upper and lower bounds on the profit function. Results: By maximizing the tight profit lower bound, we obtain the optimal robust price in closed form as well as its distribution-free, worst-case performance bound. We then extend the single-product result to study the robust pure bundle pricing problem where the seller only knows the mean and variance of each product, and we provide easily verifiable, distribution-free, sufficient conditions that guarantee the pure bundle to be more robustly profitable than à la carte (i.e., separate) sales. We further derive a distribution-free, worst-case performance guarantee for a heuristic scheme in which customers choose between buying either a single product or a pure bundle. Moreover, we generalize separate sales and pure bundling to a scheme called clustered bundling that imposes a price for each part (i.e., cluster) of a partition of all products and allows customers to choose one or multiple parts (i.e., clusters), and we provide various algorithms to compute clustered bundling heuristics. In parallel, most of our results hold for the minimax relative regret criterion as well. Managerial implications: The robust price for a single product is in closed form under the maximin profit or minimax relative regret criterion and hence, is easily computable. Its interpretation can be easily explained to pricing managers. We also provide efficient algorithms to compute various mixed bundling heuristics for the multiproduct problem.

A Novel Model of Emergency Demand Response Program for Optimal Aggregators’ Strategy

Demand response (DR) programs have been used for a variety of purposes. In this study, Emergency Demand Response Program (EDRP), as an incentive-based program, is used for peak clipping, managing the volatility and the increase of the electricity prices, monetizing consumers’ involuntary electricity outage and controlling the price in the day-ahead market. A market-driven model in the form of a combination of Diamond’s over-lapping generations (OLG) and Price Elasticity (PE) formulations is proposed for the aggregates (AGGs) by which they can manage their consumers’ demand at the peak hours and maximize the profit. Furthermore, maximizing the profit of the AGGs was performed by determining the optimal amount of demand while three technical constraints such as demand ceiling, relative risk aversion and incentive limits were also included in the proposed model. The profit function of the AGGs is considered in the form of the difference between the revenue and the cost. The problem is solved with taking into consideration the different rate of time preference and PE over a 24-hour period. The simulation results showed a successful performance of the proposed model from the considered economical and technical viewpoints.

A Pollution Sensitive Marxian Production Inventory Model with Deterioration Under Fuzzy System.

This article deals with an economic production quantity (EPQ) model with deterioration under the effect of environmental pollution in fuzzy environment. First of all, we develop a pollution generation (PG) model with the help of existing initial pollution status of the environment, and then we use it as an essential constraint in the proposed EPQ model. The model has also been studied in two different scenarios: (a) when unit selling price is given and (b) when unit selling price is associated with marginal profit respectively. However, in this article, the concept of manpower exploitation, law of surplus value and their impacts on profit function has been discussed. In fact, after the invention of Marxian production theory (1867), not a single article has been developed for studying inventory management problems/operations research using this theory. Thus, in this study, focussing Marxian principle we have developed a new production inventory model named Marxian economic production quantity (M-EPQ) model incorporating the extensions of the models developed by Harris (Mag Manag 10(2):135–136, 1913) and Taft (Iron Age 101:1410–1412, 1918) exclusively. Moreover, to deal with the non-random uncertainties of several cost components of production process we have utilized fuzzy system explicitly. A case study has been performed for numerical illustrations and we have developed a solution algorithm for numerical computations. Finally, sensitivity analysis and graphical illustrations are made to validate the new M-EPQ model followed by a conclusion.

Optimal purchase planning of initial emission permits with the paid use and trading system based on mean–variance model

The paid use and trading of emission permits system are a major mechanistic innovation in the field of environmental resources management in China. In this system, manufacturers must purchase emission permits on the primary market under the precondition that the purchase ceiling and price will be determined by the government; subsequently, they may trade emission permits with other manufacturers on the secondary market subject to established rules. This inevitably leads to uncertainty regarding the emissions trading price on the secondary market, while the manufacturer is making the initial purchase decision; it highlights the need to investigate optimal purchase planning solutions under conditions of uncertainty from the perspective of production optimisation. This paper examines the manufacturer's random profit function, as well as its mean and variance, under uncertain emission trading prices. Using the mean–variance framework, an optimisation model with differentiated decision objectives is established. Accordingly, the manufacturer's optimal initial purchase planning approach is demonstrated with respect to each decision objective. The conclusions demonstrate that when the manufacturer exhibits risk preference, the optimal purchase planning process may systematically deviate from the risk-neutral approach.

The Role of the Discount Policy of Prepayment on Environmentally Friendly Inventory Management

Nowadays, more and more consumers consider environmentally friendly products in their purchasing decisions. Companies need to adapt to these changes while paying attention to standard business systems such as payment terms. The purpose of this study is to optimize the entire profit function of a retailer and to find the optimal selling price and replenishment cycle when the demand rate depends on the price and carbon emission reduction level. This study investigates an economic order quantity model that has a demand function with a positive impact of carbon emission reduction besides the selling price. In this model, the supplier requests payment in advance on the purchased cost while offering a discount according to the payment in the advanced decision. Three different types of payment-in-advance cases are applied: (1) payment in advance with equal numbers of instalments, (2) payment in advance with a single instalment, and (3) the absence of payment in advance. Numerical examples and sensitivity analysis illustrate the proposed model. Here, the total profit increases for all three cases with higher values of carbon emission reduction level. Further, the study finds that the profit becomes maximum for case 2, whereas the selling price and cycle length become minimum. This study considers the sustainable inventory model with payment-in-advance settings when the demand rate depends on the price and carbon emission reduction level. From the literature review, no researcher has undergone this kind of study in the authors’ knowledge.

Effect of advance payment on an inventory model for a deteriorating item considering expiration time of product, restricted shelf space and age dependent selling price with discount facility

The life-time of a deteriorating product is a major issue in inventory management. In practise the quality as well as quantity of deteriorating product deteriorates over time and the quality (freshness) of the product influences the customer’s demand. With the consideration of product life time, we develop an inventory model with price and freshness dependent demand under advance payment system with discount facility. The selling price is freshness sensitive. Goal of our model are twofold. The first one is customer’s demand is dependent upon the newness/freshness state of the product as well as selling price of the product. In the last one stock level at the end of cycle is relaxed. The solution process of projected optimization model is illustrated theoretically. Couple of numerical examples and sensitivity analysis are provided to demonstrate the feature of the profit function. Concavity of the average profit function is shown by plotting graphs. This study shows that all parameters in the proposed maximization model significantly influence the optimal solution.

Live-streaming selling strategies of agricultural products:A game-theoretical analysis

With the rapid development of 5G network technology and the impact of the COVID-19, e-commerce technologycontinues to improve and develop, and the number of online shoppers increases rapidly. This series of developmentand changes also promote the formation of e-commerce form of live broadcast with goods and has become a newtrend. In this article, under the background of not considering the off-line channel, but only considering the onlinesingle channel sales, aiming at the problem of direct seeding agricultural products with goods, we use gametheory to model and study it and get the optimal pricing strategy. First, based on the pricing game of consumers’evaluation behavior, a two-stage evaluation model is made in order to analyze and calculate the optimal pricefunction and profit function and to carry out the numerical simulation. Then, based on the different transportationcosts, the Hotelling pricing game is made. Finally, the optimal pricing strategies under two assumptions areobtained. In addition, this article also puts forward four suggestions on live streaming of agricultural productsagainst the current situation.

Quality Effort Strategy of O2O Takeout Service Supply Chain under Three Operation Modes

This paper investigates channel selection and quality effort in O2O takeout service supply chain consisting of a takeout platform, a catering business, and a distribution rider. By analyzing the three operation modes of platform distribution, business self‐distribution, and business self‐built platform + distribution, the profit functions of O2O takeout service supply chain members are constructed, respectively. On the basis of game theory, the optimal quality effort and profits are obtained. Combined with numerical simulation, the effects of revenue sharing rate and market size on the optimal quality effort and profits under different scenarios are discussed. The results reveal that O2O takeout platform should cooperate with more catering businesses, and adopt appropriate strategies considering different market sizes of catering businesses. Additionally, the catering business should properly consider the market size and adopt different online and offline prices. Meanwhile, the rider should choose a reasonable quality effort according to the revenue sharing rate.

AN ECONOMIC PRODUCTION QUANTITY MODEL WITH SELLING PRICE DEPENDENT DEMAND UNDER INFLATION AND VARIABLE PRODUCTION RATE FOR DETERIORATING ITEMS

In this paper we have considered an economic production quantity model in which demand is assumed as a function of selling price with unsteady deterioration rate. We have considered variable production rate and the shortages are not allowed. The effect of inflation rate is also taken. Under this condition a profit function is formulated and suitable numerical examples or sensitivity analysis also provided by changing some parameters of the system.

Optimal Procurement Management by Reverse Auctions for a Price-Setting Newsvendor

In this paper, we study the optimal procurement management by reverse auctions for a price-setting newsvendor (retailer) in a single period setting. The retailer facing price-dependent stochastic demand first designs a procurement contract and then invites the suppliers to bid for this contract in the reverse auction. The winning supplier produces and delivers the demanded quantity. The retailer obtains the procurement quantity and simultaneously determines the retail price. By using the price elasticity of the lost-sales rate, we show that the retailer’s expected profit (excluding the procurement cost) is a concave function of the purchased quantity, which can be used to obtain the optimal procurement and retail pricing decisions for the retailer. Further, when the underlying random term of demand function is normally distributed under left-truncation (at 0), we get the analytical expressions of the purchased quantity and expected profit function for the retailer. Moreover, some numerical examples are given.

Pricing strategy of competing retailers in a two layer supply chain under nonlinear stochastic demand

This paper develops mechanisms to deal the strategic issue that arises in a two-echelon closed-loop supply chain comprising of one manufacturer and two competing retailers. The chain works under stochastic nonlinear demand. Here the manufacturer works as the supplier and the retailers compete with each other on the basis of their retail price. The prime objective is to investigate a news-vendor model to govern the optimal order quantity. A buyback contract between the manufacturer and retailer has been considered and scenario of shortage has also been contemplated. The profit functions of manufacturer and two retailers are analysed following centralised approach. A numerical example is given to illustrate the theoretical results. Computational results show that it is always beneficial in integrated system for the members of the chain.

Inventory decision for products with deterioration and expiration dates for pollution-based supply chain model in fuzzy environments

The proposed study addresses a two-echelon sustainable supply chain (SC) model with a single-vendor and a single-buyer by considering the detrimental impacts of environmental pollution due to production. Moreover, an estimation function of pollution measure due to production is developed through a separate modelling. In the entire supply chain, we assume the deterioration rate increases with time and it also depends on the product’s expiration date. On the other hand, the demand for deteriorating items at the buyer’s end is assumed to be the dense fuzzy number because of learning effect. The model is developed by defining the exact profit functions for the vendor, the buyer and the entire supply chain and solved by classical method. These lead to the determination of individual optimal policies, as well as the optimal policy for the joint integrated supply chain. Fuzzifying the final objective function via dense fuzzy rule, we have employed extended ranking procedure for its defuzzification. A comparative study on numerical illustration of the proposed objective function under centralized and decentralized policies in both crisp and dense fuzzy environment has also been studied to validate the model. Finally graphical illustrations and sensitivity analysis have been made for its global justifications.

OUTPUT SUPPLY AND INPUT DEMAND RESPONSE OF POULTRY EGG FARMERS: EVIDENCE FROM NIGERIA

This research measured the output supply and input demand response of poultry egg production in South-western Nigeria. Specifically, the research noted both elasticities of output supply and input demand for egg production, as well as the short run profit value. This is necessary due to the acute shortage of information on the study area’s elasticity of output supply and input demand for egg production. A well-structured questionnaire and in-person interviews were used to gather data from the 360 egg producers that made up the sample size. The respondents were chosen using a snowball sampling technique. Descriptive and inferential statistics were employed to evaluate the data. By taking the first derivative, six equations were constructed from the generalized Leontief restricted profit function. The parameter estimates of the formulas were examined using Seemingly Unrelated Regression (SUR). Results demonstrated that the egg’s own-price elasticities were positive as predicted, at 0.434, and the supply of spent layers was, at 1.12. Additionally, all estimated own-price elasticities of input demands were discovered to be negative, as predicted. The study found that input demands were highly responsive to own-price change except for the day-old-chicks. The results also showed that labour was the most highly elastic input employed compared to other factors. The cross-price effects between the feed demand and day-old-chicks was found to be complements, while the cross-price effect between the feed demand and labour price was found to be substitutable. The study, therefore, concludes and suggests that price elasticities of demand for labour, feed and vaccines in poultry egg farming are keys for policy formulations to stimulate competitiveness in poultry industry.

Optimisation of a fuzzy inventory model with seasonal demand rate in two different markets

The seasonal dependent demand is a major factor for the fluctuations in the demand for seasonal products. To fulfill this demand, the retailer produced a large amount of items, but due to the short time of the season, some items remain in the stock. Due to the nature of the deterioration of the product, the retailer wants to sell all the products in stock. So the alternative marketing is the best way to get more profit with low inventory costs. The presented article is all about the fuzzy seasonal demand which depends on both price and time, and retailers sell the products in both the potential markets say first and second. A second market is required to sell in good profit before all items go bad due to deterioration condition, but due to the different demand in both markets, the fluctuations comes in the demand. To deal with the vagueness of the demand parameter, we use a triangular fuzzy number and defuzzify with the signed-distance method to optimise the total profit function with a numerical example show the application of the model.

Effect of hybrid cocoa seedlings adoption on profit efficiency in Ghana

• Tree density and old farms reduce hybrid cocoa technology adoption. • Farmers require experience to successfully adopt hybrid cocoa technology. • Male gender, tree density, access to extension and technology information support adoption. • Use of hybrid cocoa seedling, hand pollination, etc., increases profit efficiency. • Hybrid cocoa adopters are 0.101 more profit efficient than non-adopters. • Farmers are encouraged to adopt hybrid cocoa seedlings in their cocoa farms. The study examined the effect of hybrid cocoa seedling adoption on the profit efficiency of cocoa production in Ghana using cross-sectional data collected from 150 farming households in the Wassa Amenfi West district of Ghana. Cragg's Double Hurdle model, stochastic frontier profit function and propensity score matching were the methods of analysis. The results showed that whereas tree density and age of farm had negative influences on hybrid cocoa seedling adoption, farming experience exerted a positive effect. Also, the intensity of adoption of hybrid cocoa seedling was influenced by being a male farmer, tree density, access to extension as well as access to technological information. The mean estimated profit efficiency was 89.9% and this was positively influenced by male gender, hand pollination, age of cocoa tree, access to technological information and education even though farming experience exerted a negative effect. Finally, the study revealed that hybrid cocoa seedlings adopters are 0.101 more profit efficient than non-adopters. Farmers are therefore encouraged to adopt hybrid cocoa seedlings in their cocoa farms. It is also important for government to put measures in place to introduce agricultural programmes on radio and other media to enable farmers get access to technological information.

EARNING EFFECTS ON RETAILER ORDERING POLICY FOR IMPERFECT QUALITY ITEMS UNDER TRADE CREDIT FINANCING WITH PRICING STRATEGIES

Nowadays customer service, pricing strategies and trade credit financing scheme are effective, essential and survival parameters for any kind of business setup in the market. In this study we have developed retailer’s ordering policy for imperfect production in which we have applied the learning effect on inspection process on each and every batch of imperfect product. To stimulate sales of product and to study the effects of trade credit financing scheme on retailers business policy we have applied trade credit financing scheme on retailers ordering policy. In this paper, we have developed, an economical order quantity (EOQ) model for retailer’s price sensitive demand of product under two stage trade credit financing scheme. In the trade credit financing scheme we have assumed that the supplier offers to the retailer a fixed credit period of payment and the retailer also offers t a fixed credit period of payment o his customers. An optimal total profit function per unit time has been formulated under the different trade credit financing periods of payment with different costs and related parameters. A numerical example has been designed to verify the optimum results also we have done sensitive analysis through tables and graphically.