Price-dependent Demand Research Articles

Bi-objective optimization modeling of a three-level supply chain in production planning and scheduling considering price-dependent demand: a case study of a soap factory

Bi-objective optimization modeling of a three-level supply chain in production planning and scheduling considering price-dependent demand: a case study of a soap factory

Economic management of microgrid using flexible non-linear load models based on price-based demand response strategies

Demand response programmes are used in microgrid research without considering the different price elasticity of distinct load types. To evaluate the impacts of demand response efforts, it is necessary to utilise a mix of nonlinear and linear models for creating load-responsive models in a manner that is realistic. With an aim to address this gap in research, an exhaustive technoeconomic investigation is being conducted to determine the effect that price-dependent demand response programmes have on the optimal scheduling of microgrids when linear and nonlinear load models are present. The flexible elasticity model is used to accurately describe how customers respond to changes in electricity price. Four load models, including exponential, hyperbolic, linear, and logarithmic, were constructed for each demand response programme. Rime is a newly created physics-based algorithm that has been deployed to handle the anticipated energy management problem that the microgrid may be experiencing. To evaluate the efficacy of the proposed strategy, four case studies based on grid price and participation scenarios have been carried out. The findings from our research are notably impactful, revealing an 8 % reduction in energy consumption when applying the critical peak price (CPP) load demand model. This efficiency gain translates into a notable enhancement in the load factor, increasing from 0.83 to 0.86, and a significant drop in overall generation costs from $25,463 to $21,823 under optimal conditions. These results vividly illustrate the practical value of our proposed research work, showcasing their ability to generate substantial energy savings and cost efficiencies in microgrid operations. The improvements in operational efficiency and cost-effectiveness underscore the potential of these models to refine microgrid management, delivering both economic and performance gains that are crucial for advancing sustainable energy solutions.

Sustainable inventory, pricing, and marketing strategies for imperfect quality perishable items with inspection errors and advertisement-, expiration date- and price-dependent demand under carbon emissions policies

The demand for perishable products is affected by freshness levels, advertising efforts and selling prices, among other factors. By virtue of being consumed mostly by humans, quality control is also an important factor in perishable production systems. Moreover, inventory management related operations in such production systems release sizeable quantities of carbon emissions that are often regulated by carbon policies. To study the interactions of all these attributes in the context of a perishable inventory system, this paper proposes four sustainable inventory models for a perishable product with imperfect quality, inspection errors and whose demand depends on the advertising frequency, expiration date and selling price. The emissions released are assumed to be governed by carbon tax and carbon cap policies. Two of the models are developed under the assumption that the quality inspection process is 100% effective while the other two models consider the possibility of committing inspection errors, and additionally, for each pair of models, one is developed under a carbon tax policy and the other under a carbon cap policy. All the models are aimed at jointly optimising the perishable product’s lot-size, advertising frequency and selling price. The numerical results show that the presence of inspection errors leads to 28% and 23% lower profits under carbon tax and cap policies, respectively. Moreover, profit can be maximised by either stocking perishable products with longer shelf lives or targeting customers that engage with advertising mediums and those that are not price-conscious, while emissions can be minimised via the enforcement of carbon policies.

Sustainable production for imperfect production system with advertisement and Bertrand’s price-dependent demand

Sustainable production for imperfect production system with advertisement and Bertrand’s price-dependent demand

An Inventory Model for Deteriorating Items with Price Dependent Demand Under Fuzzy and Neutrosophic Fuzzy Environment

This paper represents an inventory model of deteriorating items under fuzzy and neutrosophic environment without allowing shortages in inventory. Demand is price dependent and is compared between crisp, fuzzy and neutrosophic fuzzy demand. Realistically it is observed that although the cycle time of any supply chain system is uncertain but uncertainty is mainly dependent on the selling price. So, here we have compared the model using crisp, fuzzy and neutrosophic fuzzy demand. The result is illustrated with the help of numerical example under fuzzy and neutrosophic fuzzy demand. KEYWORDS: Inventory, Fuzzy and Neutrosophic Fuzzy Price dependent Demand.

Different type of pay later facility for green product with selling price dependent demand using grey wolf optimizer

The use of trade credit finance is becoming more widely acknowledged as a crucial approach to improving inventory system profitability. We review an inventory model with depending on permitted payment delays for which, if the retailer place an orders higher than or equal to a predefined quantity S1, then the supplier will provide a fully pay in later facility of ξ periods (i.e., there will be no charge of interest until ξ). On the other hand the retailer need to pay a partial amount of payment to the supplier if the order quantity is less than S1, and the remaining amount may be deferred for up to ξ periods. Main objective of this study is to investigate the inventory model with different situations under delayed payment facility. In addition, determining the product's demand also involves taking into account the item's greenness and selling price. We have also considered the fact that the cost of buying is influenced by the product's degree of greenness. We employ the meta heuristic algorithm Grey Wolf Optimizar (GWO) to assist us in solving the problem, and we compare the outcomes with the aid of a few other algorithms (Whale optimisation algorithm (WOA) and Artificial electric field algorithm (AEFA)). In the end, we resolve several numerical cases to support the model. The concavity of the desired function is graphically displayed using MATLAB software.

How power structure and markup schemes impact supply chain channel efficiency under price-dependent stochastic demand

Although considerable attention has been separately given to factors such as power structures, price-dependent demand, and markup pricing schemes, there has been limited exploration of the combined effects of these factors on supply chain efficiency and the leader’s advantage. We propose a game theoretic model in which a manufacturer sells a single product to a newsvendor retailer who sets both optimal order quantity and selling price under uncertain price-dependent demand. Furthermore, we examine a supply network wherein a single retailer fulfills orders using a global manufacturer for regular orders and a local manufacturer to clear any shortages. Through numerical analysis, we show that the retailer always prefers to charge a percentage markup. In a two-player game, channel efficiency is higher when the retailer is the leader under linear demand; however, under iso-elastic demand, the manufacturer being a leader brings a higher channel efficiency. When a local manufacturer is involved as a second manufacturer, channel efficiency is higher when the retailer remains a follower, as this induces more fierce wholesale price competition between the two manufacturers. Additionally, when demand uncertainty is high in the two-player game with linear demand, the retailer as a follower can achieve higher profits, whilst high uncertainty under iso-elastic demand decreases both players’ profits. Moreover, it becomes advantageous for the retailer to have a local manufacturer as demand uncertainty increases, even when the local manufacturer announces the wholesale price first.

Manufacturer-Retailer Integrated System for Multi-Item Considering Two-Level Trade Credit, Volume Flexible, and Selling Price Dependent Demand

Manufacturer-Retailer Integrated System for Multi-Item Considering Two-Level Trade Credit, Volume Flexible, and Selling Price Dependent Demand

A case study of the impact of carbon emissions and inflation on nonlinear dense neutrosophic fuzzy inventory system of varying demand with delayed deterioration

In a comprehensive consensus, human should reduce the carbon emission on the way to reduce the adverse effect of global warming. Manufacturing firms contributes significant amount of carbon emissions in the environment. In many countries, regulatory authorities are taking actions to reduce emissions. Thus, in this paper we have analysed the effect of carbon emissionfor non-instantaneous deteriorating items having advertisement and price dependent demand. The paper also focused on the effect of inflation where shortages are partially backlogged and partially lost in sales. In this paper a new concept of non-linear triangular dense neutrosophic number with its basic properties are developed. Further the classifications of symmetry, asymmetry is introduced and thereafter De-neutrosophication technique has been applied for crispification. Since the effect of some parameters like carbon emissions, advertising, and inflation are uncertain so we have considered it in this new aforesaid form to grab the uncertain characters of the underlying parameters. The classification of the uncertain parameter based on the symmetric and asymmetric nature and linear-nonlinear nature of triangular dense neutrosophic number have been also investigated here. Additionally, the effect of the model is examined under different situations for both linear and non-linear triangular dense fuzzy, dense intuitionistic, dense neutrosophic. Finally, a numerical example is considered to illustrate the model and it is observed that the model is optimum when the parameters are considered in Asymmetric Convex Non-Linear number for shorter replenishment cycle. Also, comparative study has been done by performing sensitivity analysis through the case study and provides managerial insight into this outcome.

A profit-cost ratio maximization approach for a manufacturing inventory model having stock-dependent production rate and stock and price-dependent demand rate

This paper discusses an optimal managerial approach regarding stock control in a manufacturing-inventory scenario. The selling price and inventory level in showrooms may impact customers’ demand. The fall in selling price creates additional demand, while shown inventory also positively enhances demand. In this paper, demand is influenced by the selling price during the productive phase and the displayed stock in idle time. The significance of selling price and stock on profit goal may not be inherited from that of the demand function. The production rate varies negatively against the inventory on hand. Instead of taking cost minimization or the profit maximization objective, this paper executes an optimization approach on the profit-cost ratio function, sharpening the manufacturer’s goal. The numerical solution and sensitivity analysis on optimal outcomes succeed the analytical solution in Mathematica software. Numerical results indicate that the profit-cost ratio rises with selling price, suppressing the negative impact of the selling price on demand. Also, the profit-cost ratio shows a concave curve for the production cycle, ensuring a global maximum for the objective function.

AN INVENTORY MODEL FOR DETERIORATING ITEMS IN FUZZY ENVIRONMENT FOR JOINT PRICING AND INVENTORY CONTROL WITH PARTIAL BACKLOGGING AND TIME AND PRICE DEPENDENT DEMAND

This study proposes an advanced inventory model that addresses the challenges associated with deteriorating items in a fuzzy environment. The model integrates joint pricing and inventory control while considering partial backlogging and time- and price-dependent demand. The deteriorating items are characterized by their decreasing value over time, and the fuzzy environment accounts for the inherent uncertainty in the real business world. The model recognizes the interdependence of pricing and inventory decisions, acknowledging that pricing strategies can influence inventory levels and vice versa. The model incorporates a partial backlog to accommodate customers who are prepared to wait for out-of-stock items, thereby minimizing lost sales and enhancing customer satisfaction. The model's application has the potential to enhance operational efficiency, improve customer satisfaction, and maximize profitability for businesses operating in diverse industries. A trapezoidal fuzzy number is assigned to the cost parameter and defuzzyfy by applying the graded mean representation method. A numerical example has been considered to illustrate the model, and the significant features of the results are discussed. Finally, based on these examples, sensitivity analyses have been studied by taking one parameter at a time and keeping the other parameters the same.

Benefits of Preservation, Green and Quality Improvement Investment for Waste Management in Sustainable Supply Chain under Fuzzy Learning and Inflation

In the modern world, waste management, incorporating the quality of the products, energy consumption, and environmental concern have become significant challenges for supply chain managers. Also, smart devices are essential for daily life in the current socioeconomic environment, and customers primarily contemplate a smart product’s price and energy usage before purchasing that. In this situation, to maintain a balance between the selling price, energy consumption, and carbon emission from supply chain operations becomes necessary. So this study develops a twoechelon sustainable inventory model for deteriorating items with an imperfect production process under energy consumption and selling price dependent demand. The producer makes a rework process and quality improvement investment to mitigate defective products and enhance the quality of the products. The present model develops under the influence of inflation. Also, preservation and green technologies are used to mitigate the rate of deterioration and carbon emission, respectively. Firstly, the model is created in a crisp sense, and then expanded into a fuzzy learning model to examine the impact of the learning effect in an imprecise environment. A numerical analysis is performed to validate the proposed model, and the cost function’s convexity is shown graphically using mathematica software. The result of the proposed model provides significant insights to decision-makers on how to efficiently reduce waste while still minimizing the total cost of the system by investing in high efficiency preservation, quality improvement and green techniques. Also, due to learning in fuzziness, the fuzzy learning model gives the lowest total cost, followed by the fuzzy and crisp model. Finally, for various parameters, a sensitivity analysis is performed to gather valuable observations and management insights.

Consumer response to adjustable price and shelf-life of fresh food products under effective preservation policy

Food products deteriorate with time, that affects their freshness and demand. Several preservation policies have been suggested in literature for controlling the deterioration. This research work proposes a supply chain model comprising of a manufacturer and a retailer for deteriorating products with controllable rates of deterioration by improving product’s lifetime (freshness) through preservation in form of storage conditions and delayed ripening agents (preservatives). Customers’ purchasing power controls the purchase quantity; thereby allowing them to buy more products for lower prices and vice versa. This observation is incorporated in this study by considering selling price dependent demand for fresh food items. The proposed model considers a variable (lifetime dependent) component of selling price to integrate consumers’ behavior of buying fresher products for higher prices. The proposed supply chain is presented as a nonlinear mathematical model which is solved by using analytical optimization methods and numerical approaches. Considering the given assumptions, this study explores optimal decision-making for selling price, investment in preservation technology (PT), and cycle time for optimizing product’s freshness, deterioration rate, and demand to maximize the total supply chain profit. The results of the numerical experiments reveal the benefits of the proposed policies by exhibiting significant improvements in product’s freshness, deterioration rate, demand, and profitability. A nexus of the product’s freshness, selling price, and demand is investigated which suggests keeping the total selling price unchanged while improving the demand by increasing freshness through the proposed preservation policy. Some managerial insights are provided for decision-making within food chains.

Price Dependent Demand and Inflation Deteriorating Inventory Model with Shortages

Price Dependent Demand and Inflation Deteriorating Inventory Model with Shortages

Optimal Order Policy based on Three-Item Inventory Models with Weibull Distribution Deterioration and Price-Dependent Demand

Optimal Order Policy based on Three-Item Inventory Models with Weibull Distribution Deterioration and Price-Dependent Demand

An integrated inventory model for non-instantaneous deteriorating item under credit policy and partial backlogging with advertising and price dependent stochastic demand

In today’s business world, advertising is one of the most important policies to attract more customers. This policy increases the retailer’s sales and makes the retailer’s business position strong. In this paper, we have considered an integrated inventory model for non-instantaneous deteriorating items with a single supplier and single retailer, where a supplier sells his/her products in the market through a retailer who faces a stochastic demand depending on both retail price and advertisement. Here, to increase the retailer’s demand, the supplier wholesales his/her products to the retailer with a credit period. Since the long credit period increases the demand rate but at the same time, it increases the supplier’s opportunity loss. In this paper, we have discussed about the credit policy and find out, how this policy effective on profit of the supplier, the retailer as well as the whole system. After purchasing, the retailer sells his/her products to his customers with a markup. This markup is based on the supplier’s wholesale price and also on advertising costs. Finally, an integrated profit function has been developed and we have illustrated numerical examples to justify the feasibility of the proposed model. The result indicates that not only the credit period but also an appropriate number of advertisements is more important for maintaining the profit of the supplier, the retailer as well as the integrated profit of the system. We have analyzed the effect of markup on the profit function. We have also analyzed how the profit structure of the suppliers and retailers changes along with the changes in the length of the credit period. An effective algorithm has been presented in the solution procedure to find the optimal solutions of the proposed model. Also, the numerical example with uniform distribution has been carried out. Finally, sensitivity analysis of major parameters has been illustrated to provide managerial insights

Inventory models for deteriorative items with price dependent demand integrated with stock dependent demand

Inventory models for deteriorative items with price dependent demand integrated with stock dependent demand

Fuzzy Inventory Model under Selling Price Dependent Demand and Variable Deterioration with Fully Backlogged Shortages

Fuzzy Inventory Model under Selling Price Dependent Demand and Variable Deterioration with Fully Backlogged Shortages

Inventory model for deteriorating goods with stock and price-dependent demand under inflation and partial backlogging to address post Covid-19 supply chain challenges

Due to Covid-19 pandemic, the supply chain and the market have been affected severely. So, the need for a model based on certain scenarios arises to restore the post-Covid-19 disruptions. In this article, an inventory model for non-instantaneous deteriorating commodities has been developed under inflation where shortages are permitted and are assumed to be partially backlogged. The demand of the product is influenced by the price and stock. The primary aim of this study is to formulate a recovery model that will increase total average profit. In this research, the selling price and the total cycle time are taken as decision variables. The maximum average profit and the optimal values of the decision variables are determined using the graphical method in Mathematica and graphs have been provided to show the relation between total profit and the decision variables. It has been observed that when the selling price rises, the overall profit rises and then declines after it reaches a certain price level. Additionally, as the rate of inflation rises, the overall profit increases. Numerical examples are illustrated to demonstrate the model and sensitivity analysis has been performed to analyze the impacts of different parameters on the optimal solutions. It has been found that the total profit is highly sensitive to the basic demand and least sensitive to the backlogging parameter.

Interval valued inventory model for deterioration, carbon emissions and selling price dependent demand considering buy now and pay later facility

Uncertainty refers to a lack of precise knowledge or information about a particular event, situation, or outcome. It is an inherent characteristic of many real-world phenomena and is often associated with the presence of risk or ambiguity. Uncertainty can arise due to various factors, such as incomplete information, unpredictability, complexity, or variability of a system or process. In many cases, uncertainty can lead to difficulties in decision-making and pose challenges in planning, forecasting, and managing risks. There are different types of uncertainty, including epistemic uncertainty, which arises from the inherent randomness or variability of a system or process. This study encompasses the inclusion of all inventory parameters as uncertainty parameters, which are expressed in the form of intervals. Furthermore, demand for the product is taken into account in interval form. The conversion of the differential equation into an interval differential equation is carried out in order to account for the variability in demand within a certain interval. The utilisation of the centre-radius technique leads to the derivation of the related optimisation problem under a ‘buy now, pay later’ (BNPL) payment scheme. In order to demonstrate the concept, a numerical case is selected and solved with the MATHEMATICA software and interval order relations. In the end, a comprehensive sensitivity analysis has been conducted to derive insightful conclusions pertaining to this study.