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This paper aims to design an inventory model for a retail enterprise with a profit maximization objective using the opportunity for a price discount facility given by a supplier. In the profit maximization objective, the demand should be increased. The demand can be boosted by lowering the selling price. However, lowering the selling price may not always give the best profit. Impreciseness plays a vital role during such decision-making. The decision-making and managerial activities may be imprecise due to some decision variables. For instance, the selling price may not be deterministic. A vague selling price will make the retail decision imprecise. To achieve this goal, the retailer must minimize impreciseness as much as possible. Learning through repetition may be a practical approach in this regard. This paper investigates the impact of fuzzy impreciseness and triangular dense fuzzy setting, which dilutes the impreciseness involved with managerial decisions. Based on the mentioned objectives, this article considers an inventory model with price-dependent demand and time and a purchasing cost-dependent holding cost in an uncertain phenomenon. This paper incorporates the all-units discount policy into the unit purchase cost according to the order quantity. In this paper, the sense of learning is accounted for using a dense fuzzy set by considering the unit selling price as a triangular dense fuzzy number to lessen the impreciseness in the model. Four fuzzy optimization methods are used to obtain the usual extreme profit when searching for the optimal purchasing cost and sale price. It is perceived from the numerical outcomes that a dense fuzzy environment contributes the best results compared to a crisp and general fuzzy environment. Managerial insights from this paper are that learning from repeated dealing activities contributes to enhancing profitability by diluting impreciseness about the selling price and demand rate and taking the best opportunity from the discount facility while purchasing. [ABSTRACT FROM AUTHOR]

This paper investigated a multistage sustainable production–inventory model for deteriorating items (i.e., raw materials and finished goods) with price-dependent demand and collaborative carbon reduction technology investment under carbon tax regulation. The model was developed by first defining the total profit of the supply chain members under carbon tax regulation and, second, considering a manufacturer (leader)–retailer (follower) Stackelberg game. The optimal equilibrium solutions that maximize the manufacturer's and retailer's total profits were determined through the method analysis. An algorithm complemented the model to determine the optimal equilibrium solutions, which were then treated with sensitivity analyses for the major parameters. Based on the numerical analysis, (a) carbon tax policies help reduce carbon emissions for both the manufacturer and retailer; (b) most carbon emissions from supply chain operations negatively impact the total profits of both members; (c) the retailer may increase the optimal equilibrium selling price to respond to an increase in carbon emissions from supply chain operations or carbon tax; and (d) autonomous consumption positively affects both members' optimal equilibrium policies and total profits, whereas induced consumption does the opposite. These findings are very managerial and instructive for companies seeking profits and fulfilling environmental responsibility and governments. [ABSTRACT FROM AUTHOR]

This article develops a sustainable electricity supply chain mathematical model that assumes linear price-dependent customer demands where the price is a decision variable under setup cost and carbon emission. The sustainable electrical supply chain system contained: (a) power generation; (b) transmission substations; (c) distribution substations; and (d) customer. The production rates depend on the demand rate, and demand for electricity by the customers is dependent on the price of electricity where the electrical energy was generated and transmitted through multiple substations to customers. Moreover, we considered that the capacities of transmission rates, power generation, and distances in between two stations are associated with the distribution costs and transmission cost. Here, we used the theory of inventory to develop a new model and suggested a procedure to deduce an optimal solution for this model. Finally, a numerical example and sensitivity analysis are employed to illustrate the present study and with managerial insights. [ABSTRACT FROM AUTHOR]

In order to identify the optimal structure of an electricity power network under the main assumption of a price dependent demand of electrical energy, we presented an optimization model that aims at analyzing the effect of price-dependent demand on the sustainable electrical supply chain system (SESCS). The system included a power generation system, transmission and distribution substations, and many customers. The electrical energy was generated and transmitted through multiple substations to our customers, and the demand for electricity by the customers is dependent on the price of electricity. In the study, we considered the transmission and the distribution costs which depend on the capacities of power generation, transmission rates and distances between stations. We utilized the inventory theory to develop our model and proposed a procedure to derive an optimal solution for this problem. Finally, numerical examples and sensitivity analysis are provided to illustrate our study and consolidate managerial insights. [ABSTRACT FROM AUTHOR]