Production Inventory Model Research Articles

FUZZY PRODUCTION MODEL WITH FUZZY VALUED DEMAND WITH NONLINEAR SELLING PRICE, WARRANTY, AND LEVEL OF GREENNESS OF THE PRODUCT UNDER FUZZY DETERMINATION RATE

Many studies on manufacturing and inventory management for increasingly problematic commodities have focused on how quality, greenness, product warranties, and environmental concerns might be incorporated into industrial operations. However, comparatively few articles have integrated these two themes. To close this knowledge gap and advance practice, these two decaying object criteria must be included in the study. The following assumptions are used to create a warranty-based, sustainable production inventory model for green products. In this article, we look at how greenness, product assurances, and reducing carbon emissions technologies impact overall profit to assist those making decisions to make better choices regarding pricing and replenishment. Due to the consideration of fuzzy valued inventory parameters along with the objective function's nonlinearity and the presence of five decision variables, we have addressed this problem with the help of the Lingo 18 software along with the defuzzification technique. The mathematical formula is quantitatively demonstrated in one experiment, and a sensitivity analysis is performed to determine the effects of various factors on overall profit and management insights.

The production-inventory model with imperfect, rework, and scrap items under stochastic demand

The production-inventory model with imperfect, rework, and scrap items under stochastic demand

An EPQ Model with Varying Demand for Uncertain Quality Products

Objectives: This article delves into a production inventory model centered on non-deteriorating items amidst fluctuating demand. Methods: To minimize the total cost using the sine function as a demand function. Findings: In the manufacturing process, there's a chance of product damage, resulting in the final products being either flawless or flawed. Quality assessments occur during production to distinguish the flawless ones for immediate sale, while the flawed ones are marked down for later sale. “In this article, we use a sine function for demand which will increase first, and after a certain point it starts decreasing”. Novelty: The existing method has discussed only increasing or decreasing demand, but the current study deals with both increasing as well as decreasing at the same time. Applications: Seasonal methods like umbrellas, Christmas decorative items, crackers, etc., have increasing demand for the particular season. Keywords: Production Model, Fluctuating Demand, Sine function, minimizing Total Cost, Flawless items

A production-inventory model to optimize the operation of distributed energy resource networks in a rolling horizon

The recent advancements in energy production, storage, and distribution are creating unprecedented opportunities in the field. Major consumers can benefit from the implementation of distributed energy resource networks capable of generating electricity or heating from sources, often renewable ones, in close proximity to the point of use, rather than relying on centralized generation sources from power plants. In this paper, we introduce a pioneering model designed to determine the optimal set of energy commands in a distributed energy resource network, minimizing operational costs in a time horizon. Indeed, we propose an innovative mixed-integer linear programming formulation rooted in the production-inventory models commonly employed in aggregate production planning. The system integrates diverse energy generation sources, storage facilities, and demand points, encompassing both electric and heating commodities. The optimum of the model is achieved for all analyzed instances of the test library (2 scenarios-20 instances) in an exceptionally short time, outperforming other approaches previously presented in the literature. We employed the Gurobi optimizer to solve the model, obtaining rapid responses that ensure real-time decision-making and facilitate effective control of the distributed energy resource network within a three-days' rolling horizon, as discussed in a simulated real-life application case study. Indeed, the proposed model solves in less than 1s, enabling near-instantaneous decision-making. This swift solution time surpasses any known references in the field, effectively shifting the bottleneck in DER network operation from the decision-making process to the forecasting of demand and weather conditions. While forecasting typically requires a minimum of 15min, our approach suggests that a reduction in this forecasting time could further enhance the control system's response time, given the model's ability to deliver optimal solutions almost immediately. The real-time availability of optimal solutions allows for the seamless incorporation of stochastic elements into the control loop via a rolling horizon process.

A Study on the Production-Inventory Problem with Omni-Channel and Advance Sales Based on the Brand Owner’s Perspective

This study explores a supply chain product-inventory problem with advance sales under the omni-channel strategies (physical and online sales channels) based on the brand owner’s business model and develops corresponding models that have not been proposed in previous studies. In addition, because the brand owner is a member of the supply chain, and has different handling methods for defective products or products returned by customers in various retail channels, defective products or returned products are included in the supply chain models to comply with actual operating conditions and fill the research gap in the handling of defective/returned products. Regarding the mathematical model’s development, we first clarify the definition of model parameters and relevant data collection, and then establish the production-inventory models with omni-channel strategies and advance sales. The primary objective is to determine the optimal production, delivery, and replenishment decisions of the manufacturer, physical agent, and online e-commerce company in order to maximize the joint total profits of the entire supply chain system. Further, this study takes the supply chain system of mobile game steering wheel products as an example, uses data consistent with the actual situation to demonstrate the optimal solutions of the models, and conducts sensitivity analysis for the proposed model. The findings reveal that increased demand shortens the replenishment cycle and raises order quantity and shipment frequency in the physical channel, similar to the online channel during normal sales. However, during the online pre-order period, higher demand reduces order quantity and cycle length but still increases shipment frequency. Rising ordering or fixed shipping costs lead to higher order quantity and cycle length in both channels, but variable shipping costs in the online channel reduce them. Market price increases boost order quantity and frequency in the online channel, while customer return rates significantly impact inventory decisions.

Reliability dependent production-inventory model for redundancy allocation via fuzzy logic

This study deals with a reliability dependent production-inventory model in two scenarios: a redundancy allocation with crisp structure and the other with fuzzy logic. Here, a manufacturer purchases some raw-materials/components in variable cycles and arranges them as series-parallel system to produce a single item with production cost dependent on system reliability. In this model, a retailer gets the opportunity of warranty period and credit period offered by the manufacturer. Also, the retailer’s demand is dependent on system reliability, credit period and selling price. In the crisp model, the component reliability is exponentially dependent on known failure rate and failure time. However, there is no dependent relationship between these two parameters. Actually, the real world is full of uncertainty and these two parameters may depend on each other following some uncertain nature which can be expressed as fuzzy logic. So, in the fuzzy model, failure time has been considered as dependent on failure rate following fuzzy logic and these fuzzy relations are defuzzified by using three fuzzy inference techniques: Mamdani, Sugeno and Tsukamoto. Main goal of this article is to determine the optimum number of cycles and components to maximize manufacturer’s profit and system reliability with some constraints. The model is solved by using elitist non-dominated sorting genetic algorithm (NSGA-II) and some numerical examples closed to real-world have been executed. Comparative analyses are done for different cases; different fuzzy inference techniques and for active and mixed strategies. Finally, some sensitivity analyses and managerial insights are drawn.

Product refurbishment in an imperfect production inventory system under carbon regulations: An interval type-2 fuzzy environment

This study develops an imperfect production inventory model focusing on the proper handling of imperfect products and addressing carbon emissions in different stages of a production process. The proposed inventory system consists of three stages: production, screening, and refurbishing. The produced products undergo a screening process, with perfect quality items being delivered to the primary market, while imperfect quality products are routed through a refurbishing process, subsequently sold in the secondary market. It is observed that in the existing literature on refurbished products, all such types of products have been sold at the end of the business period, this means that there is no continuous demand of refurbished product at the remaining time points of the business period which does not support the practical situation in a real business system. In this regards, our main objective in this study is consideration of continuous demand of refurbished products along with perfect ones. Again, we incorporate interval type-2 fuzzy uncertainty in both markets’ demand to better reflect market fluctuations introducing a new defuzzification method. In this framework, we evaluate the effectiveness of two emission regulatory strategies: carbon tax and carbon cap and trade policies. The findings of this study offer valuable insights into various aspects. Notably, our analysis reveals that if the difference between the primary and secondary markets’ demands reduces to a large extent, a negative impact on the profit is observed. It is also shown that an increase in demand for refurbished products allows for a higher permissible rate of imperfections in production. Comparing the outcomes under two emission regulations, we find that the cap and trade policy is beneficial from both economic and environmental perspectives. Additionally, it becomes evident that the manufacturer should carefully consider the duration of each inventory stage, as it leads to a significant increase in overall emissions. Regarding the uncertain nature of the market, it is observed that demand volatility in the secondary market negatively affects the profit.

A Production Inventory Model for Fractionally Time-Dependent Demand Rate with Weibull Deterioration and Partially Backlogged Items

A Production Inventory Model for Fractionally Time-Dependent Demand Rate with Weibull Deterioration and Partially Backlogged Items

Optimal production plan in a production inventory model under the coexistence of both green and regular products: A study on Indian textile industry

The necessity to restrict environmental pollution worldwide has led to the development and implementation of green products. Various sectors within the industrial domain are now placing emphasis on the creation of environmentally friendly products in order to minimize their impact on the environment. The textile industry, both in India and globally, significantly contributes to environmental pollution through the release of untreated effluents into water and the emission of carbon into the atmosphere. Consequently, the popularity of green apparel is steadily increasing as a means to alleviate this crisis. It has been reported that, despite customer preference for green apparel, factors such as the cost of these products and a lack of consumer awareness regarding their importance deter a significant portion of potential buyers from making purchases. In order to stimulate demand for green apparel, the government could implement a subsidy scheme and initiate advertising campaigns highlighting the benefits of using such products. In the market, green apparel and regular apparel are viewed as substitutes for one another and coexist. As a result, there is a constant price competition between these two types of products. This research examines the optimal inventory decisions of manufacturers in a production inventory model where both green and regular products are present and product substitution is allowed. The demand for both types of products is influenced by their respective selling prices. Furthermore, the level of greenness and the efforts put into advertising green products have positive effects on generating demand for these products. The resulting objective function in this model is non-concave, and the quantum behaved particle swarm optimization technique is utilized to solve the corresponding optimization problem. Additionally, Mathematica software has also been employed to verify the efficiency of the proposed solution algorithm. To provide economic validation of the proposed model, a numerical example is presented. Finally, a sensitivity analysis of the key parameters is conducted to gain insights into their impact on the optimal solution. The results indicate that strategic and well-executed advertising campaigns, along with government subsidy schemes, can boost the market for green products and generate greater profits for manufacturers.

A dual-rate production inventory model for deteriorating items: Addressing shortages with variable production cycles

A dual-rate production inventory model for deteriorating items: Addressing shortages with variable production cycles

A Production inventory model for deteriorating items with quadratic time dependent demand with two levels of Production

A Production inventory model for deteriorating items with quadratic time dependent demand with two levels of Production

A two-stage sustainable production-inventory model with carbon credit demand

A two-stage sustainable production-inventory model with carbon credit demand

Emission reduction investment for green products of a manufacturing system via optimal control theory and artificial hummingbird algorithm

Now, due to the global industrialization, carbon emission from the industrial section imposes a severe impact on the current environment. Due to the increasing awareness of environmental and sustainability issues, green products, also known as eco-friendly, include a considerable impact on the today’s market economy. Keeping mind of these two important issues of the current scenario, a production inventory model is developed in which time-dependent production rate is considered. In this work, the level of greenness of the products, selling price and time, influences the customers’ demand rate. Again, two different cases are considered due to the business assimilation of defectively manufactured items: rework and salvage policies. Additionally, the company uses pollution reduction technologies to lower emissions from the manufacturing firms in order to lower emission taxes. The Euler-Lagrange equation is used to solve an optimal control problem that arises in the model as time-dependent production rate is taken into the account. The optimisation problem corresponding to the proposed model is solved with the help of artificial hummingbird algorithm (AHA) as the system's average profit functions for both of the considered scenarios are highly nonlinear in nature w. r. to its decision variables. Further, the results obtained from AHA are compared with the help of other well-known metaheuristics. Finally, sensitivity analysis is conducted to arrive at meaningful conclusions and implications for the competent manager of the manufacturing firm.

A two-phase production inventory model for imperfect quality items with multivariate demand, upstream and downstream credit period offers under a carbon tax, and green subsidy

Generating customer-friendly products is a big task nowadays. Green products are famous all over the world now. In quite few manufacturing processes, carbon emissions become an unavoidable fact. To reduce emissions, the government enacted enormous rules and regulations. This developed model consists of a supply chain with two phase production containing defective products and rework through the same manufacturing system, where the product deterioration is considered after production and rework (i.e. where the deterioration starts when the product is out for sale), as three cases: (1) no deterioration, (2) instantaneous deterioration and (3) non-instantaneous deterioration. Demand function is selling price, green product price, advertisement and credit period dependent for first two cases and for case 3, the market scale of the demand is exponentially increasing considering uncertainty. Supplier offers a full credit period offer to the retailer and the retailer gives a partial credit period offer to his customer. Various methods are implemented to reduce carbon emissions during various production processes, and we have implemented preservation technology to reduce emissions even with a carbon tax policy involved. With government subsidies, the greenness of the product is considered to make it more environmental friendly. Numerical examples and sensitivity analysis are carried out to verify the results of the developed model.

Using Game Theory to Explore the Multinational Supply Chain Production Inventory Models of Various Carbon Emission Policy Combinations

This study uses Stackelberg game theory, considering different combinations of carbon emission reduction policies and that high-carbon-emission enterprises may face various carbon emission reduction regulations, to explore the production inventory problems in a multinational supply chain system. The purpose is to determine the manufacturer’s optimal production, shipping, carbon reduction investment, and the retailer’s replenishment under the equilibrium for different carbon emission policy combinations. To develop the production inventory models, this study first develops the total profit and carbon emission functions of the supply chain members, respectively, and then obtains the optimal solutions and total profits of the manufacturer and the retailer under different carbon emission policy combinations through the mathematical analysis method. Further, this study used several numerical examples to solve and compare the proposed models. The results of numerical analysis show that regardless of the increase in carbon price or carbon tax, the manufacturer and retailer will adjust their decisions to reduce carbon emissions. Specifically, an increase in the carbon price contributes to an increase in the total profit of manufacturers, while an increase in the carbon tax reduces the total profit of manufacturers. This study also explores a sensitivity analysis on the main parameters and has yielded meaningful management insights. For instance, in cases where low-carbonization strategies are required, the manufacturer or retailer can effectively reduce the carbon emissions resulting from production or purchasing activities, thereby significantly reducing overall carbon emissions. It is believed that the results of this study can provide enterprises/supply chains with reference to their respective production, transportation, carbon reduction investment, and inventory decisions under carbon emission policies, as well as information on partner selection and how to adjust decisions under environmental changes.

Production inventory control model for deteriorating complementary and substitute items with shortage

Production inventory control model for deteriorating complementary and substitute items with shortage

Three-echelon circular economic production–inventory model for deteriorating items with imperfect quality and carbon emissions considerations under various emissions policies

Traditional production systems have a sole focus of maximising economic outcomes but due to the world’s ever-growing awareness about environmental issues, circular production systems, with a dual focus of maximising economic output and minimising environmental impact, have become prevalent in recent years. These types of production systems incorporate circular economy initiatives in their operational processes with the aim of reducing their carbon footprints. However, this is a voluntary measure to reduce carbon footprints and for this reason, various governments have introduced regulatory measures to involuntarily reduce carbon footprints of production systems. These regulatory measures include carbon tax, cap, cap-and-trade and cap-and-offset policies that are designed to reduce carbon emissions from production processes. With this in mind, this paper proposes an integrated sustainable production–inventory model for a three-echelon supply chain for imperfect quality deteriorating items with a circular economy indicator under various carbon emissions regulations. Using four different combinations of functions for both the demand rate and unit gross profit and four different carbon emissions regulations, 16 variants of the model are solved and analysed using heuristic algorithms. The model variants are not only aimed at optimising inventory replenishment decisions but also the circularity economy indicator of the deteriorating inventory. Of the 16 variants, the highest profit is achieved for the logistic demand and linear profit functions combination under cap-and-offset, despite a circularity indicator of 81.75%. The results also show that carbon emissions policies are effective at reducing the supply chain’s carbon footprint, albeit with a slight impact on the profit.

An Imperfect Production Inventory Model for Instantaneous Deteriorating Items with Preservation Investment Under Inflation on Time Value of Money

Effective inventory management is crucial for businesses dealing with deteriorating items, where demand is influenced not only by traditional factors but also dependent on the selling price. This research paper proposes a comprehensive inventory model that considers the dynamic nature of demand for deteriorating items and incorporates the impact of inflation on the time value of money, all within the context of an imperfect production and screening process. To reduce the waste of products, the proposed model uses a rework process to convert imperfect items into perfect ones. Additionally, this study incorporates preservation technology investment to alleviate the rate of deterioration under partially backlogged shortages. The incorporation of an imperfect production process further enhances the model’s practical applicability by addressing real-world scenarios where production may not always be flawless. The study employs mathematical modeling and optimization techniques to derive optimal ordering policies that balance the conflicting objectives of minimizing costs. To validate the model, numerical analysis has been performed, and the convexity of the total cost function has been shown graphically and analytically using MATHEMATICA software. Sensitivity analyses are conducted to assess the robustness of the proposed model under varying parameters, providing valuable insights for decision-makers.

Integrated production-inventory model for multi-item raw materials with exponential quality degradation: a real case study

Integrated production-inventory model for multi-item raw materials with exponential quality degradation: a real case study

A Production Inventory Model with Linear Time Dependent Production Rate, Linear Level Dependent Demand and Demand and Constant Holding Cost

In this paper, a production inventory model with linear time dependent production rate is considered. The market demand is assumed to be linear level dependent while the holding cost is a constant. The model considered a small amount of decay without having any shortage. Production starts with a buffer stock reaching its maximum desired level and then the inventory begins to deplete due to demand and deterioration. The model is formulated using a system of differential equations and typical integral calculus was used to analyze the inventory problems. These differential equations were solved to give the best cycle length T_1^*=0.8273(303 days), Optimal time for maximum inventory t_1^*= 0.7015, Optimal order quantity Q_1^*=38.3404 and total average inventory cost per unit time TC(T_1)* =170.5004. The cost function has been shown to be convex and a numerical example to show the application of the model has been given. A sensitivity analysis is then carried out to see the effects of parameter changes