Inventory Model Research Articles

Dynamic pricing and inventory model for perishable products with reference price and reference quality

Reference price (quality) is a benchmark point used by consumers to make price (quality) judgements. Combining reference price and reference quality with dynamic pricing and inventory management, this paper applies differential equations theory to construct a optimal control model for perishable products when the quality of products declines exponentially. The demand of products depends on price, quality, reference price and reference quality, among which reference price and reference quality are influenced by consumers’ past memory. The aim is to maximize the retailer’s profit during the period. The conclusions are as follows. Firstly, a optimal dynamic pricing and inventory model for perishable products with reference price and reference quality is constructed, and the model is extended to dual decision variables, stochastic demand, time-dependent effects, competitive and infinite planing horizon setups. Secondly, through the Pontryagin maximum principle, the analytical expression of the optimal dynamic price is derived. Thirdly, a linear search method to solve the optimal static price is proposed. Finally, the sensitivity of the main parameters is analyzed and the corresponding management enlightenments are given. By comparison of dynamic and static pricing, we find that dynamic pricing can achieve more profits and take a shorter selling period. In addition, for the sales problem of perishable products affected by both reference price and reference quality, retailers should adopt skimming pricing strategy (the optimal price decreases with time). Furthermore, to obtain more profit, retails should strive to increase the sensitivity coefficients of two types of reference, and the reference quality memory coefficient, while to decrease the reference price memory coefficient.

Effects of model-overfit on model-assisted forest inventory in boreal forests with remote sensing data

Abstract While remote sensing can be an effective tool in building a forest inventory, field measurements and model fitting can be both expensive and challenging. One strategy to reduce forest inventory costs is to leverage forest inventory models fitted to a different population (external models), although the effectiveness of external models is poorly understood. One concern is that models may predict well to the sample data, but poorly to the population—which is termed ‘overfitting’. The effect of overfit may be especially problematic in attempts to predict for a different population (a forest area not covered by any sample plots). Assessing overfit is difficult and its consequence for estimation are not well understood, especially in the context of prediction using external models. This study assesses how overfitting affects model-assisted forest inventory estimation when using internal and external models. We used field and remotely sensed data (Sentinel-2 images and airborne laser scanning data) from two forest areas in Finland. We evaluated four modeling approaches: ordinary least square regression (OLS), random forest, k-nearest neighbors, and gaussian process regression. Both analytical and bootstrap variance estimators were used to evaluate model-assisted estimation performance. Internal models, especially OLS, were the most affected by model overfitting, leading to bias in the population means and underestimation of variance. Estimates using external models provided unbiased means and realistic intervals except in the case of deliberate excessive overfitting. The bootstrap variance estimator was found to be more robust to overfit than the analytical variance estimator for the internal model, but was not helpful for the external model. Internal models should be parsimonious to generalize well to the population and avoid bias. The bootstrap estimator of variance is recommended for internal models, especially if there is concern about model overfitting.

Study on Optimizing Inventory to Minimize Waste in the Fresh Produce Supply Chain

Abstract: The increasing demand for fresh produce, particularly greens, presents unique challenges in inventory management due to their short shelf life and susceptibility to spoilage. Inefficient management often results in significant waste, leading to financial losses for retailers and increased environmental burdens from the disposal of spoiled goods. Despite various strategies being employed in the agri-food sector, gaps remain in understanding how to optimize inventory levels to minimize waste at the retails level while maintaining high service levels for customers. This research aims to develop an inventory management model tailored to fresh produce that can mitigate these issues by balancing stock availability and minimizing wastage, particularly in large retail shops. To address the research problem, a mixed-integer linear programming (MILP) model was developed, focusing on three service levels—90%, 92%, and 95%—to evaluate the trade-offs between customer satisfaction and total inventory costs. The model incorporates key constraints, including stock balance, shelf-life limitations, and demand satisfaction. The model was validated using actual data, including stock, sales, and wastage records for the month of August, 2024. The objective function aimed to minimize total costs, encompassing holding costs, wastage, and lost revenue. The findings indicate that higher service levels, while reducing stockouts, significantly increase costs due to excess inventory and waste. The most cost-effective solution was observed at the 90% service level, which balanced waste reduction and customer satisfaction. The study also emphasizes the importance of integrating total cost reduction and minimize wastage. Future work should focus on incorporating consumer behavior patterns and extending the model to multi-echelon inventory systems, which include both distribution centers and retail outlets, to capture a more holistic view of the supply chain.

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

Research on the Comprehensive Cost of Secondary Demand Inventory Model

In this inventory model, we developed an inventory system having the time varying demand. The deterioration of items is not considered in this inventory model. The rate of inventory is a combined effect of time and demand. Shortages are also not considered in this model. Holding cost, ordering cost are major effective costs in this model. My aim in this model to study of the total cost to minimize with reference of parameters used in this model, that is major objective of any industry for establishment of business. For validation of the model, the numerical example is also illustrated in the end of study.

A Hybrid Fuzzy Mathematical Programming Approach for Manufacturing Inventory Models with Partial Trade Credit Policy and Reliability

This study introduces an inventory model for manufacturing that prioritizes product quality and cost efficiency. Utilizing fuzzy logic and mathematical programming, the model integrates fuzzy numbers to describe uncertainties associated with manufacturing costs and quality control parameters. The model extends beyond conventional inventory systems by incorporating a dynamic mechanism to halt production, employing fuzzy decision variables to optimize the economic order quantity and minimize total costs. Key innovations include the application of approaches related to graded mean integration for defuzzification and the use of Kuhn–Tucker conditions to ensure optimal solutions under complex constraints. These approaches facilitate the precise management of production rates, inventory levels, and cost factors, which are essential in achieving a balance between supply and demand. A computational analysis validates the model’s effectiveness, demonstrating cost reductions while maintaining optimal inventory levels. This underscores the potential of integrating fuzzy arithmetic with traditional optimization techniques to enhance decision making in inventory management. The model’s adaptability and accuracy indicate its broad applicability across various sectors facing similar challenges, offering a valuable tool for operational managers and decision makers to improve efficiency and reduce waste in production cycles.

Decarbonization and waste reduction in a disrupted food supply chain: a step towards achieving food sustainability

PurposeThis study aims to reduce carbon emissions and minimize waste in the event of disruptions in a short and fast-food perishable such as fruits, vegetables, packaged food items, etc. supply chain through optimal investment in green and preservation technologies.Design/methodology/approach This study utilized a Hessian matrix approach to optimize decision variables with an objective to maximize the profit function.FindingsThe study demonstrates that investing in both green and preservation technology within a short and fast-food supply chain is highly beneficial for decarbonization and waste reduction and it leads to profit maximization. It has been shown with the help of a numerical experiments with investment in both green and preservation technology that total profit is 3.09% higher than without investment made in either technology.Practical implicationsThis study aids the industry in achieving food sustainability by minimizing waste of perishables and also minimizes carbon emissions which is essential for environmental protection. It assists industries in determining the optimal investment in preservation technology to minimize waste and in green technology to reduce emissions, thereby maximizing profits.Originality/valueThe current study formulates an inventory model that helps in decarbonization and waste reduction in food supply chain with the consideration of machine learning, demand disruption, preservation technology investment, screening of purchased items, waste disposal, a double triangular distribution deterioration rate, green technology investment, carbon emissions from various supply chain activities, carbon tax policy and fuel price variation over time for perishable food products in a two-warehouse system.

The Synergy Between CO2 and Air Pollution Emissions in Chinese Cities by 2060: An Assessment Based on the Emissions Inventory and Dynamic Projection Model

Synergizing air pollution control and climate change mitigation has been of significant academic and policy concern. The synergy between air pollution and carbon emissions is one of the measures to understand the characteristics and process of the air pollution–carbon synergistic control, which will also provide valuable information for collaboratively achieving Sustainable Development Goals (SDGs) (such as SDGs 11 and 13). This study establishes a systematic framework integrating emissions inventory and projection models, correlation mining and typology analysis methods to predictively evaluate the synergy and comprehensive coordination between air pollution and carbon dioxide (CO2) emissions in Chinese cities by 2030, 2050, and 2060 under different policy scenarios for air pollution and CO2 emissions control. The results reveal the significant effects of synergistically implementing clean air and aggressive carbon-reducing policies on mitigating air pollution and CO2 emissions. Under the On-time Peak-Net Zero-Clean Air and Early Peak-Net Zero-Clean Air scenarios, the total reduction and synergy for air pollution and CO2 emissions will be more significant, particularly by 2050 and 2060. This study is the first to integrate scenario projection and synergy evaluation in air pollution and CO2 research, providing a novel supplement to the air pollution–climate change synergy methodology based on co-benefit estimation. The methods and findings will also contribute to measuring the achievement and analyzing the interaction of the SDGs.

Sustainable Inventory Management: A Bibliometric study

This paper presents a bibliometric analysis on Sustainable inventory models. The methodology applied is review on previous research and the performance evaluation based on identified attributes, using MS Excel. The data set was obtained from Library Genesis (Libgen) using the search criteria Sustainable Inventory. A total of 78 papers became available based on the search criteria and were included for our analysis. Based on the analysis of the attributes, it has been observed that the most notable authors were Mr Umakanta Mishra, Mr Jei-Zheng Wu, and Biswajit Sarkar. The notable countries were USA, India and Taiwan. The most noted Universities were Vellore Institute of Technology, University of Tehran, Soochow University, Polytechnic University of Bari, Lund University, Hajee Mohammad Danesh Science and Technology University and Fu Jen Catholic University. Among the Journals, Journal of Cleaner Production, Sustainability and IEEE are the notable ones. Among the Publishers, Elsevier, Springer and MDPI are the best contributors. There has been an increase in number of the publications during the years 2016-2020. Many significant topics pertaining to Sustainable Supply Chain, Inventory Models, Life Cycle Analysis, Environmental issues, Carbon Cap and Trade, etc have been thoroughly analysed in these papers. Solutions and the way forward have been suggested. Data on some of the practical case studies have also been provided. Such type of Bibliometric Analysis helps us to review the present state of research on the chosen topic and identify the key areas in which further research can be made.

Mitigating Grand Challenges in Life Cycle Inventory Modeling through the Applications of Large Language Models.

The accuracy of life cycle assessment (LCA) studies is often questioned due to the two grand challenges of life cycle inventory (LCI) modeling: (1) missing foreground flow data and (2) inconsistency in background data matching. Traditional mechanistic methods (e.g., process simulation) and existing machine learning (ML) methods (e.g., similarity-based selection methods) are inadequate due to their limitations in scalability and generalizability. The large language models (LLMs) are well-positioned to address these challenges, given the massive and diverse knowledge learned through the pretraining step. Incorporating LLMs into LCI modeling can lead to the automation of inventory data curation from diverse data sources and to the implementation of a multimodal analytical capacity. In this article, we delineated the mechanisms and advantages of LLMs to addressing these two grand challenges. We also discussed the future research to enhance the use of LLMs for LCI modeling, which includes the key areas such as improving retrieval augmented generation (RAG), integration with knowledge graphs, developing prompt engineering strategies, and fine-tuning pretrained LLMs for LCI-specific tasks. The findings from our study serve as a foundation for future research on scalable and automated LCI modeling methods that can provide more appropriate data for LCA calculations.

Quantitative Assessment of Green Inventory Management in Supply Chains: Simulation-Based Study of Economic and Environmental Outcomes Aligned with ISO 14083 Standard

This research employs numerical simulations and scenario analysis to assess a supply chain model’s economic and environmental performance operating under stochastic market demand, with inventory levels managed by a periodic review (R, s, S) inventory system. The inventory model in this research is designed to determine the minimal inventory levels required to achieve predefined fill rates across various operational constraints. The supply chain’s inventory model simulates optimal responses to normally distributed market demand within 365-day periods characterized by mean and two levels of demand variability through two fill rate levels, two workweek schedules, 15 review periods, and 16 lead times. By conducting an extensive analysis of the 192000 simulation experiments of the supply chain under periodic review (R, s, S) inventory system, complex influences between system variables and economic outcomes of supply chain operation measured by ordering, transportation, holding, penalty, and total costs along with greenhouse gas emissions arising from inventory-related transportation according to the ISO 14083 standard are analyzed. The insights from this research have significant practical implications, providing valuable guidance for supply chain managers, researchers, and freight companies offering guidance for improving economic and environmental performance.

Optimized Economic Production Quantity Inventory Model with Weibull Decay, Dynamic Holding Cost Under Varied Demand Scenario and Demand Series Analysis

This paper presents a sophisticated modification of the economic production quantity (EPQ) model. It incorporates Weibull-distributed progressive deterioration, dynamic holding costs, variable demand, and strong strategies for effectively handling shortages and backlogs. Targeting products that have a short-term expiration but can still be stored for a long time without significant deterioration, the model aims to increase production quantities while lowering overall variable expenses. The extended EPQ model utilizes Maclaurin series approximations to solve ordinary differential equations, effectively capturing the dynamics of inventory under three different demand patterns. The focus of this handle’s situations when the demand for a product changes in a predictable manner over time and considers the likelihood of defective goods during the manufacturing process. This approach provides useful insights for optimizing inventory management and production planning in the manufacturing of goods that are used up or consumed. The usefulness of the model is confirmed in the study through the use of two illustrative instances. Additionally, sensitivity analysis is utilized to suggest potential areas for additional investigation.

A Genetic algorithm approach for improving the probabilistic inventory model with the continuous review: A practical application in the department of pharmacy

This study investigates to shed light on artificial intelligence techniques, specifically the genetic algorithm, to improving traditional solutions, as well as finding the best policy for the problem of probabilistic inventory with continuous review by finding the optimal reorder point and the optimal economic quantity to avoid the risk of stock out (shortage), reduce total costs, and reach the optimal solution with little time and effort. The research was conducted in the stores of the department of pharmacy of the Ninawa health department for the period from January 1, 2021, to January 1, 2023, on a sample of three drugs (most demanded drugs). An analysis of the demand data for the study sample was conducted using the statistical program (SPSS Statistics Version 22) to determine the type of inventory. it was found that the type of inventory is probabilistic and the demand data follows a normal distribution. Based on this foundation, the mathematical model for the study problem was built. Given the complexity of the steps and iterations of the traditional solution, the solution steps were applied using the R programming language to reach the model's solution. Additionally, the solution steps were programmed for the genetic algorithm and applied using the R programming language. The results of the genetic algorithm showed an improvement in the traditional solution results by reducing total costs. Based on the results of the genetic algorithm, the economic order quantity, safety stock, reorder period, and safety period were found. Paper type: Research Paper

SAR-driven flood inventory and multi-factor ensemble susceptibility modelling using machine learning frameworks

Climate change has substantially increased both the occurrence and intensity of flood events, particularly in the Indian subcontinent, exacerbating threats to human populations and economic infrastructure. The present research employed novel ML models—LR, SVM, RF, XGBoost, DNN, and Stacking Ensemble—developed in the Python environment and leveraged 18 flood-influencing factors to delineate flood-prone areas with precision. A comprehensive flood inventory, obtained from Sentinel-1 Synthetic Aperture Radar (SAR) data using the Google Earth Engine (GEE) platform, provided empirical data for entire model training and validation. Model performance was assessed using precision, recall, F1-score, accuracy, and ROC-AUC metrics. The results highlighted Stacking Ensemble’s superior predictive ability (0.965), followed closely by, XGBoost (0.934), DNN (0.929), RF (0.925), LR (0.921), and SVM (0.920) respectively, establishing the feasibility of ML applications in disaster management. The maps depicting susceptibility to flooding generated by the current research provide actionable insights for decision-makers, city planners, and authorities responsible for disaster management, guiding infrastructural and community resilience enhancements against flood risks.

The effects of inflation, shortages, and partial backlogs on products that deteriorate over time in response to varied demand

This study aims to determine an optimal policy to deal with a situation where a retailer should have enough stock to meet customer demands and prevent supply loss and deterioration. In this study, we demonstrate the impact of partial backlogging, shortages, and inflation on decaying items to provide the most relevant solutions to this problem. The model uses a two-parameter Weibull deterioration distribution with an exponential demand rate. Numerical results and sensitivity analysis are combined with a graphical demonstration, and the proposed approach is reliable and accurate, providing a new explanation for a different type of system. This paper determines the total cost and optimal production run time by developing an inventory model. Sensitivity analysis is carried out to demonstrate the proposed model.

Inventory Decisions Considering Returns in Omni-channel Retailing

Omni-channel retail is a new model that is achieved by integrating online stores and offline physical stores. The inventory decision problem considering returns under omni-channel retail is studied in two cases: considering same-channel returns under omni-channel retail and considering cross-channel returns under omni-channel retail. Based on the consideration of consumer returns and resale of returned products, the newsboy model is used to construct inventory decision models with the goal of maximizing retailer profits and analyze the models. Numerical analysis shows that the online store return ratio and the cross-channel return ratio have a significant impact on the inventory and profit of the retailer's offline physical stores and online stores. In particular, when the cross-selling profit is large, the cross-channel return ratio increases, and the retailer's profit increases accordingly, but the retailer's profit may decrease with the increase of the online store return ratio.

PULPO: A framework for efficient integration of life cycle inventory models into life cycle product optimization

AbstractThis work presents the PULPO (Python‐based user‐defined lifecycle product optimization) framework, developed to efficiently integrate life cycle inventory (LCI) models into life cycle product optimization. Life cycle optimization (LCO), which has found interest in both the process systems engineering and life cycle assessment (LCA) communities, leverages LCA data to go beyond simple assessments of a limited number of alternatives and identify the best possible product systems configuration subject to a manifold of choices, constraints, and objectives. However, typically, aggregated inventories are used to build the optimization problems. Contrary to existing frameworks, PULPO integrates whole LCI databases and user inventories as a backbone for the optimization problem, considering economy‐wide feedback loops between fore‐ and background systems that would otherwise be omitted. The open‐source implementation combines functions from Brightway2 for the manipulation of inventory data and pyomo for the formulation and solution of the optimization problem. The advantages of this approach are demonstrated in a case study focusing on the design of optimal future global green methanol production systems from captured CO2 and electrolytic H2. It is shown that the approach can be used to assess sector‐coupling with multi‐functional processes and prospective background databases that would otherwise be impractical to approach from a standalone LCA perspective. The use of PULPO is particularly appealing when evaluating large‐scale decisions that have a strong impact on socioeconomic systems, resulting in changes in the technosphere on which the background system is based and which is often assumed constant in standard LCO approaches regardless of the decisions taken. This article met the requirements for a gold‐gold JIE data openness badge described at http://jie.click/badges.

Stochastic inventory control models for single item replenishment with variable demand under constrained and unconstrained conditions

Stochastic inventory control models for single item replenishment with variable demand under constrained and unconstrained conditions

A Minibatch Stochastic Gradient Descent-Based Learning Metapolicy for Inventory Systems with Myopic Optimal Policy

Stochastic gradient descent (SGD) has proven effective in solving many inventory control problems with demand learning. However, it often faces the pitfall of an infeasible target inventory level that is lower than the current inventory level. Several recent works have been successful in resolving this issue in various inventory systems. However, their techniques are rather sophisticated and difficult to apply to more complicated scenarios, such as multiproduct and multiconstraint inventory systems. In this paper, we address the infeasible target inventory-level issue from a new technical perspective; we propose a novel minibatch SGD-based metapolicy. Our metapolicy is flexible enough to be applied to a general inventory systems framework covering a wide range of inventory management problems with myopic clairvoyant optimal policy. By devising the optimal minibatch scheme, our metapolicy achieves a regret bound of [Formula: see text] for the general convex case and [Formula: see text] for the strongly convex case. To demonstrate the power and flexibility of our metapolicy, we apply it to three important inventory control problems, multiproduct and multiconstraint systems, multiechelon serial systems, and one-warehouse and multistore systems, by carefully designing application-specific subroutines. We also conduct extensive numerical experiments to demonstrate that our metapolicy enjoys competitive regret performance, high computational efficiency, and low variances among a wide range of applications. This paper was accepted by J. George Shanthikumar, data science. Funding: J. Xie and S. Yuan are supported by the National Natural Science Foundation of China (NSFC) [Grant 72331011]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/mnsc.2023.00920 .

Optimal Replenishment Strategy for a High-Tech Product Demand with Non-Instantaneous Deterioration under an Advance-Cash-Credit Payment Scheme by a Discounted Cash-Flow Analysis

This study investigated non-instantaneous deteriorating items because not all products deteriorate immediately. In the high-tech product life cycle, the product demand increases linearly substantially in the growth stage and maintains a near-constant level in the maturity stage. This is a ramp-type demand rate. To satisfy the demand as shortages occur, partial backlogging is necessary. The advance-cash-credit payment scheme, comprising advance, cash, and credit payments, has gained popularity in business transactions to improve cash flow flexibility among supply chain participants. This study explored a partial backlogging inventory model with ramp-type demand for non-instantaneous deteriorating items under generalized payment. The proposed model also incorporated discounted cash flow analysis to account for the time value of the profit function. This study attempted to determine the optimal replenishment strategy to maximize the present value of the total profit. Finally, we conducted a sensitivity analysis to examine the efficacy of the proposed model and gain managerial insights. The optimal total profit rises with an increase in the permissible delay period and sale price but decreases with an increase in ordering and purchase costs. Then, the decision-maker can refer to the managerial insights to choose the appropriate parameter value for the operation.