An Inventory Model in a Three-Echelon Supply Chain for Growing Items with Imperfect Quality, Mortality, and Shortages under Carbon Emissions When the Demand Is Price Sensitive

De-la-Cruz-Márquez, Cynthia Griselle; Cárdenas–Barrón, Leopoldo Eduardo; Mandal, Buddhadev; Smith, Neale R.; Bourguet-Díaz, Rafael Ernesto; Loera-Hernández, Imelda de Jesús; Céspedes-Mota, Armando; Treviño-Garza, Gerardo

doi:10.3390/math10244684

Cited by 14 publications

(4 citation statements)

References 55 publications

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“…Further, Manna et al 25 formulated a production model of nondeteriorating item under warranty policy and emission taxation regulation. Recently, Pan et al, 26 Handayani et al, 27 Su et al, 28 Ghosh, 29 Alharbi, 30 Mahato et al, 31 Das et al, 32 and De-la-Cruz-Márquez et al 33 have recently published several production inventory models considering the effect of carbon emission. The production rate of the items that are directly engaged in the system's optimum policy is also known for production-based firms.…”

Section: Literature Reviewmentioning

confidence: 99%

Impact of emission and service constraint for an imperfect production system under two level Hamiltonian

Das

Ali

Shaikh

et al. 2023

Optim Control Appl Methods

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Considering the impact of emission on environment, over the last few decades, reduction of emission during production process (or emission free production process) appears to be one of the most growing preferences for every manufacturing firm. Again, manufacturing companies of different products are bounded to offer various facilities to their consumers in order to survive in the current highly competitive market situation. Primarily considering these two factors taken in to account, this study addresses an imperfect manufacturing inventory model in which customers' demand increases linearly w. r. to emission reduction level, service level from the manufacturer and decreases nonlinearly w. r. to price of the items. The analytical expressions of production rates, emission levels and service levels are derived by solving a number of optimum control problems using Hamiltonian maximum principle with a values for the business period and selling price. The basic goal is to maximize the average profit of the system. In addition, a number of numerical examples are considered to elaborate four distinct instances involved in the proposed model and these are solved numerically using teaching learning based optimization algorithm. Finally, sensitivity experiment is performed to investigate the influence of various system factors on the best‐found policies. The sensitivity analysis indicates that service rate provided by the manufacturer and selling price of the items impose a huge impact on the average profit of the system. Further, the carbon reduction affects the revenue of the system less significantly.

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Section: Literature Reviewmentioning

confidence: 99%

Impact of emission and service constraint for an imperfect production system under two level Hamiltonian

Das

Ali

Shaikh

et al. 2023

Optim Control Appl Methods

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“…Sebatjane and Adetunji [8] included the effects of freshness and the level of inventory extended in the demand behavior. From a similar perspective, Pourmohammad-Zia et al [14], De-la-Cruz-Márquez et al [15], and De-la-Cruz-Márquez et al [16] supposed that the demand depends on the item's price, while Rana et al [17] assumed that the demand is a linear function of time.…”

Section: Literature Reviewmentioning

confidence: 99%

Discontinuous Economic Growing Quantity Inventory Model

Nobil

Cárdenas–Barrón

et al. 2023

Mathematics

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The classical economic growing quantity (EGQ) model is a key concept in the inventory control problems research literature. The EGQ model is commonly employed for the purpose of inventory control in the management of growing items, such as fish and farm animals, within industries such as livestock, seafood, and aviculture. The economic order quantity (EOQ) model assumes that customer demand is satisfied without interruption in each cycle; however, this assumption is not always true for some companies as they do not have continuous operations, except for item storage, during non-working times such as weekends, natural idle periods, or spare time. In this study, we extend the traditional EGQ model by incorporating the concept of working and non-working periods, resulting in the development of a new model called discontinuous economic growing quantity (DEGQ). Unlike the conventional EGQ model, the DEGQ model considers the presence of intermittent operational periods, in which the firm is actively engaged in its activities, and non-working periods, during which only storage-related operations occur. By incorporating this discontinuity, the DEGQ model provides a more accurate representation of real-world scenarios where businesses operate in a non-continuous manner, thus enhancing the effectiveness of inventory control and management strategies. The study aims to obtain the optimal number of periods in each cycle and the optimal slaughter age for the breeding items, and, subsequently, to find the optimal order size to minimize the total cost. Finally, we propose an optimal analytical procedure to determine the optimal solutions. This procedure entails finding the optimal number of periods using a closed-form equation and determining the optimal slaughter age by exhaustively searching the entire range of possible growth times.

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“…These models aim at optimizing inventory management for enhanced profitability. De-la-Cruz-Márquez et al [47] developed an optimization model for growing items within a three-stage supply chain (i.e., farmers, processors, and retailers) that considers factors such as imperfect quality, mortality, shortages with full backordering, and carbon emissions. Gharaei et al [48] enhanced a sustainable model for the economic growing quantity EGQ system, which they named "Sustainable EGQ (SEGQ)".…”

Section: ] Gharaei and Almehdawementioning

confidence: 99%

“…, calculate order quantity (y ) using Equation ( 46), calculate backordering quantity (B ) using Equation (47), and go to Step 6. Otherwise, set s = p, calculate the order quantity (y ) using Equation ( 46), calculate the backordering quantity (B ) using Equation (47), and proceed to Step 6. Step 6.…”

Section: Solution Algorithmmentioning

confidence: 99%

An Inventory Model for Growing Items When the Demand Is Price Sensitive with Imperfect Quality, Inspection Errors, Carbon Emissions, and Planned Backorders

De-la-Cruz-Márquez,

Cárdenas-Barrón,

Porter

et al. 2023

Mathematics

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Inventory models that consider environmental and quality concerns have received some attention in the literature, yet no model developed to date has investigated these features in combination with growing items. Therefore, there is a need to incorporate these three relevant aspects together in a single inventory model to support decisions, compare results, and obtain new knowledge for the complexities of the real world. Moreover, current sustainable inventory management practices aim at mitigating the ecological consequences of an industry while preserving its profitability. The present study aligns with this perspective and introduces an economic order quantity (EOQ) model that considers imperfect quality while also accounting for sustainability principles. More specifically, the model addresses growing items, which have a demand dependent on selling price and the unique ability to grow while being stored in inventory. Additionally, the analysis acknowledges the possibility of classification errors during the inspection process, encompassing both Type-I and Type-II inspection errors. Furthermore, the model permits shortages and ensures that any shortage is completely fulfilled through backorders. The optimization model produces an optimal solution for the proposed model that is derived by optimizing three decision variables: order quantity of newborn items, backordering quantity, and the selling price of perfect items. A numerical example is presented, and the results are discussed. Finally, a sensitivity analysis on variations of parameters such as Type-I and Type-II errors shows that it is advantageous to reduce the percentage of good items that are misclassified as defective (i.e., Type-I error). As there is a direct impact of such errors on sales, it is imperative to address and mitigate this issue. When defective items are mistakenly classified as good Type-II errors, adverse consequences ensue, including a heightened rate of product returns. This, in turn, results in additional costs for the company, such as penalties and diminished customer confidence. Hence, the findings clearly suggest that the presence of Type-I and Type-II errors has a negative effect on the ordering policy and on the total expected profit. Moreover, this work provides a model that can be used with any growing item (including plants), so the decision-maker has the opportunity to analyze a wide variety of scenarios.

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An Inventory Model in a Three-Echelon Supply Chain for Growing Items with Imperfect Quality, Mortality, and Shortages under Carbon Emissions When the Demand Is Price Sensitive

Cited by 14 publications

References 55 publications

Impact of emission and service constraint for an imperfect production system under two level Hamiltonian

Impact of emission and service constraint for an imperfect production system under two level Hamiltonian

Discontinuous Economic Growing Quantity Inventory Model

An Inventory Model for Growing Items When the Demand Is Price Sensitive with Imperfect Quality, Inspection Errors, Carbon Emissions, and Planned Backorders

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