An Inventory Model for Growing Items with Imperfect Quality When the Demand Is Price Sensitive under Carbon Emissions and Shortages

Nowadays, it is well known that global warming is a great hazard to the planet, and the carbon emissions are a principal source of global warming. For this reason, the customers have become more environment and quality conscious than before, and as a result, they request the firms to be ecofriendly. In this context, it is desirable that companies develop and implement inventory models which consider sustainability issues. Furthermore, the companies face problems of shortages and setting prices in order to persist in a competitive and challenging business. Besides, there exists a kind of items different than the traditional products that it is necessary to feed them until a target weight is reached in order to slaughter and sell to customers. These are named as growing items. In this sense, this research work proposes an inventory model for growing items with imperfect quality when the demand is price sensitive under carbon emissions and shortages. The shortages are fully backordered. The demand is price sensitive according to a polynomial function. The proposed inventory model determines jointly the optimal policy for the selling price of perfect-quality growing items, the order quantity, and the backordering quantity which maximize the expected total profit per unit of time. Some numerical examples are resolved in order to illustrate the use and the applicability of the inventory model. Finally, a sensitivity analysis is conducted and some managerial insights are given

Determinación de hidrocarburos aromáticos policíclicos (HAPs) en el fitobentos del Sistema Lagunar de Chelem, Yucatán, México

The contamination of bodies of water by oil derivatives has been alarming in recent years, and hydrocarbons are the most common forms of pollution in aquifer systems. Plant communities have been considered as biomonitors of pollutants, so the presence of Polycyclic Aromatic Hydrocarbons (PAHs) was determined in the phytobenthos of the Chelem´s lagoon system, as it is an impacted system. Specimens of Halodule wrightii Ascherson and Batophora oerstedii J.Agardh were selected, with 4 replications. The samples were rinsed to eliminate epiphytic organisms, and dried for 48 hours at 45 ° C, and then the hydrocarbons were extracted by microwave oven and purified on an alumina column eluted with Hexane (H), Dichloromethane (DCM) and H: DCM mixture 1:1. The determination of PAHs was carried out using GC-FID, which was used to identify and quantify a certified standard with the 16 priority HAPs of the US_EPA. The results showed Fluoranthene, Indene [1, 2, 3-cd] pyrene and Chrysene as the most common compounds. H. wrightii is the one with the highest abundance and high concentrations of 4-ring PAHs, while in B. oerstedii it predominated with 3 and 5 rings. It is important to determine the type of PAHs and the amount absorbed by the phytobenthos since they are the basis of the trophic network, and could affect the biota present in the Chelem´s lagoon system; at the same time, these species could be used as bioindicators of pollution in bodies of water.La contaminación de cuerpos de agua por derivados del petróleo ha sido alarmante en los últimos años, y los hidrocarburos son de las formas más comunes de contaminación en los sistemas acuíferos. Las comunidades vegetales han sido consideradas como biomonitores de contaminantes, por lo que se determinó la presencia de Hidrocarburos Aromáticos Policíclicos (HAP´s) en el fitobentos del sistema lagunar de Chelem, por ser un sistema impactado. Se seleccionaron especímenes de Halodule wrightii Ascherson y Batophora oerstedii J.Agardh, con 4 repeticiones. Las muestras se enjuagaron eliminando organismos epifitos y se secaron durante 48 horas a 45 oC, posteriormente los hidrocarburos fueron extraídos mediante horno de microondas y purificados en una columna de alúmina eluída con Hexano (H), Diclorometano (DCM) y mezcla de H:DCM 1:1. La determinación de HAP´s se realizó mediante GC-FID empleando para su identificación y cuantificación de un estándar certificado con los 16 HAP´s prioritarios de la US_EPA. Los resultados mostraron como compuestos más comunes el Fluoranteno, Indeno [1, 2, 3-cd] pireno y el Criseno. H. wrightii es el que presentó mayor abundancia y altas concentraciones de HAP´s de 4 anillos mientras que en B. oerstedii predominó de 3 y 5 anillos. Es de importancia determinar el tipo de HAP´sy la cantidad que absorbe el fitobentos ya que son la base de la red trófica, y podrían afectar a la biota presente en el sistema lagunar de Chelem; a la vez estas especies podrían usarse como bioindicadores de contaminación en cuerpos de agua

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

This research develops an optimization model for growing items in a supply chain with three stages: farmer, processor, and retailer while considering imperfect quality, mortality, shortages with full backordering, and carbon emissions. In the farmer stage, during the growing period, not all articles survive until the end of the period, so a density function of the probability of survival and death of the growing articles is taken into account. Moreover, it is considered imperfect quality in the retailer’s stage because as the supply chain goes down, there exists a greater probability of product defects. Here, the end customer (consumer) can detect poor-quality aspects such as poorly cut, poorly packed, expired products, etc. An inventory model that maximizes the expected total profit is formulated for a single type of growing items with price-dependent polynomial demand. An algorithm is developed to solve the optimization problem generating the optimal solution for order quantity, backordering quantity, selling price, and the number of shipments that maximizes the expected total profit per unit of time, and a numerical example is used to describe the applicability of the proposed inventory model. Finally, a sensitivity analysis has been carried out for all the input parameters of the inventory model, where the effect of each of the parameters on the decision variables is shown to extract some management knowledge. It was found that holding costs in the three stages of the supply chain have a substantial impact on the total profit per unit of time. In addition, as the demand scale parameter increases, the company must raise the selling price, which directly impacts the expected total profit per unit of time. This inventory model has the advantage that it can be applied to any growing item, including animals or plants, so it helps the owners of farms or crops to generate the most significant possible profit with their existing resources