A Study of an EOQ Model of Growing Items with Parabolic Dense Fuzzy Lock Demand Rate

In this article, the parabolic dense fuzzy set is defined, and its basic arithmetic operations are studied with graphical illustration. The lock set concept is incorporated in a parabolic dense fuzzy set. Then, it is applied to the problems of fishery culture via the modeling of an economic order quantity model. Here, the fingerlings are fed to reach the ideal size to fulfill the customer’s demand. The growth rate of the fingerlings is assumed as a linear function. After the sales of all fish, the pond is cleaned properly for a new cycle. Here, the model is solved in a crisp sense first. Then, we fuzzify the model considering the demand rate as a parabolic dense lock fuzzy number and obtain the result in a fuzzy environment. The main aim of our study was to find the quantity of the ordering items such that the total inventory cost gets a minimum value. Lastly, sensitivity analysis and graphical illustrations were added for better justification of our model.

Sustainable integrated and pricing decisions for two-echelon supplier-retailer supply chain of growing Items

In today's market, supply chain players have to cooperate mutually for extra benefits, long lasting paybacks, and to control carbon emission for a clean environment. In this study, a two-echelon sustainable supply chain model with a supplier-retailer scenario is considered to investigate the overlooked area of growing items and reducing carbon emissions. These joint effects will benefit the firms for interim financing as well as minimize carbon emission for a clean environment. The main task for the supplier is to breed new-born animals with respect to a biologic growth pattern, then slaughters them and controls the carbon emission to maintain the sustainability. The supplier then delivers the slaughtered items to the retailer where it is used as final products to satisfy customers demand and also experienced deterioration during the inventory replenishment cycle. Carbon emission is considered due to transportation of slaughtered items to the retailer. The main goal of this paper is to analyze the model under decentralized and centralized chain structures and in the centralized case profit-sharing contract is incorporated as the cooperation tool. The model has been solved with an analytic solution approach to obtain the global optimum solution. Sensitivity analysis is carried out to investigate the impact of different input parameters. The results support the claim that centralized chain structure can provide the partners with more benefits if an appropriate coordination mechanism is applied. Moreover, it is shown that the unit purchasing cost of each echelon has a significant effect on the profit in comparison to the other cost factors. Finally the results reveal that the supplier's inventory cycle is more dependent on the growth pattern rather than external cost factors.

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.