An inventory model with screening of items through machinery system for supply chain under fuzzy logic system

Abstract

These days it is very difficult to produce 100% good quality items. Hence, delivered lot may have some defective items in the lot. Thus, inspection of lot becomes necessary. The machinery system reduces labour cost and it is more beneficial in the inventory management. Day by day labour cost increases due to effect of human need increase and retailer faces some economic issues. During manufacturing and production, some produced products are not in good shape teemed as defective items.  The buyer inspects the whole received lot from the seller through inspection machine and includes screening cost. The screening cost is the sum of various expenditures of machinery system. In this paper, we deal with an inventory model with pullulated free demand rate under eco-friendly environment. Now days a lot of carbon units emit from the different sources like factories, firms and some other production factories in the form of poisonous gases and these gases effect the neat and clean environment. Due to the carbon emissions carbon dioxide, sulphor dioxide and methane are more responsible for these issues and some cities like Delhi, Noida and Ghaziabad more effected currently on account of such reason. There are more problems create related to the environment like air pollution, water pollution and the quality of the eco-friendly foods deteriorate as soon as.

The Government tries to control such of issues by including of some cost like pollution cost, carbon emision cost ect. Finally, we minimized the inventory cost with respect to the order quantity for the eco-friendly foods and has been shown the numerical example for the justification of the proposed model. The sensitivity observation has been presented for the ordering policies as well as decision makers and future scope of this scenario also presented.

ntroduction: In this paper Hill’s model (1997) has been considered as a base model and we have added fuel cost and the emission tax to understand the impact of environmental issues on the inventory model. Total cost has been minimized with the help of derivative method and optimal order quantity is obtained by minimizing the total cost. Numerical example is provided with sensitivity analysis to know the robustness of the model.

Objectives: Total cost has been minimized with the help of derivative method and optimal order quantity is obtained by minimizing the total cost. Numerical example is provided with sensitivity analysis to know the robustness of the model.

Methods: We adopt the property of maxima and minima property for the calculation of integrated fuzzy cost, if   we calculated the value of lot size,  by using of Mathematica 9.0, and suppose it is  (consider) and now we calculates   and if we get  then  is called optimal value of and denoted by. The convexity of joint total fuzzy cost for supply has been shown in the figure with help of Mathematica 9.0 software.

Results: From Table-3, we can conclude that the percentage of defective items increase then optimal shipment lot size increase while joint total cost decreases. From Table-4, it can easily be analysed that as production rate increase, the order quantity almost constant and joint total cost increases. From Table-5, it can easily be analysed that as the number of  truck increases with keeping other model parameter constant then order quantity and  Joint total cost increases.

Conclusions The machine learning algorithm is good tools for the reduction of labour cost as well the total cost is decreasing which includes. inspection cost, holding cost, setup cost, item cost, transportation cost, emission tax cost.