In this article, an order-level inventory system for deteriorating items has been developed with demand rate as a function of selling price. The demand and the deterioration rate are price dependent and time proportional, respectively. We have considered a perishable item that follows a three-parameter Weibull distribution deterioration. Shortages are not permitted in our model. The optimal solution is illustrated with a numerical example and the sensitivity analysis of parameters is carried out.

Aims: The scope of the model lies in its applicability in the management inventories of time-quadratic demand. It is also seen that large pile of goods displayed in a supermarket will motivate the customer to buy more. So the presence of inventory has a motivational effect on the people around it. Also there may be occasional shortages in inventory due to many reasons. Therefore, we develop an EOQ model for the inventory of a deteriorating item, taking demand rate and allowing shortages in inventory. Study Design: This paper presents an inventory model for deteriorating items with quadratic demand. In the model, shortages are allowed and partially backordered. The backlogging rate is a variable and dependent on the waiting time for the next replenishment. A numerical example is taken to illustrate the model and the sensitivity analysis is also studied. Methodology: Our purpose is to devise a mathematical model on inventory management taking all these factors into consideration. Results: Convexity condition of the cost function is established to ensure the existence of unique point of minimum. Conclusion: The proposed model can be extended in several ways. For instance, we may extend the demand function to stochastic fluctuating demand patterns or stock-dependent demand rate. Finally, we could extend the model to incorporate some more realistic features such as quantity discounts, permissible delay in payments, time value of money and inflation etc.

We obtain exact solutions to the field equations for five-dimensional locally rotationally symmetric (LRS) Bianchi type-I spacetime in the $f(R,T)$ theory of gravity, where specifically, the following three cases are considered: (i) $f(R,T)=\mu (R+T)$, (ii) $f(R,T)=R\mu +RT{\mu }^2$, and (iii) $f(R,T)=R+\mu R^2+\mu T$, where R and T, respectively, are the Ricci scalar and trace of the energy–momentum tensor. It is found that the equation of state (EOS) parameter w is governed by the parameter $\mu$ involved in the $f(R,T)$ expressions. We fine-tune the parameter $\mu$ to obtain the effect of phantom energy in the model. However, we also restrict this parameter to obtain a stable model of the universe.