This study is an inventory model with consideration of price, stock dependent demand, partially backlogged shortages, and two constant deterioration rates. In this model, demand function depends on price and stock while during the shortage time, demand depends only on price of the product. The deterioration is taken into account as a non-instantaneous, once the item is stocked in retailer’s house, any time deterioration can start with a constant rate for a certain period, then this deterioration rate increases. Shortages are allowed and it is partially backlogged. The corresponding inventory problem constitutes a non-linear constraint optimization problem. Here this problem has been solved using Lingo 15 software and also give 3D graph with the help of MATLAB2010a to show the convexity of the objective function. Finally, to illustrate and validate the inventory model, a numerical example is used considering fixed price. To study the effect of changes of different inventory parameters, a sensitivity analysis has been carried out changing one parameter at a time holding other parameters unchanged.

This paper derives a production inventory model over infinite planning horizon with flexible but unreliable manufacturing process and the stochastic repair time. Demand is stock dependent and during the period of sale it depends on reduction on selling price. Production rate is a function of demand and reliability of the production equipment is assumed to be exponentially decreasing function of time. Repair time is estimated using uniform probability density function. The objective of the study is to determine the optimal policy for production system, which maximizes the total profit subject to some constraints under consideration. The results are discussed with a numerical example to illustrate the theory.

Keeping in view the concern about environmental protection, the study investigates effects of remanufacturing in an integrated production inventory model consisting of forward and reverse supply chain over infinite planning horizon. This article is developed for the deteriorating products with stock dependent demand under shortages. To make the model more realistic, flexibility of production system has been incorporated during forward manufacturing. We derive total cost function and using the results of calculus, optimum production policy is derived, which minimizes the total cost incurred. The results are discussed with a numerical example to illustrate the theory.

The objective of this study is to develop of an inventory policy for deteriorating items, in which demand for the products is stock dependent and the retailer invests in preservation technology to reduce the rate of product deterioration. In many real-life situations, for certain types of consumer goods, the consumption rate is sometimes influenced by the stock-level. It is usually observed that a large pile of goods on a shelf in a supermarket will lead the customer to buy more and then generate higher demand. The consumption rate may go up or down with the on-hand stock level. This paper is developed with the realistic conditions of demand, allowable credit period, partial backlogging and variable ordering cost. A solution procedure is given to find the optimal preservation technology cost and total cost of the system. A numerical example and sensitivity analysis are presented to illustrate the model.

This article develops a supply chain coordination model with a single-vendor and a singlebuyer.
The vendor manufactures the product in lots and delivers to the buyer in equal
shipments. The vendor’s production process is not perfectly reliable. During a production run,
the process may shift from an in-control state to an out-of-control state at any random time and
produces some defective items. The buyer whose demand is assumed to be a linear function of
the on-hand inventory performs a screening process immediately after each replenishment.
Moreover, the buyer’s inventory is deteriorated at a constant rate over time. The vendor-buyer
coordination policy is determined by minimizing the average cost of the supply chain. It is
observed from the numerical study that channel coordination earns significant cost savings over
the non-coordinated policy.