An Inventory Model for Deteriorating Items with Stock Dependent Demand and Partial Backlogging

In this paper, we formulate a deteriorating inventory model with stock-dependent demand Moreover, it is assumed that the shortages are allowed and partially backlogged, depending on the length of the waiting time for the next replenishment. The objective is to find the optimal replenishment to maximizing the total profit per unit time. We then provide a simple algorithm to find the optimal replenishment schedule for the proposed model. Finally, we use some numerical examples to illustrate the model. Keywords- Inventory, Deteriorating items, Stock dependent demand, Partial backlogging

Control of Non-instantaneous Degrading Inventory under Trade Credit and Partial Backlogging

Inventory management is an extremely difficult task. It has become usual practice for a provider during the last few decades to provide a retailer with a credit term. In this article, a non-instantly degradable products inventory system is built with a price-sensitive demand and a Weibull credit term allocation reduction rate. Some backlogged deficiencies are permitted. The aim is to maximize the total profit in this study by taking three cases into account. Numerical examples, graphical representations and sensitivity analysis demonstrate the application of the approach developed in this study.

Learning Effect on Inventory Model for Deteriorating and Ameliorating Items under Inflation and Partial Backlogging

Now-a-days, learning’s awareness is increasing in various disciplines because effect of learning has a direct impact on profit or loss, and it is a promotional deemed effective tool for inventory management. The basic concept of the inventory model is that 100% of the articles in an ordered lot are of good quality but this concept is not practically justifiable for the production process owing to product deterioration and related factors and so deterioration of items cannot be ignored. Again due to lack of considering the influence of demand, the ameliorating items for the amount of inventory is increasing gradually and it is a natural phenomenon observing in much life stock models. In addition, as the deep financial crisis continues to haunt the global economy, the effects of inflation and time value of money cannot be oblivious to an inventory system. Again another important factor is shortages which no retailer would prefer, and in practice are partially backlogged and partially lost. In order to convert the lost sales into sales, the retailer offers such customers an incentive, by charging them the price prevailing at the time of placing an order, instead of the current inflated price. Therefore, bearing in mind these facts, the present paper develops an inventory model for a retailer dealing with deteriorating and ameliorating items with stock dependent demand under the influence of inflation and time-value of money over a fixed planning horizon where holding cost follows the learning curve. Finally, a numerical example is provided to illustrate the proposed model. Comparative study of the optimal solutions with respect to major parameters under different special cases is carried out graphically and some managerial inferences have been presented. Subject classification: AMS Classification No. 90B05. Keywords: Inventory, Learning effect, Deteriorating, Ameliorating, Inflation, Time-value of money, Shortages and Partial backlogging.