Assistant Professor Department of Mathematics, Holy Cross College (Autonomous) Trichy -620 002
This paper examines an inventory system for growing items, so that the new-born items are fed to reach the ideal weight for consumers after which they are slaughtered. All the slaughtered items are gone through the screening process so that we could identify the good quality items from those of imperfect quality. So the shortage is occurring and the shortages are fully backordered. And also this paper develops the model under the concept of proper disposal of animal mortality during their growth period. Due to the certain circumstances the animals are fall into the sick and dead, and for the environmental concern they are properly disposed from their places. To encourage the purchasing companies the supplier offers the incremental quantity discounts but it will leads to increase the holding cost of the purchasing company and this problem is sort out by using budget capacity constraint. So that the main aim of this proposed model is to reduce the total cost of the system.