An inventory model displayed stock and price dependent demand under non-instantaneous deterioration with inflation for partially backlogged shortages.

Abstract

In this paper we have considered stock and price dependent demand and developed a non-instantaneous economic order quantity model for decaying goods under inflation. Shortages are allowed in this model and they are partially backlogged. Stock and price constantly plays an essential part and influence the demand rate. Demand function is depending on price and stock. Deterioration of the growing inventory can be understood as when stock remains for a longer period in a vendor's home following that deterioration will begin with price and stock dependent demand. It is implicit that the deterioration rate arises as soon as items are received into inventory. Aside from deterioration, the effect of inflation is another important factor of inventory. General increase in price of goods is reflected due to decrease in the purchase power of money is inflation. The plan of this representation is to establish the best solution including the estimated Total cost (Holding cost, Shortage cost, Ordering cost, Deterioration cost, Purchase cost, partially backlog cost) diminished. Additional, compulsory and satisfactory circumstances are afforded to illustrate the survival and exclusivity of the best solution. Here we have solved this problem by using Wolfram Mathematica 12.0 software. Lastly, numerical exemplifications, perceptivity study all along graphical demonstrations are revealed to exemplify the realistic purpose of the projected model.