Supply chain model with stock dependent demand, quadratic rate of deterioration with allowable shortage (Q1635439)

Summary: The goal of this devotion of time and attention to acquiring knowledge is to develop assist calculations and prediction for supply chain (three echelons), in which an optimal ordering decision for the manufacturer-supplier-retailer chain is developed when the supplier's lead-time is considered. This paper examines deterministic inventory model with variable deterioration and stock dependent demand, where the unsatisfied demand is partially backlogged which depends on waiting time. A solution procedure is presented to determine a stock dependent demand, variable deterioration rate, shortage period and the demand during the shortage is partially backlogged which is dependent on the waiting time such that the difference between an initial outlay and the subsequent amount earned for the supply chain is maximised. Sensitivity analyses are given to illustrate the model with the help of profit maximum principle.