A deteriorating inventory model with displayed stock-level-dependent demand and partially backlogged shortages with all unit discount facilities via particle swarm optimisation

The goal of this research is to develop a price break inventory model for a single deteriorating item with imprecise inventory costs by considering all unit discount policy and variable demand rate dependent on displayed stock level. Shortages are partially backlogged with a variable rate dependent on the length of the waiting time up to the arrival of fresh lot. Analysing the relative size of the displayed stock-level-dependency parameters of demand and the storage capacity of the showroom/shop, different scenarios have been considered. Then, for each scenario, the model has been formulated as a constrained optimisation problem with interval objective and solved with the help of different versions of particle swarm optimisation (PSO) and interval order relations. To illustrate the model, three numerical examples have been solved by different versions of PSO and the results have been compared. Finally, to study the effect of changes of different parameters on optimal policies, sensitivity analyses have been presented numerically.