On single item time weighted mixture inventory models with independent stochastic lead times

In this paper, mixture inventory models are developed considering shortages as combination fixed and time weighted backorders with lost sales. The inventory policy assumes single item having deterministic demand where the lead time is stochastic. For the time weighted backorders case, the backorder cost depends on the length of time of shortage. A numerical example is shown to illustrate the results. A sensitivity analysis is conducted to see changes in the optimal parameters with the changing proportion of backorders in the mixture of backorders and lost sales. Finally, the paper shows the benefits of order crossover by comparing interchangeable demand case over non‐interchangeable demand.