Supply chain models for deteriorating products with ramp type demand rate under permissible delay in payments

In this paper an order level inventory model for deteriorating items with general ramp type demand rate under conditions of permissible delay in payments is proposed. In this model shortages are allowed and partially backlogged. The backlogging rate is variable and dependent on the waiting time for the next replenishment. Its study requires exploring the feasible ordering relations between the time parameters appeared, which leads to three models. For each model the optimal replenishment policy is determined. The sufficient conditions of the existence and uniqueness of the optimal solutions are also provided. Suitably selected numerical examples highlight the obtained results. Sensitivity analysis of the optimal solution with respect to major parameters of the system has been carried out and the implications are discussed.

► We propose an inventory model with general ramp type demand rate, constant deterioration rate, partial backlogging of unsatisfied demand and conditions of permissible delay in payments.
► The necessary and sufficient conditions of the existence and uniqueness of the optimal solutions are also provided.
► An easy-to-use algorithm is proposed to find the optimal replenishment policy and the optimal order quantity.
► Numerical examples are presented to demonstrate the developed model and the solution procedure.