In an article published in JORS, Aggarwal and Jaggi (1995) considered the inventory model with an exponential deterioration rate under the condition of permissible delay in payments. Later on, Jamal et al (1997) extended Aggarwal and Jaggi's model to allow for shortages. This viewpoint complements the shortcomings of Jamal et al (1997). First, it shows that the optimal solution for each case not only exists but is unique under specific circumstance. Then, it provides a procedure for finding the optimal solution and shows in a rigorous way that the solution is indeed global minimum. In a specific circumstance, without the extremely high backorder cost, the model reduces to the case with no shortage and obtains the negative minimum cost.
Journal of the Operational Research Society 59(6), pp.867-870