Analysis and optimisation of periodic inventory models for perishable items with a general lifetime

We considered two periodic review perishable inventory systems. The first system is controlled by a periodic review $ ({T,S} ) $ (T,S) policy, where orders are triggered at each review period $ T $ T and when the stock is less than $ S $ S. The second one is controlled by a periodic review $ ({s,S} ) $ (s,S) policy, where orders are triggered only if the stock level is below $ s $ s. For both models, the lifetime of each product was assumed to follow a general distribution, whereas the lead time was constant. The demands followed a Poisson process, and all unsatisfied demand was lost. Using an approximate solution of the steady-state probabilities of the inventory level, we obtained a closed form of cost expression. Next, we conducted a simulation study to identify our solution accuracy. Finally, we performed a sensitivity analysis to evaluate the effect of the lifetime variation and cost parameters on the best policy and its cost. The obtained results were close to those of the optimal policy with an average accuracy of 3.7% for the periodic review $ ({T,S} ) $ (T,S) policy and 3.8% for the periodic review $ ({s,S} ) $ (s,S) policy. For the worst cases, where the accuracy is higher than 7%, we provided an analytical approach to improve the system accuracy.