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We consider an inventory system for continuous decaying items with stochastic lead time and Poisson demand. Shortage is allowed and all the unsatisfied demands are backlogged. Moreover, replenishment is one for one. Our objective is to minimize the long-run total expected cost of the system. Firstly, we have developed the mathematical model with deterministic lead time. Since the stochastic lead time makes the model complex especially when lead time has complicated probability distribution and it is difficult to prove convexity of the objective function, we have applied simulation modeling approach. The simulation model has no limitation on lead time or any other parameters. The simulation model is validated by comparing its outputs and analytical model's results for the deterministic lead time case. Furthermore, we use optimizer module of the applied software to find near optimal solutions for a number of examples with stochastic lead time.