The inventory model for deteriorating items, which is developed by the Evidential Reasoning Algorithm (ERA) and imprecise inventory costs, is one of the most important factors in complex systems that plays a vital role in payment. The ERA is able to strengthen the precision of the model and give the perfect interval-valued utility. In this model, during lead-time and reorder level two di erent cases can occur in which the mathematical model turns into an imposed nonlinear mixed integer problem with an interval objective for each case. The placement of an order, which has been overlooked by many researchers until now, is normally connected with Advance Payment (AP) in business. Specifying the optimal pro t and the optimal number of cycles in the nite time horizon and lot-sizing in each cycle, are the goals of this paper. In order to solve this model, the Real-Coded Genetic Algorithm (RCGA) with ranking selection is applied. Using the model, some numerical examples are represented and a sensitivity analysis with a variation in di erent inventory parameters.
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