| Summary: | The classical inventory control policies assume that orders are paid for at the time of their receipts, but in practice, suppliers may require retailers to pay a fraction of the purchasing cost in advance, and sometimes allow them to pay this cost in several prepayments during a predetermined period. Planning inventory replenishments and prepayments become challenging when decisions must be made under uncertainty, especially when delivery time is stochastic, and shortages may occur. This paper develops an inventory control model in a purchasing system in which a visitor sells the product of a manufacturer, and a buyer receives call from the visitor to make an order and items arrives at stochastic time. Both partial prepayments and partial backordering are assumed in the model. The main aim of the paper is to determine the optimal level of inventory of the buyer such that his total profit is maximized. A mathematical model with a general probability distribution for lead time is developed and globally optimal solutions are derived for the model. The applicability of the model is discussed through two special cases for uniform and exponential probability distributions. The results are supportive of the proposed ideas and they reflect an efficient approach. © The authors. Published by EDP Sciences, ROADEF, SMAI 2022.
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