An optimal ordering policy for a visitor-based purchasing system with stochastic delivery time and partial prepayment for profit maximization

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 purchasing cost advance, and sometimes allow them this several prepayments during predetermined period. Planning replenishments become challenging when decisions must be made under uncertainty, especially delivery is stochastic, shortages occur. This paper develops an model system which visitor sells product manufacturer, buyer receives call from make order items arrives stochastic time. Both partial backordering assumed model. main aim determine optimal level such his total profit maximized. A mathematical with general probability distribution lead developed globally solutions derived applicability discussed through two special cases uniform exponential distributions. results supportive proposed ideas they reflect efficient approach.