This article discusses a vendor-buyer inventory model with permissible delay in payments and controllable lead time in which the order quantity, lead time and the number of shipments delivered from vendor to the buyer in a production cycle are decision variables. Here the production process is imperfect. The lead time is crashed and the crashing cost is an exponential function of lead time. Based on the lead time demand, two models are developed, that is, lead time demand follows a normal distribution in the first model and then distribution free approach is considered in the second model to minimize the joint total expected cost per unit time. Efficient computational algorithm is designed to find the optimal solution. Numerical examples are provided to illustrate the results obtained. Sensitivity analysis is carried out to study the changes in the effect on optimal solution and some managerial phenomena are obtained through sensitivity analysis.
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