Min-max distribution free continuous-review model with a service level constraint and variable lead time

In this paper, we provide a continuous-review (Q, r, L) inventory model with a fill rate service constraint and a negative exponential crashing cost function with a variable lead time. Tajbakhsh [1] developed a closed-form solution that considered an order quantity and a reorder point. We extend the distribution free continuous-review inventory model to minimize the total cost by using a negative exponential lead time crashing cost function, and derive closed-form expressions for the optimal order quantity, reorder point, and lead time. Some numerical examples are presented to illustrate the model. We perform a sensitivity analysis to see the effects of parameter changes on the objective function. We have made the comparisons with the existing model.