optimal flexible capacity in newsboy problem under stochastic demand and lead-time

In this paper, we consider a newsvendor who is going to invest on dedicated or flexible capacity, our goal is to find the optimal investment policy to maximize total profit while the newsvendor faces uncertainty in lead-time and demand simultaneously. as highlighted in literature, demand is stochastic, while lead-time is constant. however, in reality lead-time uncertainty decreases newsvendor's performance and increases purchasing cost. analytical results suggest an approach for decision makers to decide which situation is optimal to invest in flexible capacity. furthermore, we derive a closed-form solution for optimal production and capacity under dedicated and flexible policy when demand and lead-time follow uniform and normal distribution. an approximation method introduced in this paper to find the optimal production quantity and investment policy results show that this approximation is useful when the coefficient of variation is low under uniform distribution, and it is useful when the coefficient of variation is high under normal distribution. finally, we show a threshold, considering the fact that it is optimal for the newsvendor to invest on flexible capacity when flexible capacity cost is less than the threshold. to sum up, we measure the effect of lead-time variability on optimal solution.