The tradeoff between maximizing expected profit and minimizing the maximum regret in the newsvendor problem

We introduce a multi-objective variant of the newsvendor problem in which we maximize the expected profit and minimize the maximum regret associated with the decision of how many items to procure from a supplier in the face of unknown demand. When the demand distribution is bounded, the problem is relatively simple. With an unbounded demand distribution, the maximum regret is undefined. In that case, we introduce a chance-constrained variant of the model in which we minimize the maximum regret over a range of demand values whose probability is at least a user-specified value, \(\gamma\). We provide an algorithm for finding the tradeoff between the expected profit and the \(\gamma\)-level maximum regret. We also show that, when operating near the optimal single-objective newsvendor solution, we can significantly reduce the \(\gamma\)-level maximum regret with little degradation in the expected profit.