Multi-product newsvendor problem with hybrid demand and its applications to ordering pharmaceutical reference standard materials

Uncertainty is inherent in the newsvendor problem. Most of the existing literature is devoted to characterizing the uncertainty either by randomness or by fuzziness. However, in many cases, randomness and fuzziness simultaneously appear in the same problem. Motivated by this observation, we investigate the multi-product newsvendor problem by considering the demands as hybrid variables which are proposed to describe quantities with double uncertainties. According to the expected value criterion, we formulate an expected profit maximization model and convert it to a deterministic form when the chance distributions are given. We discuss two special cases of hybrid variable demands and give their chance distributions. Then we design hybrid simulation to estimate the chance distribution and use genetic algorithm to solve the proposed models. Finally, we proceed to present numerical examples of purchasing pharmaceutical reference standard materials to illustrate the applicability of our methodology and the effectiveness of genetic algorithm.