Research On Robust Optimization Model And Strategy Of A Multi-market Newsvendor Based On Risk Aversion

Due to the universality in the real economic life, newsvendor model has been an important part in the field of the supply chain management, especially the supply chain inventory management of perishable products.With the fast upgrading speed of products and personalized styles of consumers, the demand of short life-cycle products is always uncertain. The classic newsvendor model in supply chain literature often assumes that demand distribution is known and gets optimal decisions by optimizing the expected profit or cost. However, researches show that inventory managers prefer to order less than that from the traditional newsvendor model based on expected profit or cost. When demand is uncertain, inventory managers often tend towards some risk attitude, which affects the final decision. In addition, with the rapid development of information technology and logistics systems, companies are no longer limited to the single market, but consider the integration of multiple markets, which provides the opportunity to get more profits for the companies. Therefore, the multi-market newsvendor robust optimization model is studied under the uncertain demand probability distribution based on risk aversion. The results of the study will provide decision support for decision makers faced with multiple demand markets and demand uncertainty. The following is the main research content of this paper.Firstly, the model based on expected profit maximization is robustly formulated under the assumption of box discrete distribution and again under the ellipsoid discrete distribution. The robust models can be mathematically transformed into a general convex optimization problem for box uncertainty or into a second-order cone program for ellipsoid uncertainty. Both transformed problems can be optimally solved directly. We offer propositions with proof to show the equivalence of the transformed problems with the original ones. Further, considering risk-averse attitude of decision makers who face with demand uncertainty, taking the conditional value-at-risk (CVaR) as objective functions, the robust newsvendor model is studied under box and ellipsoid uncertainty set.Secondly, robust multi-market newsvendor models are established based on expected profit maximization and CVaR-based loss minimization. The robust models can be mathematically transformed into a general convex optimization problem for box uncertainty or into a second-order cone program for ellipsoid uncertainty.Finally, Numerical examples are given to validate the proposed approach. The results show that, compared with the optimal situation when the true demand distribution is known, although some performance loss will be incurred for the lack of full demand distribution information, the loss is very limited, which indicates that the robust strategies obtained by the approach proposed in this paper have good robustness and can restrain the effect of uncertainty on system performance effectively. Furthermore, the performance loss can be interpreted as the highest cost decision makers would pay to acquire the true demand distribution information. Besides, sensitivity analysis with respect to risk-averse levels is conducted to validate the proposed models and solution approaches. The results show that with the increase of risk-averse level of the decision makers, quantity of products and the system performance show a trend of decrease.