Robust multi-product newsvendor model with uncertain demand and substitution

• Develop exact and approximation algorithms to solve the model. Derived closed-form solutions for three special cases. Conservative algorithm dominates large-scale instances. Seek best budget of uncertainty by cross validation method. This work studies a Robust Multi-product Newsvendor Model with Substitution (R-MNMS), where demand substitution rates are stochastic subject cardinality-constrained sets. The goal this is determine optimal order quantities multiple products maximize worst-case total profit. To achieve this, we first show that given quantities, computing profit, in general, NP-hard. Therefore, derive following cases: (1) if there only two products, (2) no among different (3) equal number products. For general R-MNMS, formulate it as mixed-integer linear program an exponential constraints develop branch cut it. problem instances, further propose conservative R-MNMS prove under some certain conditions, yields solution R-MNMS. numerical study demonstrates effectiveness proposed approaches robustness our