An Estimation of Distribution Algorithm for Mixed-Variable Newsvendor Problems

As one of the classical problems in the economic market, the newsvendor problem aims to make maximal profit by determining the optimal order quantity of products. However, the previous newsvendor models assume that the selling price of a product is a predefined constant and only regard the order quantity as a decision variable, which may result in an unreasonable investment decision. In this article, a new newsvendor model is first proposed, which involves of both order quantity and selling price as decision variables. In this way, the newsvendor problem is reformulated as a mixed-variable nonlinear programming problem, rather than an integer linear programming problem as in previous investigations. In order to solve the mixed-variable newsvendor problem, a histogram model-based estimation of distribution algorithm (EDA) called <inline-formula> <tex-math notation="LaTeX">${\mathrm{ EDA}}_{mvn}$ </tex-math></inline-formula> is developed, in which an adaptive-width histogram model is used to deal with the continuous variables and a learning-based histogram model is applied to deal with the discrete variables. The performance of <inline-formula> <tex-math notation="LaTeX">${\mathrm{ EDA}}_{mvn}$ </tex-math></inline-formula> was assessed on a test suite with eight representative instances generated by the orthogonal experiment design method and a real-world instance generated from real market data of Alibaba. The experimental results show that, <inline-formula> <tex-math notation="LaTeX">${\mathrm{ EDA}}_{mvn}$ </tex-math></inline-formula> outperforms not only the state-of-the-art mixed-variable evolutionary algorithms, but also a commercial software, i.e., Lingo.