Risk-averse multi-product selective newsvendor problem with different market entry scenarios under CVaR criterion

- We model three cases of risk-averse multi-product multi-market newsvendor problem.
- Market demands are assumed to be independent and normally distributed.
- The decision variables are the order quantity of each product and markets to serve.
- We provide binary nonlinear and conic quadratic mixed integer formulations.
- Solution algorithms are proposed to solve the models in polynomial time.

We study the CVaR risk-averse Multi-Product Selective Newsvendor Problem (MPSNVP). The MPSNVP involves the integration of the procurement decisions with the market selection decisions. Prior to the demand realization, the decision maker has to select markets (from available markets) to serve, and decide the order quantity for each product, in order to maximize profit under CVaR risk criterion. The products are procured from an external supplier with a lower purchasing cost relative to the local suppliers. It is assumed that the realized demand for each product should be satisfied; and in the case of shortages, the firm expedites from a local supplier with a higher purchasing cost. Specifically, three cases of the MPSNVP are discussed: flexible, full and partial market entry problems. The mathematical models result in binary nonlinear programs. We propose solution algorithms to these models. In addition, we transform the obtained programs into conic quadratic mixed integer programs. The computational tests show that the proposed solution algorithms outperform the state-of-the-art commercial solvers. In addition, the paper provides managerial insights into the effect of the risk aversion level along with the number of products and market pool size.