The multi-product price-setting newsvendor with resource capacity constraints

In this paper, we consider a newsvendor problem commonly encountered in retail stores that cater to budget-sensitive shoppers. The newsvendor sells multiple products, and in addition to determining order quantities must also determine the selling price of each product sold. The demand for each product is of a stochastic nature and depends on the demands of other products, i.e., is cross-elastic. We transform the objective function into a form that is amenable to developing integer-programming solutions and then develop a numeric optimization procedure rooted in the Nelder–Mead search technique. We obtain encouraging numerical results on some small-scale and large-scale problems. To the best of our knowledge, this is the first work that produces implementable solutions for a scenario that is particularly relevant to retailers catering to budget-sensitive customers who are abundant in the current economy.