Multi-product newsvendor with budget constraint including product setup cost

The paper develops heuristic algorithm solution to the optimal multi-product inventory ordering policy called assortment planning problem. We are to maximize the expected profit from multi-product inventory selling to random demand subject to purchase budget including item specific setup cost. Including the cost of new edition design and product administration cost or license fee for example. The Kuhn–Tucker conditions ensure non-negativity of Lagrangian solution but usually lead to the violation of budget constraint. In the literature mostly iterative numerical methods of solving were proposed. However, solving the budget constraint including selected items setup costs has received little attention so far. Dedicated procedures combine Lagrangian approach with product subset selection discrete optimization methods so need high computational effort. We replicate one of them, namely Lagrangian dual heuristic procedure. Hereby, in the paper is proposed novel alternative solution procedure. The procedure reduces computational effort due to simple profitability-rank rule of solving discrete variables of product selection into the assortment. Finally, we compare both approaches performance to show under what conditions the proposed procedure is effective.