A multiple-item budget-constraint newsboy problem with a reservation policy

In contrast to the classical newsboy-style problem, this paper develops a model for the multiple-item budget-constraint newsboy problem considering a reservation policy to meet marketing needs. A discount rate is provided to those customers who are willing to make a reservation. In addition to the demand from the original customers, extra demand is also included in the model due to the motivation of the discount rate. A solution algorithm, namely the MCR algorithm, is proposed to solve the problem. The proposed algorithm can actually be considered as a generalization of the classical newsboy-style problem. The MCR algorithm not only provides a business unit with the optimal order quantity, but also the discount rate necessary to achieve the maximal total expected profit under a limited budget. From the illustrated example, it is shown that the expected profit from the proposed model is greater than that from the classical model, due to the consideration of reservations, even though the budget constraint is tight. The increase in the expected profit could be treated as an information value from the willingness function. Although the proposed model is developed for multiple-item problems, it also can be applied to single-item ones. From the sensitivity analysis, the application of the single-item problem to the proposed model can still obtain greater expected profit than the classical model under different budgetary levels.