In this paper, we develop an efficient approach to solve a multiple-item budget-constraint newsboy problem with a reservation policy. A conventional approach for solving such problem utilizes an approximation for the evaluation of an inverse of a Gaussian cumulative density function when the argument of the function is small, and a heuristic method for finding an optimal Lagrangian multiplier. In contrast to the conventional approach, this paper proposes more accurate method of evaluating the function by using the normalization and an effective numerical integration method. We also propose an efficient way to find an optimal Lagrangian multiplier by proving that the equation for the budget-constraint is in fact a monotonically increasing function in the Lagrangian multiplier. Numerical examples are tested to show the performance of the proposed approach with emphases on the behaviors of the inverse of a Gaussian cumulative density function and the Lagrangian multiplier. By using sensitivity analysis of different budget constraints, we show that the reservation policy indeed provides greater expected profit than the classical model of not having the reservation policy.

• 이창용(공주대학교 산업시스템공학과) | Chang-Yong Lee Corresponding Author