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.

In this paper, the single-period inventory problem, what is called newsboy problem, has been revisited with two different conditions, uncertain supply and risk-averseness. Eeckhoudt et al. [5] investigated the effect of risk-averseness of a newsboy on the optimal order quantity in a stochastic demand setting. In contrary to Eeckhoudt et al. [5] this paper investigates the effect of risk-averseness in a stochastic supply setting. The findings from this investigation say that if  represents the optimal order quantity without risk-averseness then the risk-averse optimal order quantity can be greater than  and can be less than  as well.