Optimal order quantity by maximising expected utility for the newsboy model

Abstract

The classical newsboy problem deals with profit maximisation by choosing the optimal ordering quantity. In contrast to the earlier newsboy type problems, this study assumes that the investor makes the investment decision so as to maximise expected utility instead of expected profit. Accordingly, this paper discusses the newsboy problem, who tries to find the optimal ordering quantity so as to maximise his expected utility at a given level of initial wealth. In addition to this, it is assumed that the newsboy is a risk averse investor and the log utility function is introduced to show the level of utility associated with different levels of wealth, conforming to the assumption of risk aversion. Finally, we have developed a method to maximise the expected utility by determining the optimal ordering quantity based on the different levels of investor's initial wealth. From the numerical examples, it is clear that the optimal ordering quantity varies depending on investor's different levels of initial wealth and the sensitivity analysis demonstrates how an investor can choose the initial wealth and optimal ordering quantity to maximise his expected utility.