Balancing desirable but conflicting objectives in the newsvendor problem

In this paper we study the problem of balancing two desirable but conflicting objectives in the newsvendor model. The standard objective in the newsvendor model is the expected profit maximization. Another objective (known as the "satisficing"--or, "aspiration-level"--objective) that has been studied in the literature is the probability of exceeding a prespecified and fixed target profit level. Since it may not always be obvious what the fixed target profit level should be, we introduce a more flexible satisficing objective where the target does not have to be prespecified. Our satisficing/aspiration-level objective is defined as the probability of exceeding the expected profit and it is a "moving" target that is a function of the order quantity. We provide a discussion of the properties of the newly introduced probability maximization objective. As a departure from previous work where the individual objectives were considered in isolation, in this paper we develop a model that unifies and integrates the two objectives. We use a scalarization method to combine the standard objective of expected profit maximization with the new objective of maximizing the probability of exceeding the moving target. A decision framework is developed within compromise programming that involves minimizing a generalized distance function measuring the "distance" from an ideal point to the efficient frontier. Several examples illustrate the results.