In practice, there are many optimization problems with uncertain parameters. Liu [28] proposed uncertain programming
including expected value model, chance constrained programming and dependent-chance programming, which have been
used to model system reliability design, project scheduling problem, vehicle routing problem and facility location problem.
As far as we know, no researcher before us has investigated the single period inventory model in uncertain environment.
Thus, this paper considers a single-period inventory model where the demand is assumed to be an uncertain variable.
The goal of the model is to find the optimal order quantity to maximize the profit with respect to the expected value. Especially,
the relationship between uncertainty distribution and parameters is obtained. The main contribution of the paper is to
provide decision-makers with explicit results in practical problems or as a foundation for complex inventory management.
The rest of the paper is organized as follows. Section 2 recalls some basic concepts and results of uncertain variables. The
expected value model for the single-period inventory problem is formulated in Section 3. In Section 4 under the assumption
that demand is uncertain we derive two important results. Finally, in Section 5 some conclusions and remarks are listed