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Inventory management (IM) is an important area in logistics. The goal is to manage the inventory of a vendor as efficiently as possible. Its practical relevance also makes it an important real-world application for research in optimization. Because inventory must be managed over time IM optimization problems are dynamic and online (i.e. they must be solved as time goes by). Dynamic optimization is typically harder than non-dynamic optimization. Much research in IM is devoted to finding specific algorithms that solve specific abstractions. For each new aspect to be taken into account, a new algorithm must be designed. In this paper, we aim at a more general approach. We employ general insights into online dynamic problem solving. A recently proposed framework is also employed. We point out how IM problems can be solved in a much more general fashion using evolutionary algorithms (EAs). Here, time-dependence (i.e. decisions taken now have consequences in the future) is an important practical type of problem difficulty that is characteristic of practical dynamic optimization problems. Time-dependence is usually not taken into account in the literature and myopic (i.e. blind to future events) algorithms are often designed. We show that time- dependence is automatically tackled by our novel approach. We extend the common definition of IM problems with time- dependence by introducing customer satisfaction. We show that customer satisfaction for IM problems with superior solutions can be achieved when this form of time-dependence is properly taken into account. This also demonstrates our conclusion that taking into account the existence of time-dependence in practical online dynamic optimization problems such as IM is very important.