The fit-gap analysis of enterprise applications allows to identify their customization needs during implementation at a company. The enterprise applications provide a set of customization tools and customization flexibility is affected by a deployment mode. The on-premise deployment requires effort to install the application and its updates while there are a few restrictions on depths and breath of customization. The cloud deployment of Software as a Service applications is easier to setup while there are some restrictions of kind of customizations made. This paper elaborates an optimization model to select an enterprise application customization strategy as a part of the fit-gap analysis in the case of the choice between on-premise and cloud deployment of the enterprise application. The model also takes into account newly released standard features provided by the vendor of the enterprise applications. The model analysis is performed to investigate factors affecting the choice between on-premise and cloud deployment and an impact of company’s customization preferences on the gaps resolution strategy. An application example is also provided.