Platform as a Service (PaaS) is the correct choice because it provides a complete development and deployment environment in the cloud, without the need for the client to manage the underlying infrastructure such as servers, storage, or operating systems. This allows the company to focus on the deployment and management of their applications only.

Infrastructure as a Service (IaaS) would be incorrect because it provides virtualized computing resources over the internet and the customer is still responsible for managing the servers and operating systems. Software as a Service (SaaS) would also be incorrect because it refers to cloud-based software that is provided on a subscription basis and is managed entirely by the service provider, which does not fit the scenario where a company wants to deploy its own application. An in-house data center would not qualify as a cloud service model and would involve managing the entire IT infrastructure on-premises.