Health services are organized in remarkably diverse ways and yet manage to produce comparable outcomes. Countries should build on the strengths of their own systems, rather than feel pressure to adopt health service organization models imported from elsewhere. Most countries have centralized and decentralized elements that coexist and generally are embedded in a wider governance and political economy context. Efforts to use decentralization to improve health outcomes succeed when they build organizational capacity to exercise newfound decision rights and ensure robust accountability systems. The private sector encompasses a diverse set of actors that play a critical role in delivering health services but that are often inappropriately neglected in public policy and planning efforts. There is no one perfect model of care, the best ones are adaptable and evolve to address shifting epidemiological patterns, emerging threats such as pandemics, and climate change. Addressing the organization and management of health services inevitably involves a focus on supply-side factors, but demand-side considerations play a critical role in improving health outcomes and cannot be ignored.

In this chapter, we introduce linear programming. We start with a simple algebra problem that can be modeled as a system of equations. However, that problem has no solution, so we modify the model to make it more realistic. The result is a standard form linear programming problem. This shows how linear programming arises naturally from the modeling process. Next, we show how to solve these problems in the case when there are two decision variables by the standad graphical technique, which we call graphing in the decision space. This leads naturally to a discussion of the corner point theorem. Finally, we exhibit an alternate graphical approach to solving these problems in the case when there are just two constraints but an arbitrary number of decision variables. We call this method graphing in the constraint space. This technique is a feature of this text; it is not covered in most texts. It is based on linear combinations of vectors in a plane and basic solutions to systems of linear equations, and it sets the stage for the simplex algorithm in Chapter 5.