Input-Output Analysis and Linear Programming

Input-output analysis of inter-industry exchange has proved to be useful in LCA. Input-output has a long history in economics. Less known, is that input-output in fluenced

linear programming

(LP) in its early development. In fact, Input-output models can be regarded as special cases of

linear programming

problems. Linear programming is the most useful practical tool in helping us to make the best use of scarce resources when faced with complex decision problems. Firms routinely use linear programming and other optimization techniques in planning their activi ties, for example in logistics of supply chains, production scheduling, and resource allocation in general. In this chapter, we show the historical relationship of input-output analysis and linear programming. Next, we show that an input-output model is a special case of an LP formulation. Through a series of examples, we show how an LP formulation more generally can tackle situations with multifunctional units and multiple technologies. Furthermore, we show how a detailed LP model of an industry sector can be linked with an aggregated IO model. The last section of this chapter provides a brief survey of applications where LCA and input-output analysis has been integrated with optimization models.