P-graph optimization of energy crisis response in Leontief systems with partial substitution

Input-output analysis is used for modelling economic networks with linear equations representing intersectoral links. These models are used extensively to determine the effects of policies and decisions, taking into account sectoral interdependencies. They have also been used to identify optimal responses to various natural or man-made disruptions. An alternative graph theoretic approach to optimizing input-output systems using P-graph has also been developed. However, that approach is limited by the restrictive assumption of the Leontief production function, where each economic sector requires an invariant set of inputs to produce each unit of output; it is assumed in the basic model that these inputs have no substitutability, since their relative proportions are determined by a fixed state of technology. Relaxing this unrealistic assumption is a critical research gap. An improved P-graph model for optimizing input-output systems with partial substitution is developed in this paper. This modelling approach is demonstrated with two case studies involving energy shortages triggered by extreme weather and by military action. Both examples show that the capacity for partial substitution makes economic systems more robust to disruptions.