An efficient linear programming model and optimization algorithm for trigeneration

Trigeneration is a booming technology for efficient and clean provision of energy. It has potential for reducing pollution emissions dramatically. Similar to combined heat and power (CHP) production, cost-efficient operation of a trigeneration system can be planned using an optimization model based on hourly load forecasts. A long-term planning model decomposes into thousands of hourly models, which can be solved separately. In this paper, we model the hourly trigeneration problem as a linear programming (LP) model with a joint characteristic for three energy components to minimize simultaneously the production and purchase costs of three energy components, as well as CO ₂ emissions costs. Then we explore the structure of the problem and propose the specialized Tri-Commodity Simplex (TCS) algorithm that employs this structure efficiently. The speed of TCS is based on extremely fast basis inverse operations and reuse of old basic solutions from previously solved hourly models. We compare the performance of TCS with realistic models against an efficient sparse Simplex code using the product form of inverse. In test runs, TCS is from 36 to 58 times faster when starting from the initial basis and from 43 to 179 times faster when reusing the old basis.