A model for optimization of process integration investments under uncertainty Elin Svensson a, * , Ann-Brith Strömberg b , Michael Patriksson b a Heat and Power Technology, Department of Energy and Environment, Chalmers University of Technology, SE-412 96 Göteborg, Sweden b Department of Mathematical Sciences, Chalmers University of Technology and Department of Mathematical Sciences, University of Gothenburg, SE-412 96 Göteborg, Sweden article info Article history: Received 23 September 2010 Received in revised form 8 February 2011 Accepted 9 February 2011 Available online 21 March 2011 Keywords: Process integration Multistage stochastic programming Mixed-integer linear programming Scenario-based modelling Decision support Investment planning abstract The long-term economic outcome of energy-related industrial investment projects is difficult to evaluate because of uncertain energy market conditions. In this article, a general, multistage, stochastic programming model for the optimization of investments in process integration and industrial energy technologies is proposed. The problem is formulated as a mixed-binary linear programming model where uncertainties are modelled using a scenario-based approach. The objective is to maximize the expected net present value of the investments which enables heat savings and decreased energy imports or increased energy exports at an industrial plant. The proposed modelling approach enables a long-term planning of industrial, energy-related investments through the simultaneous optimization of immediate and later decisions. The stochastic programming approach is also suitable for modelling what is possibly complex process integration constraints. The general model formulation presented here is a suitable basis for more specialized case studies dealing with optimization of investments in energy efficiency. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction 1.1. Background Through electricity production, fuel imports, and district heat- ing cooperation, industrial plants are closely connected with the constantly changing energy market. Energy investments are often capital-intensive with long expected lifetimes during which the energy market conditions are very likely to change, especially considering the assumed adoption of more stringent greenhouse gas targets and renewable policy. The long-term economic outcome of energy-related investment projects is thus difficult to evaluate. A systematic approach for optimization of process integration and other energy efficiency investments, considering explicitly the energy market uncertainties, is therefore needed. Because of the difficulty of evaluating the options, there is, otherwise, a risk that no investments are made with the consequence of lost reductions in energy costs and CO 2 emissions. Several recent studies dealing with energy-related investment decisions confirm the importance of accounting for uncertainty and timing, see e.g. [1e5]. These studies all rely on the theory of real options [6]. The real options problem can be solved using methods such as dynamic programming or valuation by arbitrage. The optimization model presented in this article is also used to solve what is essentially a real options problem, but using a method based on stochastic programming. In a stochastic programming approach, the uncertainties are explicitly incorporated into the optimization model and it is assumed, as in reality, that investments are made before the outcome of the uncertain parameters is revealed, see e.g. [7e11]. The objective is to maximize the expected net present value of the investments over all future scenarios. The multistage modelling approach provides a way to plan the process integration projects from a long-term perspective since decisions made now will affect the opportunities for later improvements of overall plant energy efficiency. The main reason for the choice of a stochastic programming approach is that we are not only dealing with a choice between a limited set of different investment options. Heat savings in industry can be achieved through a variety of process integration and other energy efficiency measures, such as improved heat exchange, integration of combined heat and power units, or heat pumping. There are, however, limitations on whether and how different measures can be combined. We therefore also need numerous, sometimes complex constraints to model these, often site-specific, process integration aspects. For this purpose, stochastic programming is in this context considered to be the best approach. For a discussion about the link between stochastic programming and real options theory, see e.g. [12]. * Corresponding author. Tel.: þ46 31 772 3016; fax: þ46 31 821 928. E-mail addresses: elin.svensson@chalmers.se (E. Svensson), anstr@chalmers.se (A.-B. Strömberg), mipat@chalmers.se (M. Patriksson). Contents lists available at ScienceDirect Energy journal homepage: www.elsevier.com/locate/energy 0360-5442/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2011.02.013 Energy 36 (2011) 2733e2746