The value of flexibility for pulp mills investing in energy efficiency and future biorefinery concepts

Changing conditions in biomass and energy markets require the pulp and paper industry to improve energy efficiency and find new opportunities in biorefinery implementation. Considering the expected changes in the pulp mill environment and the variety of potential technology pathways, flexibility should be a strong advantage for pulp mills. In this context, flexibility is defined as the ability of the pulp mill to respond to changing conditions. The aim of this article is to show the potential value of flexibility in the planning of pulp mill energy and biorefinery projects and to demonstrate how this value can be incorporated into models for optimal strategic planning of such investments. The paper discusses the requirements on the optimization models in order to adequately capture the value of flexibility. It is suggested that key elements of the optimization model are multiple points in time where investment decisions can be made as well as multiple scenarios representing possible energy price changes over time. The use of a systematic optimization methodology that incorporates these model features is illustrated by a case study, which includes opportunities for district heating cooperation as well as for lignin extraction and valorization. A quantitative valuation of flexibility is provided for this case study. The study also demonstrates how optimal investment decisions for a pulp mill today are influenced by expected future changes in the markets for energy and bioproducts

Integration of expert knowledge into radial basis function surrogate models

A current application in a collaboration between Chalmers University of Technology and Volvo Group Trucks Technology concerns the global optimization of a complex simulation-based function describing the rolling resistance coefficient of a truck tyre. This function is crucial for the optimization of truck tyres selection considered. The need to explicitly describe and optimize this function provided the main motivation for the research presented in this article. Many optimization algorithms for simulation-based optimization problems use sample points to create a computationally simple surrogate model of the objective function. Typically, not all important characteristics of the complex function (as, e.g., non-negativity)—here referred to as expert knowledge—are automatically inherited by the surrogate model. We demonstrate the integration of several types of expert knowledge into a radial basis function interpolation. The methodology is first illustrated on a simple example function and then applied to a function describing the rolling resistance coefficient of truck tyres. Our numerical results indicate that expert knowledge can be advantageously incorporated and utilized when creating global approximations of unknown functions from sample points

Optimering av underhållsplaner leder till strategier för utvecklingsprojekt

Inom många typer av industriell verksamhet, t ex process-, kraft- och flygindustri, används dyrbar produktionsutrustning som måste vara tillgänglig i mycket hög utsträckning eftersom produktionsstopp är mycket kostsamma. För att dessa industrier ska kunna maximera lönsamheten måste de kunna utnyttja produktionsstopp för att även utföra bästa möjliga förebyggande underhåll. Chalmers Matematik och Volvo Aero har tillsammans utvecklat en matematisk modell som ser till ekonomiska och funktionella samband mellan komponenter i det system som skall underhållas, samt kostnader för underhållsaktiviteter och reservdelar. En studie utförd i en verkstad för underhåll av flygmotorer vid Volvo Aero visar på en signifikant potential för kostnadsbesparingar som till stor del beror av ökade möjligheter till aktiv samordning av framtida underhåll via balansering av komponenternas livslängder. Studien har även medfört en nyttig genomlysning av systemet. Den visar att möjligheten att reducera underhållskostnader i hög grad beror på livslängderna hos de i systemet ingående komponenterna. Olika komponenter har därför olika potential för reduktion av underhållskostnader. Dessa potentialer kan beräknas genom optimering av en serie modeller där livslängden för de olika delarna – var för sig – har förlängts stegvis. På detta sätt kan optimering av underhållsplaner även utnyttjas för att skapa beslutsunderlag för val av utvecklingsprojekt som syftar till att förlänga livslängder hos enskilda komponenter

The stochastic opportunistic replacement problem: A two-stage solution approach

In Almgren et al. 2009 we studied the opportunistic replacement problem, which is a multicomponent maintenance scheduling problem with deterministic component lives. The assumption of deterministic lives is a strong simplification, but valid in applications where critical components are assigned a technical life after which replacement is enforced. Here, we study the stochastic opportunistic replacement problem, which is a more general setting in which component lives are allowed to be stochastic. We consider a stochastic programming approach for the minimization of the expected cost over the remaining planning horizon. Further, we present a means to compute lower bounds on the recourse function. The lower bounds are used in the construction of a decomposition method which extends the integer L-shaped method to incorporate stronger optimality cuts. In order to obtain a computationally tractable model, a two-stage sample average approximation scheme is utilized. Numerical experiments on problem instances from the wind power and aviation industry as well as on two test instances are performed. The results show that the decomposition method is faster than solving the deterministic equivalent on the three more complex instances out of the four instances considered. Furthermore, the numerical experiments show that decisions based on the stochastic programming approach yield a lower average total maintenance cost compared to that of decisions based on simpler maintenance

Ergodic Results In Subgradient Optimization

: Subgradient methods are popular tools for nonsmooth, convex minimization, especially in the context of Lagrangean relaxation; their simplicity has been a main contribution to their success. As a consequence of the nonsmoothness, it is not straightforward to monitor the progress of a subgradient method in terms of the approximate fulfilment of optimality conditions, since the subgradients used in the method will, in general, not accumulate to subgradients that verify optimality of a solution obtained in the limit. Further, certain supplementary information, such as convergent estimates of Lagrange multipliers, is not directly available in subgradient schemes. As a means for overcoming these weaknesses of subgradient optimization methods, we introduce the computation of an ergodic (averaged) sequence of subgradients. Specifically, we consider a nonsmooth, convex program solved by a conditional subgradient optimization scheme (of which the traditional subgradient optimization method is ..