32 research outputs found
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)âhere referred to as expert knowledgeâare 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
Efficient solution of many instances of a simulation-based optimization problem utilizing a partition of the decision space
Optimering av underhÄllsplaner leder till strategier för utvecklingsprojekt
Inom mÄnga typer av industriell verksamhet, t ex process-, kraft- och flygindustri, anvÀnds dyrbar produktionsutrustning som mÄste vara tillgÀnglig i mycket hög utstrÀckning eftersom produktionsstopp Àr mycket kostsamma. För att dessa industrier ska kunna maximera lönsamheten mÄste de kunna utnyttja produktionsstopp för att Àven utföra bÀsta möjliga förebyggande underhÄll.
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 underhÄllas, samt kostnader för underhÄllsaktiviteter och reservdelar. En studie utförd i en verkstad för underhÄll av flygmotorer vid Volvo Aero visar pÄ en signifikant potential för kostnadsbesparingar som till stor del beror av ökade möjligheter till aktiv samordning av framtida underhÄll via balansering av komponenternas livslÀngder.
Studien har Ă€ven medfört en nyttig genomlysning av systemet. Den visar att möjligheten att reducera underhĂ„llskostnader i hög grad beror pĂ„ livslĂ€ngderna hos de i systemet ingĂ„ende komponenterna. Olika komponenter har dĂ€rför olika potential för reduktion av underhĂ„llskostnader. Dessa potentialer kan berĂ€knas genom optimering av en serie modeller dĂ€r livslĂ€ngden för de olika delarna â var för sig â har förlĂ€ngts stegvis. PĂ„ detta sĂ€tt kan optimering av underhĂ„llsplaner Ă€ven utnyttjas för att skapa beslutsunderlag för val av utvecklingsprojekt som
syftar till att förlÀnga livslÀngder 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 ..