The opportunistic replacement problem with individual component lives
Preprint, 2011

We consider an extension of the opportunistic replacement problem, which has been studied by Dickman, Epstein and Wilamowsky [3], Andréasson [2], and Andréasson et al. [1], that allows the individuals of the same component to have nonidentical lives. Formulating and solving this problem defines a first step towards solving the opportunistic replacement problems with uncertain component lives. We show that the problem is NP-hard even with time independent costs, and present two mixed integer linear programming models for the problem. We show that in model I the binary requirement on the majority of the variables can be relaxed; this is in contrast to model II and Andréasson’s [2] model. We remove all superfluous variables and constraints in model I and show that the remaining constraints are facet inducing. We also utilize a linear transformation of model I to obtain a stronger version of model II, model II+, that inherits the polyhedral properties of model I. Numerical experiments show that the solution time of model I is significantly lower than the solution times of both model II and Andréasson’s model. It is also somewhat lower than the solution time of model II+.

Author

Michael Patriksson

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Ann-Brith Strömberg

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Adam Wojciechowski

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Driving Forces

Sustainable development

Areas of Advance

Transport

Energy

Subject Categories

Computational Mathematics

Roots

Basic sciences