On the product selection and plant dimensioning problem under uncertainty

A general algorithm for solving two-stage stochastic mixed 0–1 first-stage problems

“…For a brief study of the relevance of scenario cluster number choice, see Escudero et al [22]. So, the number of scenarios to consider in a given model basically depends on the dimensions of the scenario related model MIP (6). The criterion for scenario clustering in the sets, say, 1 , ... , p , wherep is the number of clusters to consider, could alternatively be based on the smallest internal deviation of the uncertain parameter, the greatest deviation, etc.…”

“…Let us introduce the elements that we use in our depth first strategy, see Alonso-Ayuso et al [6] and Sherali and Zhu [13], among others, for selecting the branching variable and the two descendant TNFs from one given, where i is the selection parameter for the -variables to branch. By convention, z TNF = +∞, for the infeasible problem LP TNF (10) related to a given TNF integer set, and z f = +∞, for the infeasible problem LP f (11).…”

“…Alonso-Ayuso et al [4], provide an efficient branch-and-fix coordination (BFC) methodology for solving two types of stochastic 0-1 problems, namely, mixed 0-1 problems for two-stage environments, where the first stage has only 0-1 variables, and pure 0-1 problems for multistage environments, where uncertainty appears only in the objective function coefficients and in the rhs. This methodology is used by Alonso-Ayuso et al [5,6] for solving such a model in production planning applications.…”

On a mixture of the fix-and-relax coordination and Lagrangian substitution schemes for multistage stochastic mixed integer programming

“…The presentation of the scheme below is an extension of the scheme presented in Alonso- Ayuso et al (2003b). See Alonso-Ayuso et al (2003a, 2005a, 2005b for applications to the two-stage mixed 0-1 problem, where the first stage is only included by 0-1 variables, Escudero et al (2007Escudero et al ( , 2009a for an application to the two-stage mixed 0-1 problem where the first stage is included by 0-1 variables and continuous variables, and Alonso-Ayuso et al (2007) for an application to the multistage pure 0-1 problem.…”

“…This circumstance allows one to use Stochastic Integer Programming (SIP) for solving multistage mixed 0-1 programs under uncertainty. It has a broad application field, mainly, in production planning (Ahmed et al 2003;Alonso-Ayuso et al 2007, 2003a, 2005a, 2005bSen 2002, 2004;MirHassani et al 2000;Santoso et al 2005), energy generation planning (Groewe-Kuska et al 2001;Hemmecke and Schultz 2001;Klein Haneveld and van der Vlerk 2001;Nürnberg and Römisch 2002;Schultz et al 2005;Takriti and Birge 2000;Triki et al 2005), finance Ziemba and Mulvey 1998), vehicle routing (Gendreau et al 1996;Laporte and Louveaux 2002), and site and road locations Hernández et al 2009), among others, see also Uryasev and Pardalos (2001), Wallace and Ziemba (2005).…”