Material stochastic programming

Chemical process systems are subject to uncertainties due to many random events such as raw material variations, demand fluctuations, equipment failures, and so on. In this chapter we will utilize stochastic programming (SP) methods to deal with these uncertainties that are typically employed in computational finance applications. These methods have been very useful in screening alternatives on the basis of the expected value of economic criteria as well as the economic and operational risks involved. Several approaches have been reported in the literature addressing the problem of production planning under uncertainty. Extensive reviews surveying various issues in this area can be found in Applequist et al. (1997), Shah (1998), Cheng, Subrahmanian, and Westerberg (2005) and Mendez et al. (2006). 

The majority of the tools proposed are deterministic, although some can be extended to expectations on profit distributions and therefore decision trees are presented as advanced material in introductory finance books. Quite clearly, one would benefit from using two-stage stochastic programming instead. 

Optimization of decentralized control supply chain logistics planning under uncertain environment is studied in the book. On the basis of conception of supply chain cell, the uncertainty of price factor of up/downstream materials of nodal enterprises is taken into consideration and stochastic chance constrained programming model of integrated logistics planning for decentralized control... 

The three-pulse EOM-PMA can be formulated not only in terms of density matrices and master equations but also in terms of wavefunctions and Schrodinger equations [29]. The EOM-PMA can therefore be straightforwardly incorporated into computer programs which provide the time evolution of the density matrix or the wavefunction of material systems. Besides the multilevel Redlield theory, the EOM-PMA can be combined with the Lindblad master equation [49], the surrogate Hamiltonian approach [49], the stochastic Liouville equation [18], the quantum Fokker-Planck equation [18], and the density matrix [50] or the wavefunction [14] multiconfigurational time-dependent Hartree (MCTDH) methods. When using the... 

---