Flow-shop scheduling with a learning effect

The paper is devoted to some flow-shop scheduling problems with a learning effect. The objective is to minimize one of the two regular performance criteria, namely, makespan and total flowtime. A heuristic algorithm with worst-case bound m for each criteria is given, where m is the number of machines. Furthermore, a polynomial algorithm is proposed for both of the special cases: identical processing time on each machine and an increasing series of dominating machines. An example is also constructed to show that the classical Johnson's rule is not the optimal solution for the two-machine flow-shop scheduling to minimize makespan with a learning effect. Some extensions of the problem are also shown.     

Internal modification of poly(dimethylsiloxane) microchannels with a borosilicate glass coating

We report on an original technique for the in situ coating of poly(dimethylsiloxane) (PDMS) microchannels with borosilicate glass, starting from an active nonaqueous and alkali-free precursor solution. By chemical reaction of this active solution inside the microchannel and subsequent thermal annealing, a protective and chemically inert glass borosilicate coating is bonded to the PDMS. Attenuated total reflectance Fourier transform infrared (ATR-FTIR) spectroscopy and nuclear magnetic resonance spectroscopy of the active solution show that it is composed of a silicon oxide network with boron connectivity. Thermal gravimetric analysis demonstrates the absence of organic content when curing is done above 150 degrees C. The borosilicate nature of the glass coating covalently bonded to the PDMS is demonstrated using ATR-FTIR spectroscopy and X-ray photoelectron spectroscopy. Atomic force microscopy and scanning electron microscopy show a smooth and crack-free coating. The latter is used as an efficient protective barrier against diffusion in PDMS of fluorescent rhodamine B dye that is dissolved either in water or in toluene. Moreover, the coating prevents swelling and consequent structural damage of the PDMS when the latter is exposed to harsh chemicals such as toluene.     

Stochastic variational inequalities: single-stage to multistage

Variational inequality modeling, analysis and computations are important for many applications, but much of the subject has been developed in a deterministic setting with no uncertainty in a problem’s data. In recent years research has proceeded on a track to incorporate stochasticity in one way or another. However, the main focus has been on rather limited ideas of what a stochastic variational inequality might be. Because variational inequalities are especially tuned to capturing conditions for optimality and equilibrium, stochastic variational inequalities ought to provide such service for problems of optimization and equilibrium in a stochastic setting. Therefore they ought to be able to deal with multistage decision processes involving actions that respond to increasing levels of information. Critical for that, as discovered in stochastic programming, is introducing nonanticipativity as an explicit constraint on responses along with an associated “multiplier” element which captures the “price of information” and provides a means of decomposition as a tool in algorithmic developments. That idea is extended here to a framework which supports multistage optimization and equilibrium models while also clarifying the single-stage picture.     

Multivariate Epi-splines and Evolving Function Identification Problems

The broad class of extended real-valued lower semicontinuous (lsc) functions on ? ⁿ captures nearly all functions of practical importance in equation solving, variational problems, fitting, and estimation. The paper develops piecewise polynomial functions, called epi-splines, that approximate any lsc function to an arbitrary level of accuracy. Epi-splines provide the foundation for the solution of a rich class of function identification problems that incorporate general constraints on the function to be identified including those derived from information about smoothness, shape, proximity to other functions, and so on. As such extrinsic information as well as observed function and subgradient values often evolve in applications, we establish conditions under which the computed epi-splines converge to the function we seek to identify. Numerical examples in response surface building and probability density estimation illustrate the framework.     

Zero field splitting of the chalcogen diatomics using relativistic correlated wave-function methods

The spectrum arising from the (π*)(2) configuration of the chalcogen dimers, namely, the X(2)1, a2, and b0(+) states, is calculated using wave-function theory based methods. Two-component (2c) and four-component (4c) multireference configuration interaction (MRCI) and Fock-space coupled cluster (FSCC) methods are used as well as two-step methods spin-orbit complete active space perturbation theory at 2nd order (SO-CASPT2) and spin-orbit difference dedicated configuration interaction (SO-DDCI). The energy of the X(2)1 state corresponds to the zero-field splitting of the ground state spin triplet. It is described with high accuracy by the 2- and 4-component methods in comparison with experiment, whereas the two-step methods give about 80% of the experimental values. The b0(+) state is well described by 4c-MRCI, SO-CASPT2, and SO-DDCI, but FSCC fails to describe this state and an intermediate Hamiltonian FSCC ansatz is required. The results are readily rationalized by a two-parameter model; Δε, the π* spinor splitting by spin-orbit coupling and K, the exchange integral between the π(1)* and the π(-1)* spinors with, respectively, angular momenta 1 and -1. This model holds for all systems under study with the exception of Po(2).     

An isomerization-induced cage-breaking process in a molecular glass former below T(g)

A recent experimental [P. Karageorgiev, D. Neher, B. Schulz, B. Stiller, U. Pietsch, M. Giersig, L. Brehmer, Nature Mater. 4, 699 (2005)] study has found liquidlike diffusion below the glass-transition temperature in azobenzene-containing materials under irradiation. This result suggests that the isomerization-induced massive mass transport that leads to surface relief gratings formation in these materials, is induced by this huge increase of the matrix diffusion coefficient around the probe. In order to investigate the microscopic origin of the increase of the diffusion, we use molecular dynamics simulations of the photoisomerization of probe dispersed red 1 molecules dispersed inside a glassy molecular matrix. Results show that the increased diffusion is due to an isomerization-induced cage-breaking process. A process that explains the induced cooperative motions recently observed in these photoactive materials.     

Probabilistic bounds (via large deviations) for the solutions of stochastic programming problems

Several exponential bounds are derived by means of the theory of large deviations for the convergence of approximate solutions of stochastic optimization problems. The basic results show that the solutions obtained by replacing the original distribution by an empirical distribution provides an effective tool for solving stochastic programming problems.Supported in part by a grant from the US-Israel Science Foundation.     

Convergence of set-valued mappings: Equi-outer semicontinuity

The concept of equi-outer semicontinuity allows us to relate the pointwise and the graphical convergence of set-valued-mappings. One of the main results is a compactness criterion that extends the classical Arzelà-Ascolì theorem for continuous functions to this new setting; it also leads to the exploration of the notion of continuous convergence. Equi-lower semicontinuity of functions is related to the outer semicontinuity of epigraphical mappings. Finally, some examples involving set-valued mappings are re-examined in terms of the concepts introduced here.Research supported in part by a grant of the National Science Foundation.     

Production planning via scenario modelling

Several Linear Programming (LP) and Mixed Integer Programming (MIP) models for the production and capacity planning problems with uncertainty in demand are proposed. In contrast to traditional mathematical programming approaches, we use scenarios to characterize the uncertainty in demand. Solutions are obtained for each scenario and then these individual scenario solutions are aggregated to yield a nonanticipative or implementable policy. Such an approach makes it possible to model nonstationarity in demand as well as a variety of recourse decision types. Two scenario-based models for formalizing implementable policies are presented. The first model is a LP model for multi-product, multi-period, single-level production planning to determine the production volume and product inventory for each period, such that the expected cost of holding inventory and lost demand is minimized. The second model is a MIP model for multi-product, multi-period, single-level production planning to help in sourcing decisions for raw materials supply. Although these formulations lead to very large scale mathematical programming problems, our computational experience with LP models for real-life instances is very encouraging.     

Single-machine scheduling to minimize total absolute differences in waiting times with deteriorating jobs

In this paper we consider a single-machine scheduling problem with simple linear deterioration. By simple linear deterioration, we mean that the processing time of a job is a simple linear function of its execution starting time and its deterioration rate. The objective is to find a schedule that minimizes total absolute differences in waiting times. We show that the optimal schedule is V-shaped: jobs are arranged in descending order of their deterioration rates if they are placed before the job with the smallest deterioration rate, but in ascending order of their deterioration rates if placed after it. We prove other several properties of an optimal schedule, and introduce two efficient heuristic algorithms that are tested against a lower bound. We also provide computational results to evaluate the performance of the heuristic algorithms.