Problems of an additional experiment

In some situations estimates of unknown parameters must be corrected by additional measurements. It is in principle no problem to calculate the corrected estimates, however, it is of more interest to find formulae for correction itself. The formulae enable us to design an additional experiment and to judge its usefulness. The aim of the paper is to find such formulae for several situations. Supported by the grant of the Council of Czech Government MSM 6 198 959 214.     

A note on generalized averaged Gaussian formulas

We have recently proposed a very simple numerical method for constructing the averaged Gaussian quadrature formulas. These formulas exist in many more cases than the real positive Gauss–Kronrod formulas. In this note we try to answer whether the averaged Gaussian formulas are an adequate alternative to the corresponding Gauss–Kronrod quadrature formulas, to estimate the remainder term of a Gaussian rule.     

Mixing characteristics of motionless mixers

Motionless mixers have found a large range of applications, including blending, reaction, dispersion, heat transfer and mass transfer. Understanding the mixing processes that occur in these diverse systems is essential for predicting many aspects of practical importance. The objective of this study is to perform the experimental investigations of mixing characteristics for three different motionless mixers. The red color dye tracer was mixed in the main stream of green hair styling gel, and then the mixing efficiency was quantified by calculating the percentage area concentration of red color at the outlet cross section using a digital image processing technique. In the Sulzer SMX and YHC mixer, a single element mixes the fluid nearly in two dimensions, and three-dimensional mixing is accomplished by the next elements aligned at 90o to their former one. In the Sulzer SMX mixer, the flow appears to be globally well mixed after 5 elements, while in the YHC and YNU mixers, it is necessary to globally well mix more than 1 and 2 elements.     

A tabu search heuristic for solving the CLSP with backlogging and set-up carry-over

In this paper, the multi-item, single-level, capacitated, dynamic lot sizing problem with set-up carry-over and backlogging, abbreviated to CLSP⁺, is considered. The problem is formulated as a mixed integer programming problem. A heuristic method consisting of four elements: (1) a demand shifting rule, (2) lot size determination rules, (3) checking feasibility conditions and (4) set-up carry-over determination, provides us with an initial feasible solution. The resulting feasible solution is improved by adopting the corresponding set-up and set-up carry-over schedule and re-optimizing it by solving a minimum-cost network flow problem. Then the improved solution is used as a starting solution for a tabu search procedure, with the value of moves assessed using the same minimum-cost network problem. Computational results on randomly generated problems show that the algorithm, which is coded in C++, is able to provide optimal solutions or solutions extremely close to optimal. The computational efficiency makes it possible to solve reasonably large problem instances routinely on a personal computer.     

Traces of functions with a dominating mixed derivative in ℝ<Superscript>3</Superscript>

We investigate traces of functions, belonging to a class of functions with dominating mixed smoothness in ℝ³, with respect to planes in oblique position. In comparison with the classical theory for isotropic spaces a few new phenomenona occur. We shall present two different approaches. One is based on the use of the Fourier transform and restricted to p = 2. The other one is applicable in the general case of Besov-Lizorkin-Triebel spaces and based on atomic decompositions.     

Fractional extensions of some boundary value problems in oil strata

In the present paper, we solve three boundary value problems related to the temperature field in oil strata — the fractional extensions of the incomplete lumped formulation and lumped formulation in the linear case and the fractional generalization of the incomplete lumped formulation in the radial case. By using the Caputo differintegral operator and the Laplace transform, the solutions are obtained in integral forms where the integrand is expressed in terms of the convolution of some auxiliary functions of Wright function type. A generalization of the Laplace transform convolution theorem, known as Efros’ theorem is widely used.     

Allocation of jobs and identical resources with two pooling centers

We examine the resource allocation problem of partitioning identical servers into two parallel pooling centers, and simultaneously assigning job types to pooling centers. Each job type has a distinct Poisson arrival rate and a distinct holding cost per unit time. Each pooling center becomes a queueing system with an exponential service time distribution. The goal is to minimize the total holding cost. The problem is shown to be polynomial if a job type can be divided between the pooling centers, and NP-hard if dividing job types is not possible. When there are two servers and jobs cannot be divided, we demonstrate that the two pooling center configuration is rarely optimal. A heuristic which checks the single pooling center has an upper bound on the relative error of 4/3. The heuristic is extended for the multiple server problem, where relative error is bounded above by the number of servers.      

Impact of demand uncertainty on coordinating supply chain inventories through common replenishment epochs

Prior studies have shown that inventories in a one vendor, multi-buyer supply chain with deterministic demands can be coordinated effectively through the use of common replenishment epochs (CRE). In this paper, we study the impact of demand uncertainty on the effectiveness of coordinating such a supply chain. We develop a model to analyse the coordination mechanism using CRE in a one-vendor, multi-buyer supply chain, when the demand faced by the buyers is stochastic. Our numerical study based on the model found that coordination through CRE may not always be beneficial when the demand variance is high. We also investigate a strategy of advance order processing by the vendor to improve the effectiveness of coordination through CRE.     

ASYMPTOTIC APPROXIMATION METHOD AND ITS CONVERGENCE ON SEMI-INFINITE PROGRAMMING

The aim of this article is to discuss an asymptotic approximation model and its convergence for the minimax semi-infinite programming problem. An asymptotic surrogate constraints method for the minimax semi-infinite programming problem is presented by making use of two general discrete approximation methods. Simultaneously, the consistence and the epi-convergence of the asymptotic approximation problem are discussed.