Solution approaches for the cutting stock problem with setup cost

In this paper, we study the Cutting Stock Problem with Setup Cost (CSP-S) which is a more general case of the well-known Cutting Stock Problem (CSP). In the classical CSP, one wants to minimize the number of stock items used while satisfying the demand for smaller-sized items. However, the number of patterns/setups to be performed on the cutting machine is ignored. In most cases, one has to find the trade-off between the material usage and the number of setups in order to come up with better production plans. In CSP-S, we have different cost factors for the material and the number of setups, and the objective is to minimize total production cost including both material and setup costs. We develop a mixed integer linear program and analyze a special case of the problem. Motivated by this special case, we propose two local search algorithms and a column generation based heuristic algorithm. We demonstrate the effectiveness of the proposed algorithms on the instances from the literature.     

Dynamic tensile testing of fabric–cement composites

Dynamic tensile tests were conducted using a high speed servo-hydraulic testing machine on three types of fabric reinforced cement composites. The high speed testing procedure and data processing method are presented. Quasi-static tests were also conducted on the composites. Effects of strain rate on the mechanical properties of fabric–cement composites are noted. A good correlation was found between the properties of the fabrics and the composites, with the carbon fabric exhibiting the highest strength and ductility performance in high speed tensile tests. The differences in tensile behavior of the various composites were correlated with the differences in the role of the fabric materials. Composites tested under high speed loading exhibited different responses as compared to similar composites tested under quasi-static condition.     

Preparation of Silane-Grafted and Moisture Cross-Linked Low Density Polyethylene: Part I: Factors Affecting Performance of Grafting and Cross-Linking

In the present work, the silane grafting and water cross-linking of low density polyethylene (LDPE) were investigated. The grafting reaction was carried out in an internal mixer and polyethylene cross-linking was done in hot water. The effect of silane, peroxide, catalyst, carbon black, cross-linking time, and cross-linking temperature on the grafting and cross-linking processes are reported. Vinyl trimethoxy silane (VTMO) and di-cumyl peroxide (DCP) were selected as grafting agent and initiator respectively. Silane grafting on polyethylene was determined using Fourier transform infrared (FTIR) spectroscopy and torque monitoring of the mixer. Absorption peak due to –Si–OCH₃ groups in FTIR and torque increasing due to silane grafting in the mixer illustrated that silane-grafting reactions occurred. The FTIR data demonstrated that the extent of silane grafting was increased as the concentration of silane and peroxide was increased. Thermogravimetry analysis (TGA) determined that the thermal stability of LDPE increased by increasing the amount of silane grafting. Gel fraction increased with silane and peroxide concentration. As the percent of of catalyst increase the time scale for specified gel content shifted to shorter times. Incorporation of carbon black into LDPE decreased the extent of silane grafting and gel fraction. Water temperature increasing in cross-linking stage reduced the time to maximum degree of cross-linking.     

Integer-based constellation-shaping method for PAPR reduction in OFDM systems

In this paper, the problem of reducing the peak-to-average-power ratio (PAPR) in an orthogonal frequency-division multiplexing system is considered. We design a cubic constellation, called the Hadamard constellation, whose boundary is along the bases defined by the Hadamard matrix in the transform domain. Then, we further reduce the PAPR by applying the selective-mapping technique. The encoding method, following the method introduced in the work of Kwok, is derived from a decomposition known as the Smith normal form. This new technique offers a PAPR that is significantly lower than those of the best-known techniques without any loss in terms of energy and/or spectral efficiency, and without any side information being transmitted. Moreover, it has a low computational complexity.     

Fairness in Multiuser Systems With Polymatroid Capacity Region

For a wide class of multiuser systems, a subset of capacity region which includes the corner points and the sum-capacity facet has a special structure known as polymatroid. Multiple-access channels with fixed input distributions and multiple-antenna broadcast channels are examples of such systems. Any interior point of the sum-capacity facet can be achieved by time-sharing among corner points or by an alternative method known as rate-splitting. The main purpose of this paper is to find a point on the sum-capacity facet which satisfies a notion of fairness among the active users. This problem is addressed in two cases: (i) where the complexity of achieving interior points is not feasible, and (ii) where the complexity of achieving interior points is feasible. For the first case, the corner point for which the minimum rate of the active users is maximized is desired. A simple greedy algorithm is introduced to find such an optimum corner point. In addition, it is shown for single-antenna Gaussian multiple-access channels, the resulting corner point is leximin maximal with respect to the set of the corner points. For the second case, the properties of the unique leximin maximal rate vector with respect to the polymatroid are reviewed. It is shown that the problems of deriving the time-sharing coefficients or rate-splitting scheme to attain the leximin maximal vector can be solved by decomposing the problem into some lower dimensional subproblems. In addition, a fast algorithm to compute the time-sharing coefficients to attain a general point on the sum-capacity facet is presented.     

Correlation of tensile and flexural responses of strain softening and strain hardening cement composites

Closed form equations for generating moment–curvature response of a rectangular beam of fiber reinforced concrete are presented. These equations can be used in conjunction with crack localization rules to predict flexural response of a beam under four point bending test. Parametric studies simulated the behavior of two classes of fiber reinforced concrete: strain softening and strain hardening materials. The simulation revealed that the direct use of uniaxial tension and compression responses under-predicted the flexural response for strain softening material while a good prediction for strain hardening material was obtained. The importance of strain softening range on the flexural response is discussed using non-dimensional post-peak parameters. Results imply that the brittleness and size effect are more pronounced in the flexural response of brittle materials, while more accurate predictions are obtained with ductile materials. It is also demonstrated that correlations of tensile and flexural results can be established using normalized uniaxial tension and compression models with a single scaling factor.