An investigation of free vibrations of a strain gradient Timoshenko beams with the method of initial values

Investigated herein is the free vibrations of beams based on the strain gradient Timoshenko beam theory with the method of initial values. For the vibration of strain-gradient Timoshenko beam (SGTB), the sixth-order ordinary differential equation and three boundary conditions at each end have been obtained by using the Hamilton principle. The effect of the characteristic length on the frequencies of free vibrations is shown. The frequencies of the SGTB are compared to the frequencies of the strain gradient Euler beam (SGEB), classical Timoshenko beam (CTB) and classical Euler beam (CEB). It has been observed that the high-frequency values of conventional and strain-gradient beams are very different. This result can be used to determine the value of the material characteristic length for a nanobeam for which lengthscale effects are believed to be dominant.

     

Heuristics for capacity planning problems with congestion

Motivated by a problem in the semiconductor industry, we develop improved formulations for the problem of planning capacity acquisition and deletion over time when resources are subject to congestion, motivated by a problem in the semiconductor industry. We use nonlinear clearing functions to relate the expected output of a production resource in a planning period to the expected work in process (WIP) inventory level. Exploiting the properties of the clearing function allows us to formulate the single workcenter problem as a shortest path problem. This forms the basis for two greedy constructive heuristics and a Lagrangian heuristic for the multistage problem. The latter procedure also provides lower bounds on the optimal value. We present computational experiments showing that the proposed heuristics obtain high-quality solutions in modest CPU times.     

Sulfur dioxide adsorption by activated carbons having different textural and chemical properties

Activated carbons from Turkish lignite were prepared with different methods to investigate the influence of physico-chemical characteristics of the carbon materials on the sulfur dioxide (SO₂) adsorption. The effects of SO₂ concentration, adsorption temperature, and sample particle size on adsorption were investigated using a thermogravimetric analysis system. An intraparticle diffusion model based on Knudsen diffusion and Freundlich isotherm (or Henry isotherm) was applied for predicting the amount of SO₂ adsorbed. The textural and chemical properties of the activated carbon samples, resulted from the effects of activation conditions and demineralization of the carbon precursor, on the SO₂ adsorption were also analyzed.     

A problem reduction approach for scheduling semiconductor wafer fabrication facilities

Most scheduling procedures used in industry are based on the dispatching paradigm, where decisions are made based on the jobs available at the time the machine becomes free. While optimization-based scheduling procedures have repeatedly been shown to yield significantly better schedules under ideal circumstances, their practical implementation is hampered by high computational requirements. We present a problem reduction procedure that allows a workcenter-based global scheduling heuristic to be implemented in very low CPU times. The procedure partitions the workcenters in a fab into heavily loaded and lightly loaded classes and solves the global scheduling problem only for the heavily loaded workcenters. The proposed technique is tested on instances drawn from an International SEMATECH wafer fab model. The proposed problem reduction approach yields superior results with modest computational effort, enabling the practical use of the decomposition heuristic.     

Stepwise demineralisation and chemical isolation of the mineral matter of Göynük lignite

The mineral matter of coal contains a number of inorganic constituents, which play an important role in almost all coal utilisation systems. Some techniques have been applied to coal to separate its mineral matter from its organic part. In this study, an alternative method was applied to separate the mineral matter content of a Turkish lignite. For this purpose, Göynük lignite was treated, in sequence, with acetic acid, ammonia, hydrochloric acid, hydrofluoric acid and nitric acid at 70°C for 60 min in order to remove individual mineral species. After each stage, the lignite was treated with performic acid, the product of reaction between hydrogen peroxide and formic acid, at 50°C. The organic coal matrix was decomposed as a result of performic acid oxidation, and consequently, the recovered mineral species were isolated. Ammonia, which has the potential of chemical comminution, was used to increase the effects of the subsequent reagents and enhance the extent of separation between the organic and inorganic phases. In each mineral matter removal stage, the lignite was treated with the reagents of the previous stage, and then, a new reagent was added to investigate whether the last stage has a different effect on the mineral species. FT-IR and X-ray diffractometry techniques were used to determine the constituents of the isolated mineral matter after each stage.     

The impact of lot-sizing in multiple product environments with congestion

We present a production planning model for a multiple product single machine dynamic lot-sizing problem with congestion. Using queuing models, we develop a set of functions to capture the nonlinear relationship between the output, lot sizes and available work in process inventory levels of all products in the system. We then embed these functions in a nonlinear optimization model with continuous variables, and construct an approximate solution to the original problem by rounding the resulting fractional solution. Computational experiments show that our model with congestion provides significantly better flow time and inventory performance than a benchmark model that does not consider the effects of congestion. These advantages arise from the use of multiple smaller lots in a period instead of a single large lot as suggested by conventional fixed-charge models without congestion.     

A single-product network design model with lead time and safety stock considerations

Most existing network design and facility location models have focused on the trade-off between the fixed costs of locating facilities and variable transportation costs between facilities and customers. However, operational performance measures such as service levels and lead times are what motivates customers to bring business to a company and should be considered in the design of a distribution network. While some previous work has considered lead times and safety stocks separately, they are closely related in practice, since safety stocks are often set relative to the distribution of demand over the lead time. In this paper we consider a two-stage supply chain with a production facility that replenishes a single product at retailers. The objective is to locate Distribution Centers (DCs) in the network such that the sum of the location and inventory (pipeline and safety stock) costs is minimized. The replenishment lead time at the DCs depends on the volume of flow through the DC. We require the DCs to carry enough safety stock to maintain the prescribed service levels at the retailers they serve. The explicit modeling of the relationship between the flows in the network, lead times and safety stocks allows us to capture the trade-off between them. We develop a Lagrangian heuristic to obtain near-optimal solutions with reasonable computational requirements for large problem instances.