Browsing by Subject "Performance bounds"
Now showing 1 - 3 of 3
Results Per Page
Sort Options
Item Open Access Beyond Nyquist sampling: a cost-based approach(Optical Society of America, 2013) Özçelikkale, A.; Özaktaş, Haldun M.A sampling-based framework for finding the optimal representation of a finite energy optical field using a finite number of bits is presented. For a given bit budget, we determine the optimum number and spacing of the samples in order to represent the field with as low error as possible. We present the associated performance bounds as trade-off curves between the error and the cost budget. In contrast to common practice, which often treats sampling and quantization separately, we explicitly focus on the interplay between limited spatial resolution and limited amplitude accuracy, such as whether it is better to take more samples with lower amplitude accuracy or fewer samples with higher accuracy. We illustrate that in certain cases sampling at rates different from the Nyquist rate is more efficient.Item Open Access Minimizing schedule length on identical parallel machines: an exact algorithm(Bilkent University, 1991) Akyel, H. CemalThe primary concern of this study is to investigate the combinatorial aspects of the single-stage identical parallel machine scheduling problem and to develop a computationally feasible branch and bound algorithm for its exact solution. Although there is a substantial amount of literature on this problem, most of the work in this area is on the development and performance analysis of approximation algorithms. The few optimizing algorithms proposed in the literature have major drawbacks from the computer implementation point of view. Even though the single-stage scheduling problem is known to be unary A/’P-hard, there is still a need to develop a computationally feasible optimizing algorithm that solves the problem in a reasonable time. Development of such an algorithm is necessary for solving the multi-stage parallel machine scheduling problems which are currently an almost untouched issue in the deterministic scheduling theory. In this study, a branch and bound algorithm for the single-stage identical parallel machine scheduling problem is proposed. Promising results were obtained in the empirical analysis of the performance of this algorithm. Furthermore, the procedure that is developed to determine tight bounds at a node of the enumeration tree, is an approximation algorithm that solves a special class of identical parallel machine scheduling problems of practical interest. This algorithm delivers a solution that is arbitrarily close to 4/3 times the optimum. To our knowledge this is the best result obtained for this problem so far.Item Open Access Performance bounds on optimal fixed prices(2013) Şen, A.We consider the problem of selling a fixed stock of items over a finite horizon when the buyers arrive following a Poisson process. We obtain a general lower bound on the performance of using a fixed price rather than dynamically adjusting the price. The bound is 63.21% for one unit of inventory, and it improves as the inventory increases. For the one-unit case, we also obtain tight bounds: 89.85% for the constant-elasticity and 96.93% for the linear price-response functions.