In the Sequential Selection Problem (SSP), immediate and irrevocable decisions need to be made while candidates from a finite set are being examined one-by-one. The goal is to assign a limited number of @math available jobs to the best possible candidates. Standard SSP variants begin with an empty selection set (cold-starting) and perform the selection process once (single-round), over a single candidate set. In this paper we introduce the Multi-round Sequential Selection Problem (MSSP) which launches a new round of sequential selection each time a new set of candidates becomes available. Each new round has at hand the output of the previous one, i.e. its @math selected employees, and tries to update optimally that selection by reassigning each job at most once. Our setting allows changes to take place between two subsequent selection rounds: resignations of previously selected subjects or and alterations of the quality score across the population. The challenge for a selection strategy is thus to efficiently adapt to such changes. For this novel problem we adopt a cutoff-based approach, where a precise number of candidates should be rejected first before starting to select. We set a rank-based objective of the process over the final job-to-employee assignment and we investigate analytically the optimal cutoff values with respect to the important parameters of the problem. Finally, we present experimental results that compare the efficiency of different selection strategies, as well as their convergence rates towards the optimal solution in the case of stationary score distributions.
A very limited number of papers study algorithmic notions related to repeated selections @cite_5 , as well as the human capacity to learn the right cutoff after reviewing multiple independent candidate sets @cite_3 @cite_22 . However, @cite_5 develops a non cutoff-based strategy and is implemented regarding two distinct aims: to maximize the probability of selecting the best, or to maximize the expected score of the selected . Its conclusion states that learning the score distribution does contribute to the efficiency of the selection only the second aim. An experimental comparison of simpler and intuitive non cutoff-based heuristics is provided in @cite_24 . More sophisticated adaptive strategies worth mentioning are the @cite_6 and the work in @cite_18 . A rather different scenario concerns a startup company (or a new ambitious business unit) which is initially funded by a handful of people but is about to grow larger. The so-called @cite_8 refers to the process that aims at driving the optimal growth of personnel using an adaptive selection threshold based on the already employed individuals. Among heuristics, such as hiring above the worst or best employees, hiring above the mean employee score shown to be the best performing strategy.
@cite_18 @cite_22 @cite_8 @cite_3 @cite_6 @cite_24 @cite_5
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Consider a decision maker who is responsible to dynamically collect observations so as to enhance his information about an underlying phenomena of interest in a speedy manner while accounting for the penalty of wrong declaration. Due to the sequential nature of the problem, the decision maker relies on his current information state to adaptively select the most informative'' sensing action among the available ones. In this paper, using results in dynamic programming, lower bounds for the optimal total cost are established. The lower bounds characterize the fundamental limits on the maximum achievable information acquisition rate and the optimal reliability. Moreover, upper bounds are obtained via an analysis of two heuristic policies for dynamic selection of actions. It is shown that the first proposed heuristic achieves asymptotic optimality, where the notion of asymptotic optimality, due to Chernoff, implies that the relative difference between the total cost achieved by the proposed policy and the optimal total cost approaches zero as the penalty of wrong declaration (hence the number of collected samples) increases. The second heuristic is shown to achieve asymptotic optimality only in a limited setting such as the problem of a noisy dynamic search. However, by considering the dependency on the number of hypotheses, under a technical condition, this second heuristic is shown to achieve a nonzero information acquisition rate, establishing a lower bound for the maximum achievable rate and error exponent. In the case of a noisy dynamic search with size-independent noise, the obtained nonzero rate and error exponent are shown to be maximum. We study an online unit-job scheduling problem arising in buffer management. Each job is specified by its release time, deadline, and a nonnegative weight. Due to overloading conditions, some jobs have to be dropped. The goal is to maximize the total weight of scheduled jobs. We present several competitive online algorithms for various versions of unit-job scheduling, as well as some lower bounds on the competitive ratios. We first give a randomized algorithm RMix with competitive ratio of e (e-1) 1.582. This is the first algorithm for this problem with competitive ratio smaller than 2. Then we consider s-bounded instances, where the span of each job (deadline minus release time) is at most s. We give a 1.25-competitive randomized algorithm for 2-bounded instances, matching the known lower bound. We also give a deterministic algorithm Edf"@a, whose competitive ratio on s-bounded instances is 2-2 s+o(1 s). For 3-bounded instances its ratio is @f 1.618, matching the known lower bound. In s-uniform instances, the span of each job is exactly s. We show that no randomized algorithm can be better than 1.25-competitive on s-uniform instances, if the span s is unbounded. For s=2, our proof gives a lower bound of 4-22 1.172. Also, in the 2-uniform case, we prove a lower bound of 2 1.414 for deterministic memoryless algorithms, matching a known upper bound. Finally, we investigate the multiprocessor case and give a 1 (1-(mm+1)^m)-competitive algorithm for m processors. We also show improved lower bounds for the general and s-uniform cases. We consider the problem of scheduling a number of jobs on a single machine against a restrictive common due date. The paper consists of two parts: firstly a new and appropriate problem representation is developed. As the restrictive common due date problem is known to be intractable we decided, secondly, to apply meta-heuristics, namely evolutionary strategies, simulated annealing and threshold accepting. We demonstrate that our application of these meta-heuristics is efficient in obtaining near-optimal solutions by solving 140 benchmark problems with up to 1000 jobs. Furthermore, we compare their solution quality and find that a new variant of threshold accepting is superior to the other approaches. In this paper, we study the problem of designing new mechanisms for selling reserved instances (also referred to as virtual machines) in cloud computing. Unlike the practice in today's clouds in which users only have a few predefined options to reserve instances (i.e., either 1-year reservation or 3-year reservation), we allow users to reserve resources for any length and from any time point in the future. Our goal is to maximize the social welfare. We propose two mechanisms, one for the case where all the jobs are tight (their lengths are exactly their reservation time intervals), and the other for the more general case where jobs are delayable and have some flexibility on their reservations. Both of the mechanisms are prompt in the sense that the acceptance and the payment for a job is determined at the very moment of its arrival. We use competitive analysis to evaluate the performance of our mechanisms, and show that both of the mechanisms have a competitive ratio of O(ln(kT)) under some mild assumption, where k (res. T) is the maximum ratio between per-instance-hour valuation (res. length) of any two jobs. We then prove that no algorithm can achieve a competitive ratio better than ln(2kT) under the same assumption. Therefore, our mechanisms are optimal within a constant factor.