Optimal television schedules in alternative competitive environments

We formulate network-television-scheduling problems as integer programs for three different competitive environment—smyopic, Nash competitive, and cooperative. To provide input data for the scheduling models, we develop and estimate a regression model in which show-part ratings are regressed on variables that influence television viewership, including day, time slot, show attribute, and competitive effects, as well as lead-in from the previous show part. We apply our models by solving for optimal myopic (noncompetitive) and Nash competitive week-long prime-time schedules for the three major networks for two specific weeks. We find that there are substantial gains to optimization and that those gains are not diminished much by competition. We illustrate the cooperative problem for six time slots and show how the solution differs from the Nash solution. We discuss the use of simple programming heuristics such as counterprogramming.     

Optimal average approximations for functions mapping in quasi-Banach spaces

In 1994, M.M. Popov [6] showed that the fundamental theorem of calculus fails, in general, for functions mapping from a compact interval of the real line into the _?p${?}_p$-spaces for 0<p<1$0<p<1$, and the question arose whether such a significant result might hold in some other non-Banach spaces. In this article we completely settle the problem by proving that the fundamental theorem of calculus breaks down in the context of any non-locally convex quasi-Banach space. Our approach introduces the tool of Riemann-integral averages of continuous functions, and uses it to bring out to light the differences in behavior of their approximates in the lack of local convexity. As a by-product of our work we solve a problem raised in [1] on the different types of spaces of differentiable functions with values on a quasi-Banach space.     

Optimal control problems via a direct method

Summary In this paper we deal with the minimization problem of a cost functional associated to a nonlinear boundary value control problem of a general form, defined in the fixed time interval [0, 1]. Specifically, we first give conditions which ensure that the nonlinear boundary value control problem is solvable and we study the structure of the relative solution set. Then, based on the properties of this set, we establish conditions ensuring both the existence of quasisolutions and that of solutions of the minimization problem under consideration. Such conditions will depend also on the choice of the control space L^r([0, 1],R ^m) where 1 r + Partially supported by the research project M.P.I. (40%) «Teoria del controllo dei sistemi dinamici».     

Optimal control by direct inversion of a positive-definite operator in a Hilbert space

A well-known perturbation theorem for linear operators is used to provide a series expansion for the inverse of a positive-definite operator in a Hilbert space. With this expansion, feasible computational procedures are obtained for solving some optimal control problems with quadratic cost functionals. The methods presented here are compared to alternate methods available in the literature.     

Optimal cooperative advertising integration strategy for organizations adding a direct online channel

Since the advent of the Web, retailers who served consumers offline (ie in stores or via catalogue) have grappled with how to effectively integrate the Internet into their marketing strategies and tactics. Clearly, how a firm elects to integrate the Internet into its retailing process, and how it coordinates offline and online strategic decisions, can impact its performance. In this paper, we examine integration decisions from a cooperative advertising perspective to determine the profitability of various integration strategies. We find that profit is greater when using a ‘partial-integration’ strategy rather than a ‘separation’ strategy; moreover, we find that profit is yet greater when using a ‘full-integration’ strategy rather than a ‘partial-integration’ strategy.     

Flocking in noisy environments

In recent years, a number of articles proposed mathematical models for emergent phenomena. This is the case, for instance for the flocking of birds or the schooling of fish. In particular, in [F. Cucker, S. Smale, Emergent behavior in flocks, IEEE Trans. on Autom. Control 52 (2007) 852–862], a model was proposed for flocking and it was proved that under certain conditions on the initial positions and velocities of the birds, flocking occurs. In this paper we modify this model by adding random noise to it. We prove that, under conditions similar to those just mentioned, (nearly) flocking occurs in finite time with a certain confidence.     

含参广义集值向量均衡问题有效解映射下半连续的最优条件

在实Hausdorff拓扑向量空间中研究一类含参广义集值向量均衡问题弱有效解与有效解映射的下半连续性. 在近似锥-次类凸的条件下, 运用标量化的方法得到弱有效解的标量化结果. 在适当条件下, 得到含参广义集值向量均衡问题弱有效解与有效解映射下半连续性定理.     

Advection-mediated competition in general environments

We consider a reaction–diffusion–advection system of two competing species with one of the species dispersing by random diffusion as well as a biased movement upward along resource gradient, while the other species by random diffusion only. It has been shown that, under some non-degeneracy conditions on the environment function, the two species always coexist when the advection is strong. In this paper, we show that for general smooth environment function, in contrast to what is known, there can be competitive exclusion when the advection is strong, and, we give a sharp criterion for coexistence that includes all previously considered cases. Moreover, when the domain is one-dimensional, we derive in the strong advection limit a system of two equations defined on different domains. Uniqueness of steady states of this non-standard system is obtained when one of the diffusion rates is large.     

Decision making in uncertain environments

In the paper some problems of decision making in fuzzy and probabilistic fuzzy environments are formulated. The goals and constraints in such decision situations may be simultaneously fuzzy and random by their nature. Looking for a decision set which should be any reasonable function of goals and constraints, it leads to operations on probabilistic sets which are also of interest in that work. Some numerical examples of decision making are illustrating the theoretical considerations presented in this paper.     

Jump-diffusion processes in random environments

In this paper we investigate jump-diffusion processes in random environments which are given as the weak solutions of SDEs. We formulate conditions ensuring existence and uniqueness in law of solutions. We investigate the Markov property. To prove uniqueness we solve a general martingale problem for càdlàg processes. This result is of independent interest. Application of our results to generalized exponential Lévy model are present in the last section.     

Selection hyper-heuristics in dynamic environments

Current state-of-the-art methodologies are mostly developed for stationary optimization problems. However, many real-world problems are dynamic in nature, where different types of changes may occur over time. Population-based approaches, such as evolutionary algorithms, are frequently used for solving dynamic environment problems. Selection hyper-heuristics are highly adaptive search methodologies that aim to raise the level of generality by providing solutions to a diverse set of problems having different characteristics. In this study, the performances of 35 single-point-search-based selection hyper-heuristics are investigated on continuous dynamic environments exhibiting various change dynamics, produced by the Moving Peaks Benchmark generator. Even though there are many successful applications of selection hyper-heuristics to discrete optimization problems, to the best of our knowledge, this study is one of the initial applications of selection hyper-heuristics to real-valued optimization as well as being among the very few which address dynamic optimization issues using these techniques. The empirical results indicate that learning selection hyper-heuristics incorporating compatible components can react to different types of changes in the environment and are capable of tracking them. This study shows the suitability of selection hyper-heuristics as solvers in dynamic environments.     

Testing equality in lisp-like environments

A function is presented to test equality between lists. In any case the function requires at most one single traversal of the lists and behaves as follows:

1. if there are no cycles, it works as standardEQU AL functions;
2. if there are cycles, it does not give information about equality, but it can detect cycles, i.e. it signals which lists are cyclic.

A simplified version of the function is also considered which is always at least as efficient as standardEQU AL; it grants protection against cycles without signaling them. A coroutine organized version of the function is shown.     

Population models in almost periodic environments

We establish the basic theory of almost periodic sequences on ?₊. Dichotomy techniques are then utilized to find sufficient conditions for the existence of a globally attracting almost periodic solution of a semilinear system of difference equations. These existence results are, subsequently, applied to discretely reproducing populations with and without overlapping generations. Furthermore, we access evidence for attenuance and resonance in almost periodically forced population models.     

Access mechanisms in block structured environments

Statistics from dynamic analysis of programs are used to compare the efficiency of different methods to access global variables. The method where static links are used for access is shown to be at least as efficient as the display method. The use of the linked list method also leads to a simpler runtime system and allows separately compiled modules to execute at any level in the resulting program. The results of the dynamic analysis are presented in a form which allows comparison of the access methods in language implementations on specific computers. Experience with using two different access methods in an implementation of Simula67 concludes the paper.     

Cost-based decision-making in middleware virtualization environments

Middleware virtualization refers to the process of running applications on a set of resources (e.g., databases, application servers, other transactional service resources) such that the resource-to-application binding can be changed dynamically on the basis of applications’ resource requirements. Although virtualization is a rapidly growing area, little formal academic or industrial research provides guidelines for cost-optimal allocation strategies. In this work, we study this problem formally. We identify the problem and describe why existing schemes cannot be applied directly. We then formulate a mathematical model describing the business costs of virtualization. We develop runtime models of virtualization decision-making paradigms. We describe the cost implications of various runtime models and consider the cost effects of different managerial decisions and business factors, such as budget changes and changes in demand. Our results yield useful insights for managers in making virtualization decisions.     

Age-dependent branching processes in random environments

We consider an age-dependent branching process in random environments. The environments are represented by a stationary and ergodic sequence ξ = (ξ0,ξ1,...) of random variables. Given an environment ξ, the process is a non-homogenous Galton-Watson process, whose particles in n-th generation have a life length distribution G(ξn) on R , and reproduce independently new particles according to a probability law p(ξn) on N. Let Z(t) be the number of particles alive at time t. We first find a characterization of the conditional probability generating function of Z(t) (given the environment ξ) via a functional equation, and obtain a criterion for almost certain extinction of the process by comparing it with an embedded Galton-Watson process. We then get expressions of the conditional mean EξZ(t) and the global mean EZ(t), and show their exponential growth rates by studying a renewal equation in random environments.     

Multi-objective optimization in uncertain random environments

Uncertain random variables are used to describe the phenomenon of simultaneous appearance of both uncertainty and randomness in a complex system. For modeling multi-objective decision-making problems with uncertain random parameters, a class of uncertain random optimization is suggested for decision systems in this paper, called the uncertain random multi-objective programming. For solving the uncertain random programming, some notions of the Pareto solutions and the compromise solutions as well as two compromise models are defined. Subsequently, some properties of these models are investigated, and then two equivalent deterministic mathematical programming models under some particular conditions are presented. Some numerical examples are also given for illustration.     

Managing capacity flexibility in make-to-order production environments

This paper addresses the problem of managing flexible production capacity in a make-to-order (MTO) manufacturing environment. We present a multi-period capacity management model where we distinguish between process flexibility (the ability to produce multiple products on multiple production lines) and operational flexibility (the ability to dynamically change capacity allocations among different product families over time). For operational flexibility, we consider two polices: a fixed allocation policy where the capacity allocations are fixed throughout the planning horizon and a dynamic allocation policy where the capacity allocations change from period to period. The former approach is modeled as a single-stage stochastic program and solved using a cutting-plane method. The latter approach is modeled as a multi-stage stochastic program and a sampling-based decomposition method is presented to identify a feasible policy and assess the quality of that policy. A computational experiment quantifies the benefits of operational flexibility and demonstrates that it is most beneficial when the demand and capacity are well-balanced and the demand variability is high. Additionally, our results reveal that myopic operating policies may lead a firm to adopt more process flexibility and form denser flexibility configuration chains. That is, process flexibility may be over-valued in the literature since it is assumed that a firm will operate optimally after the process flexibility decision. We also show that the value of process flexibility increases with the number of periods in the planning horizon if an optimal operating policy is employed. This result is reversed if a myopic allocation policy is adopted instead.