Efficient Simulation Budget Allocation for Ranking the TopmDesigns

Existing research in ranking and selection has focused on the problem of selecting the best design, subset selection and selecting the set of Pareto designs. Few works have addressed the problem of complete ranking. In this research, we consider the problem of ranking all alternatives completely with consideration of input uncertainty. Given a fixed simulation budget, we aim to maximize the probability of correct ranking among all designs based on their worst-case performances. The problem is formulated as an optimal computing budget allocation model. To make this optimization problem computationally tractable, we develop an approximated probability of correct ranking and derive the asymptotic optimality condition based on it. A sequential ranking procedure is then suggested to implement the proposed simulation budget allocation rule. The high efficiency of the proposed simulation procedure is demonstrated via a set of numerical experiments. In addition, useful insights and analysis on characterizing the optimality condition and implementing the efficient budget allocation rule are provided.

Revenue-Sharing Allocation Strategies for Two-Sided Media Platforms: Pro-Rata versus User-Centric

We derive the optimum power and rate allocation rule for CDMA downlink networks, which minimizes mean transmission delay of the simultaneous users experiencing different channel gains under total transmission power and the required SIR constraints. The amount of reduction in average mean transmission delay by the proposed optimum allocation rule against the equal rate and equal power allocation schemes is also derived for the case when each user undergoes independent shadowing and path loss. It is shown that the proposed allocation rule not only achieves the minimum mean transmission delay but also minimizes the probability of the data rate being less than a tolerable threshold, against the equal rate or equal power allocation schemes.

The performance of a retail store depends on its ability to attract customer traffic, match labor with incoming traffic, and convert the incoming traffic into sales. Retailers make significant investments in marketing activities (such as advertising) to bring customers into their stores and in‐store labor to convert that traffic into sales. Thus, a common trade‐off that retail store managers face concerns the allocation of a store's limited budget between advertising and labor to enhance store‐level sales. To explore that trade‐off, we develop a centralized model to allocate limited store budget between store labor and advertising with the objective of maximizing store sales. We find that a store's inherent potential to drive traffic plays an important role, among other factors, in the relative allocation between advertising and store labor. We also find that as advertising instruments become more effective in bringing traffic to stores, managers should not always capitalize this effectiveness by increasing their existing allocations to advertising. In addition, we discuss a decentralized setting where budget allocation decisions cannot be enforced by a store manager and present a simple mechanism that can achieve the centralized solution. In an extension, we address the budget allocation problem in the presence of marketing efforts to shift store traffic from peak to off peak hours and show that our initial findings are robust. Further, we illustrate how the solution from the budget allocation model can be used to facilitate store level sales force planning/scheduling decisions. Based on the results of our model, we present several insights that can help managers in budget allocation and sales force planning.

Optimal asset allocation and consumption rules for commodity-based sovereign wealth funds

Many applications in the areas of finance, environments, service systems, and statistical learning require the computation for a general function of the expected performances associated with one or many random objects. When complicated stochastic systems are involved, such computation needs to be done by stochastic simulation and the computational cost can be expensive. We design simulation algorithms that exploit the common random structure shared by all random objects, referred to as stratified splitting. We discuss the optimal simulation budget allocation problem for the proposed algorithms. A brief numerical experiment is conducted to illustrate the performance of the proposed algorithm with various budget allocation rules.

Efficient Global Optimization (EGO) is a popular method that searches sequentially for the global optimum of a simulated system. EGO treats the simulation model as a black-box, and balances local and global searches. In deterministic simulation, EGO uses ordinary Kriging (OK), which is a special case of universal Kriging (UK). In our EGO variant we use intrinsic Kriging (IK), which eliminates the need to estimate the parameters that quantify the trend in UK. In random simulation, EGO uses stochastic Kriging (SK), but we use stochastic IK (SIK). Moreover, in random simulation, EGO needs to select the number of replications per simulated input combination, accounting for the heteroscedastic variances of the simulation outputs. A popular selection method uses optimal computer budget allocation (OCBA), which allocates the available total number of replications over simulated combinations. We derive a new allocation algorithm. We perform several numerical experiments with deterministic simulations and random simulations. These experiments suggest that (1) in deterministic simulations, EGO with IK outperforms classic EGO; (2) in random simulations, EGO with SIK and our allocation rule does not differ significantly from EGO with SK combined with the OCBA allocation rule.

The Multiscale Spectral Generalized Finite Element Method (MS-GFEM) was developed in recent work by Babuska and Lipton. The method uses optimal local shape functions, optimal in the sense of the Kolmogorov n-width, to approximate solutions to a second order linear elliptic partial differential equation with L-infinity coefficients. In this dissertation an implementation of MS-GFEM over a two subdomain partition of unity is outlined and several numerical experiments are presented. The method is applied to compute local fields inside high contrast particle suspensions. The method's performance is evaluated for various examples with different contrasts between reinforcement particles and matrix material. The numerical experiments are shown to agree with a new theoretical estimate that shows the convergence rate is independent of the elastic properties of particles and matrix materials. A new domain decomposition method based on MS-GFEM is presented. Numerical computations using this iterative method are discussed and the theoretical convergence rate is provided. It is shown that the convergence rate is given by the same near-exponential bound given for MS-GFEM. A systematic method for identifying the worst case load amongst all boundary loads of a fixed energy is introduced. Here the worst case load delivers the largest fraction of input energy into a prescribed subdomain of interest. This leads to an eigenvalue problem, for which the largest eigenvalue is the maximum fraction of energy which concentrates in the subdomain. The associated eigenfunctions are the worst case solutions. These eigenfunctions are related back to the MS-GFEM shape functions and numerical results are presented for several different geometries.

ABSTRACTCommercial plant breeders improve economically important traits by selectively mating individuals from a given breeding population. Potential pairings are evaluated before the growing season using Monte Carlo simulation, and a mating design is created to allocate a fixed breeding budget across the parent pairs to achieve desired population outcomes. We introduce a novel objective function for this mating design problem that accurately models the goals of a certain class of breeding experiments. The resulting mating design problem is a computationally burdensome simulation optimization problem on a combinatorially large set of feasible points. We propose a two-step solution to this problem: (i) simulate to estimate the performance of each parent pair and (ii) solve an estimated version of the mating design problem, which is an integer program, using the simulation output. To reduce the computational burden when implementing steps (i) and (ii), we analytically identify a Pareto set of parent pairs that will receive the entire breeding budget at optimality. Since we wish to estimate the Pareto set in step (i) as input to step (ii), we derive an asymptotically optimal simulation budget allocation to estimate the Pareto set that, in our numerical experiments, out-performs Multi-objective Optimal Computing Budget Allocation in reducing misclassifications. Given the estimated Pareto set, we provide a branch-and-bound algorithm to solve the estimated mating design problem. Our approach dramatically reduces the computational effort required to solve the mating design problem when compared with naïve methods.

This paper proposes an H∞ robust control scheme for a wave-piercing catamaran (WPC) ride control system (RCS) in rough water. The control signal is assigned to the T-foils and trim tabs by an improved genetic algorithm. To reduce the vertical oscillation of a WPC in wave turbulence at high speeds, based on the uncertain parameters model of the coupled heave/pitch motion of a catamaran with an RCS, an H∞ robust controller is designed according to μ-synthesis theory. The RCS includes two T-foils and two trim tabs; the cooperation control is studied and an allocation rule based on the principle of minimum system driving energy is optimized by an improved genetic algorithm with pattern search algorithm. Finally, comparative simulations demonstrate that the proposed RCS has superior anti-heave/pitch performance and robustness.

The massive deployment of Internet of Things (IoT) devices, including sensors and actuators, is ushering in smart and connected communities of the future. The massive deployment of Internet of Things (IoT) devices, including sensors and actuators, is ushering in smart and connected communities of the future. The availability of real-time and high-quality sensor data is crucial for various IoT applications, particularly in healthcare, energy, transportation, etc. However, data collection may have to be outsourced to external service providers (SPs) due to cost considerations or lack of specialized equipment. Hence, the data market plays a critical role in such scenarios where SPs have different quality levels of available data, and IoT users have different application-specific data needs. The pairing between data available to the SP and users in the data market requires an effective mechanism design that considers the SPs’ profitability and the quality-of-service (QoS) needs of the users. We develop a generic framework to analyze and enable such interactions efficiently, leveraging tools from contract theory and mechanism design theory. It can enable and empower emerging data sharing paradigms such as Sensing-as-a-Service (SaaS). The contract design creates a pricing structure for on-demand sensing data for IoT users. By considering a continuum of user types, we capture a diverse range of application requirements and propose optimal pricing and allocation rules that ensure QoS provisioning and maximum profitability for the SP. Furthermore, we provide analytical solutions for fixed distributions of user types to analyze the developed approach. For comparison, we consider the benchmark case assuming complete information of the user types and obtain optimal contract solutions. Finally, a case study based on the example of virtual reality application delivered using unmanned aerial vehicles (UAVs) is presented to demonstrate the efficacy of the proposed contract design framework.

The challenges of using technology in the insurance field are opening new horizons for developing and distributing innovative products. Among these, peer-to-peer insurance schemes attract the interest of policyholders and insurance companies. Different types of peer-to-peer insurance have been introduced, from pure models to hybrid ones, as in the case of the broker model. In this paper, we focus on the broker model, where the groups of peers are formed by an insurance broker according to similar risk characteristics. The participants in the network pay an initial contribution defined by a cooperative rule that must be transparent and shared. A part or the whole of the collected contributions is set aside in a common fund. At the end of the year, if the common fund is sufficient to pay for the claims, the members obtain the excess over-retained premiums that is shared according to a capital allocation rule. We propose a cashback distribution mechanism based on the participant’s marginal contribution to the risk, framing the issue in a cooperative game and applying the concept of Shapley value to define an optimal allocation rule of the remaining capital. A numerical application based on a portfolio of motor third-party liability policies is developed to show how the model works.

Strategy-proofness and Essentially Single-valued Cores: A Comment

Suppose two treatments with binary responses are available for patients with some disease. Sequential allocation rules based on the theory of Bayesian bandit processes are examined. The patient horizon is assumed to be random and the objective is to maximize the total expected number of successes. This problem is equivalent to the classical two—armed bandit problem if we assume that the only information acquired during the trial about the patient horizon is whether or not it has so far been reached. When one treatment has a known success rate, the optimal allocation rule may sometimes be expressed in terms of dynamic allocation indices. The calculation of the indices is discussed, and in particular error bounds for the accuracy of the calculation are given in terms of the starting point of the backward induction process. When both treatments have unknown success rates the use of dynamic allocation indices with geometric discounting is suggested. Simulation results indicate that this rule works well even when the distribution of the number of the patients is not geometrical, and that the choice of the discount factor is also not crucial.

In order to allocate airport slots efficiently and fairly, the auction theory was used to design slot auction mechanism, including allocation rules and payment rules. Firstly, aiming at the 1-1 slot trading, optimal allocation model was presented, under the guidance of allocation rules. Secondly, the payments of airlines and traffic flow management department were calculated, according to the vickrey payment rules. Thirdly, in order to meet the demand of budget balance, an improved model based on optimal allocation model was presented and several payment rules were proposed to solve this model. Finally, an example simulation was carried out. The results show that the new model can satisfy budget balance requirements. It is concluded that the optimal allocation results, pricing policy and payment rules have significant impact on the new model.