Optimal budget allocation for bridge portfolios with element-level inspection data: a constrained integer linear programming formulation

In a highway asset maintenance management system involving more than one highway asset type, identifying an equitable optimal allocation of available budget to individual asset systems is a major challenge. This is because the following outcomes are desirable: (1) the maintenance needs of all assets are adequately addressed, (2) the objectives of individual asset systems are optimally satisfied in an equitable manner, and (3) the objectives of the overall highway asset system are achieved optimally. To achieve these desirable outcomes, this paper proposes a two-stage approach in solving the dual-level multiasset, multiobjective pavement network maintenance optimal budget allocation problem. Stage I of the approach analyzes the individual multiobjective asset systems independently to establish for each a family of optimal Pareto solutions. Minimization of maintenance cost is selected as a common objective for the individual asset systems. This serves as the link for interaction with the Stage II analysis. Stage II adopts an optimal algorithm to allocate budget to individual assets by performing a cross-asset trade-off to achieve the optimal budget solution for the given overall system-level objectives. By defining a minimum performance threshold level for each asset type, the Stage II optimization analysis aims to achieve an equitable allocation of budget by maintaining equivalent amounts of performance improvements for the individual asset systems above their respective minimum threshold levels. The conceptual framework of the proposed approach is presented in this paper with a numerical example to illustrate the detailed working of the procedure.

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.

Real estate ratios have increased in recent years. This article thus examines the diversification potential of real estate investments that German investors can achieve at a global scale. To this end, it analyzes how the illiquidity of some real estate investments or the illiquidity preference of an investor can bring about optimal investment ratios. Optimum allocation quotas for German investors with a wide range of mixed-asset allocations are examined. In addition to traditional optimizations, this article applies the three-fund theorem to include liquid and illiquid forms of real estate investment and to determine optimum allocation ratios. While real estate may be an essential component in a mixed-asset portfolio, it is not included in all optimal portfolios. An optimal portfolio also depends on the investment form, insofar as real estate vehicles are not always suitable for diversifying the portfolio risk or for improving the performance of a mixed-asset portfolio. Moreover, illiquid investment vehicles can often provide strong diversification benefits. The optimum allocations to real estate thus depend on the investor’s illiquidity acceptance, even if allocation dominance has increased in recent years. While many studies have demonstrated the advantage that investors gain from adding certain real estate assets, such as those obtained by direct investments, this study goes further by examining the comparative advantage of different real estate investment forms within a variety of asset classes. New insights can thus be gained by considering investors’ liquidity preferences within a given portfolio. One of these insights is that there is a trade-off between illiquidity and diversification potential. Another is that optimum portfolio allocations depend on illiquidity acceptance. These findings therefore also provide practical guidance not only to German investors with a global portfolio diversification but also to practitioners who add illiquid asset classes to their portfolio, to say nothing of the valuable field knowledge it offers to researchers in this field.

In this paper, we study a strategic model of marketing and product consumption in social networks. We consider two competing firms in a market providing two substitutable products with preset qualities. Agents choose their consumptions following a myopic best response dynamics which results in a local, linear update for the consumptions. At some point in time, firms receive a limited budget which they can use to trigger a larger consumption of their products in the network. Firms have to decide between marginally improving the quality of their products and giving free offers to a chosen set of agents in the network in order to better facilitate spreading their products. We derive a simple threshold rule for the optimal allocation of the budget and describe the resulting Nash equilibrium. It is shown that the optimal allocation of the budget depends on the entire distribution of centralities in the network, quality of products and the model parameters. In particular, we show that in a graph with a higher number of agents with centralities above a certain threshold, firms spend more budget on seeding in the optimal allocation. Furthermore, if seeding budget is nonzero for a balanced graph, it will also be nonzero for any other graph, and if seeding budget is zero for a star graph, it will be zero for any other graph too. We also show that firms allocate more budget to quality improvement when their qualities are close, in order to distance themselves from the rival firm. However, as the gap between qualities widens, competition in qualities becomes less effective and firms spend more budget on seeding.

In recent years, the issue of maximizing submodular functions has attracted much interest from research communities. However, most submodular functions are specified in a set function. Meanwhile, recent advancements have been studied for maximizing a diminishing return submodular (DR-submodular) function on the integer lattice. Because plenty of publications show that the DR-submodular function has wide applications in optimization problems such as sensor placement impose problems, optimal budget allocation, social network, and especially machine learning. In this research, we propose two main streaming algorithms for the problem of maximizing a monotone DR-submodular function under cardinality constraints. Our two algorithms, which are called StrDRS1 and StrDRS2, have (1/2−ϵ), (1−1/e−ϵ) of approximation ratios and O(nϵlog(logBϵ)logk), O(nϵlogB), respectively. We conducted several experiments to investigate the performance of our algorithms based on the budget allocation problem over the bipartite influence model, an instance of the monotone submodular function maximization problem over the integer lattice. The experimental results indicate that our proposed algorithms not only provide solutions with a high value of the objective function, but also outperform the state-of-the-art algorithms in terms of both the number of queries and the running time.

Marketing managers allocate extraordinary amounts of budgets for supporting their organization’s marketing plans. Choosing the right measure for allocation of promotional budgets to customers has always been a challenging issue and consequently has drawn considerable attention in the past few years. Related studies emphasize using Customer Lifetime Value or Customer Equity (CE) as a measure of customer’s profitability, based on which a firm can efficiently allocate its marketing budget to customers. In this study, the focus is on allocating the limited promotion budgets to customers to maximize CE. Using Markov decision process (MDP), the firm’s actions are linked to the customers’ behavior and the corresponding values. To solve MDP with a budget constraint, a heuristic method is proposed for finding the optimal or near-optimal policies for each customer segment. To confirm the validity of the method, the decision model is implemented in a business-to-business context to maximize CE by determining the optimal sales promotions to customers. The result of the proposed heuristic method is compared with a stochastic dynamic programming model. The result of experiments shows that the discount factor increases the difference between the obtained solutions becomes more significant. The difference approves the importance of accounting the optimal level of promotional budget for each customer segment. The average improvement gained by the optimal budget allocation ranges from 2 to 5.5%. The findings of this research indicate the essential of adopting different marketing policies for each customer segment.

We analyze optimal strategies for the allocation of a finite budget that can be invested in different advertising channels over time with the objective of influencing social opinions in a network of individuals. In our analysis, we consider both exogenous influence mechanisms, such as advertising campaigns, as well as endogenous mechanisms of social influence, such as word-of-mouth and peer-pressure, which are modeled using diffusion dynamics. We show that for a broad family of objective functions, the optimal influence strategy at every time uses all channels at either their maximum rate or not at all, i.e., a bang-bang strategy. Furthermore, we prove that the number of switches between these extremes is bounded above by a term that is typically much smaller than the number of agents. This means that the optimal influence strategy is to exert maximum effort in waves for every channel, and then cease effort and let the effects propagate. We also show that, at the beginning of the campaign, the total cost-adjusted reach of an exogenous advertising channel determines its relative value. In contrast, as we approach our investment horizon (e.g., election day), the optimal strategy is to invest in channels able to target individuals instead of broad-reaching channels. We demonstrate that the optimal influence strategies are easily computable in several practical cases, and explicitly characterize the optimal controls for the case of linear objective functions in closed form. Finally, we see that, in the canonical example of designing an election campaign, identifying late-deciders is a critical component in the optimal design.

In this correspondence, we propose a constant quality rate allocation algorithm for fine granularity scalability (FGS) coded videos. The rate allocation problem is formulated as a constrained minimization of quality fluctuation. The minimization is solved using a composite rate distortion (R-D) analysis. For a set of video frames, a composite R-D curve is first computed and then used for computing the optimal rate allocation. This algorithm is efficient because it is neither iterative nor recursive. After the composite R-D curve is computed, it can be used for optimal rate allocation of any rate budget. Moreover, the composite R-D curve can be updated efficiently over sliding windows. Experimental results have shown both the effectiveness and the efficiency of the proposed algorithm.

Optimizing budget allocation for educational facilities in Islamic boarding schools is essential to ensure sustainable education quality. This study aims to optimize budget allocation to support educational facilities at Al-Qutub Islamic Boarding School, Wonopringgo, Pekalongan Regency, using a Bayesian Decision Making approach with the Markov Chain Monte Carlo (MCMC) method. Data were collected through questionnaires, observations, and interviews to gather insights on facility conditions, current budget allocation, and additional facility needs. Data analysis employed the MCMC method, enabling decision-making based on the probabilistic distribution of the collected data. The findings indicate that budget allocation optimized through the Bayesian model results in a more effective distribution, addressing urgent facility priorities that directly enhance educational quality. This study contributes a budget analysis model applicable to Islamic educational institutions in Indonesia. Theoretically, it enriches the literature on educational budget management in Islamic boarding schools using Bayesian statistical approaches, while practically, it assists school administrators in allocating budgets more efficiently and accurately in line with educational needs.

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.

In this paper, a simulation-based optimization approach, named NHOCBA, for a typical resource allocation problem is presented. The hybrid algorithm based on neighborhood algorithm is applied to explore toward optimal direction in design space. For increasing efficiency, an optimal computing budget allocation (OCBA) is adopted to compute the optimal number of replications and to provide reliable evaluation of variance. In addition, we deal with the resource allocation problem which exist multiple global optima in design space. Therefore, a trim procedure which prevents to allocate extra numbers of replication to local optima has been proposed to enhance efficiency. Then, we use confidence interval at the end of algorithm procedure to find an optimal set instead of an optimal solution from design space. Finally, we compare the NHOCBA with different algorithms by experimentation study which shows that NHOCBA approach can perform better than the other algorithms under certain conditions.

This study examines the impact of digital transformation (DT) on organizational performance and operational risks in the banking sector. Internal factors analyzed include communication, comprehension of DT, operational technology readiness, process complexity, risk monitoring, and operational risk training, while external factors encompass regulatory compliance, digital experience, budget constraints, and cyber resilience. Using fuzzy-set qualitative comparative analysis (fsQCA) on survey data from 100 Indonesian banking professionals, the findings highlight the critical role of risk monitoring and operational technology readiness among internal factors, and cyber resilience and budget allocation among external factors. The interplay of these elements, such as combining risk monitoring with cyber resilience, is key to optimizing performance and mitigating risks. This study provides actionable insights for practitioners, policymakers, and scholars, emphasizing the alignment of internal capabilities with external demands. It highlights the importance of streamlined processes, cybersecurity frameworks, and supportive regulations for sustainable DT. While limited by sample size and subjective data, the research identifies opportunities for future studies, including cross-sectoral analyses and the use of objective performance metrics.

This paper presents a mathematical model that provides soccer clubs with optimal player transfer recommendations. Using publicly available data on soccer clubs and players, we create a data-driven optimization model that aids soccer clubs in making informed decisions on how to optimally allocate their multi-million dollar transfer budgets. First, some performance attributes, market value, and salary of 7377 real players from across the world are forecasted using a simple moving average method. Next, these forecasted values are input into an integer programming model that solves for the optimal transfer decisions for any club with the objective of maximizing the club’s utility. This utility is a function of the forecasted values, and increases in the market values of the club’s players. Constraints are imposed to reflect the rules and regulations of club soccer. The model focuses on the Premier League (PL), the first-division soccer league in England and Wales. Numerical results are provided for twelve selected clubs in the PL, for the transfer periods during 2016–2017 and 2017–2018. The results show that transfers recommended by the model could help the clubs achieve better market values. The model can be easily customized to fit any club from any country. Our study provides significant contributions to the literature on optimal budget allocation and team selection in sports, by addressing some important ideas that are not considered in the literature.

In the light of past development failures, coupled with the pressure on government to deliver on their promises made, a framework is needed to improve the success of rural agricultural development. Consequently, detailed agricultural development plans were drafted with the intent to provide a framework or roadmap that will enable small-scale farmers to be more successful over the long term. However, development plans can only improve the success of agricultural development once they are implemented. This conveys another dimension of agricultural development, with government that is often faced with strict budget constraints. Budget allocations to agricultural development initiatives should therefore be done in a way that will yield the highest economic, social and environmental returns. Such a decision can become extremely complicated when in search of optimal allocation of limited budget resources. Consequently, a decision support system that will guide budget allocation for agricultural development initiatives is sorely needed. This article provides a framework on how multiple-criteria analysis can be used as a decision support tool that will ensure optimal budget allocation for agricultural development.

In this article, we consider the problem of optimizing the connectivity of a landscape under a budget constraint, by improving habitat areas and ecological corridors between them. We model this problem as a discrete optimization problem over graphs, in which vertices represent the habitat areas and arcs represent the connections between them. We propose a new flow‐based integer linear programming formulation that improves upon the existing models for this problem. By following an approach similar to Catanzaro et al. for the robust shortest path problem, we design an improved preprocessing algorithm that reduces the size of the graphs on which we compute generalized flows. Computational experiments show the benefits of both contributions, by enabling to solve instances of the problem larger than previous models. These experiments also show that several versions of greedy algorithms perform relatively well in practice, while returning arbitrarily bad solutions in the worst case.