Expected Opportunity Cost Research Articles

Adaptive budget allocation in simheuristics applied to stochastic home healthcare routing and scheduling

The organization of home care is of pivotal importance in response to the trend of delivering more care directly to clients’ residences. With more vulnerable clients residing at home, variability in care durations needs careful consideration. This paper addresses the operational home healthcare routing and scheduling problem (HHCRSP) with uncertainty in travel and service times. The quality of the routes is evaluated based on the expected objective function, incorporating travel time, waiting time, and shift overtime. Due to the complexity of the problem, a simheuristic approach is applied that carefully integrates the optimization of the deterministic HHCRSP with simulation. This study proposes a new framework, based on optimal computing budget allocation and the expected opportunity costs, to dynamically determine when to employ optimization and when to use simulation. A practical case study demonstrates the effectiveness of the approach and reveals the substantial impact of accounting for randomness in the HHCRSP.

An efficient simulation procedure for the expected opportunity cost using metamodels

Many decision problems in modern industries involve the performance optimization of discrete-event dynamic systems. Because of the stochasticity of these systems, performance usually is evaluated through simulation. Finding the optimal designs of these systems can be modeled as a ranking and selection problem. This research considers the problem of selecting the best design from among numerous designs. We minimized the expected opportunity cost (EOC) of incorrect selection with a limited computing budget. The entire domain of designs could be divided into several adjacent partitions, and the performances of designs in each partition were estimated using a regression metamodel. We assumed the underlying function in each partition to be quadratic. Using large deviations theory, we then derived an asymptotically optimal budget allocation rule and developed a sequential allocation algorithm to implement the allocation rule. The EOC measure was compared with the probability of correct selection measure in a set of large-scale simulation optimization problems. Numerical experiments verified the effectiveness of our proposed simulation procedure.

Convergence rate analysis for optimal computing budget allocation algorithms

Ordinal optimization (OO) is a widely-studied technique for optimizing discrete-event dynamic systems (DEDS). It evaluates the performance of the system designs in a finite set by sampling and aims to correctly make ordinal comparison of the designs. A well-known method in OO is the optimal computing budget allocation (OCBA). It builds the optimality conditions for the number of samples allocated to each design, and the sample allocation that satisfies the optimality conditions is shown to asymptotically maximize the probability of correct selection for the best design. In this paper, we investigate two popular OCBA algorithms. With known variances for samples of each design, we characterize their convergence rates with respect to different performance measures. We first demonstrate that the two OCBA algorithms achieve the optimal convergence rate under measures of probability of correct selection and expected opportunity cost. It fills the void of convergence analysis for OCBA algorithms. Next, we extend our analysis to the measure of cumulative regret, a main measure studied in the field of machine learning. We show that with minor modification, the two OCBA algorithms can reach the optimal convergence rate under cumulative regret. It indicates the potential of broader use of algorithms designed based on the OCBA optimality conditions.

ANALYSIS OF LABOR RESOURCES WASTAGE IN CHINA’S REAL ESTATE BROKERAGE: FROM THE PERSPECTIVE OF OPPORTUNITY COSTS

Real estate brokerage has experienced the rapid growth over the past two decades in China, with a significant increase of employees. In particular, in the megacities like Beijing, the growth of employees exceeds the growth of real estate transaction volume. This may lead to the wastage of labor resources. In this regard, the optimal employee size (OES) in China’s real estate brokerage is proposed from the perspective of opportunity costs, which include both under-size and over-size costs. In the proposed OES models, a real estate brokerage firm makes the optimal decisions of number of employees by minimizing expected opportunity costs. In addition, an iterative algorithm is employed to obtain the optimal employee size in different scenarios. The result reveals that high profit gained from the business does attract more employees than what is needed. By addressing various scenarios based on the game model, it is found that asymmetric competition, the increase of market participants, and demand fluctuations also contribute to the labor resources wastage in real estate brokerage industry. The theoretical analysis results are verified by taking Beijing as the case study. Finally, suggestions for reducing labor resources wastage in real estate brokerage of China are provided.

Optimizing resource allocation in service systems via simulation: A Bayesian formulation

The service sector has become increasingly important in today's economy. To meet the rising expectation of high‐quality services, efficiently allocating resources is vital for service systems to balance service qualities with costs. In particular, this paper focuses on a class of resource allocation problems where the service‐level objective and constraints are in the form of probabilistic measures. Further, process complexity and system dynamics in service systems often render their performance evaluation and optimization challenging and relying on simulation models. To this end, we propose a generalized resource allocation model with probabilistic measures, and subsequently, develop an optimal computing budget allocation (OCBA) formulation to select the optimal solution subject to random noises in simulation. The OCBA formulation minimizes the expected opportunity cost that penalizes based on the quality of the selected solution. Further, the formulation takes a Bayesian approach to consider the prior knowledge and potential performance correlations on candidate solutions. Then, the asymptotic optimality conditions of the formulation are derived, and an iterative algorithm is developed accordingly. Numerical experiments and a case study inspired by a real‐world problem in a hospital emergency department demonstrate the effectiveness of the proposed algorithm for solving the resource allocation problem via simulation.

Posterior-Based Stopping Rules for Bayesian Ranking-and-Selection Procedures

Sequential ranking-and-selection procedures deliver Bayesian guarantees by repeatedly computing a posterior quantity of interest—for example, the posterior probability of good selection or the posterior expected opportunity cost—and terminating when this quantity crosses some threshold. Computing these posterior quantities entails nontrivial numerical computation. Thus, rather than exactly check such posterior-based stopping rules, it is common practice to use cheaply computable bounds on the posterior quantity of interest, for example, those based on Bonferroni’s or Slepian’s inequalities. The result is a conservative procedure that samples more simulation replications than are necessary. We explore how the time spent simulating these additional replications might be better spent computing the posterior quantity of interest via numerical integration, with the potential for terminating the procedure sooner. To this end, we develop several methods for improving the computational efficiency of exactly checking the stopping rules. Simulation experiments demonstrate that the proposed methods can, in some instances, significantly reduce a procedure’s total sample size. We further show these savings can be attained with little added computational effort by making effective use of a Monte Carlo estimate of the posterior quantity of interest. Summary of Contribution: The widespread use of commercial simulation software in industry has made ranking-and-selection (R&S) algorithms an accessible simulation-optimization tool for operations research practitioners. This paper addresses computational aspects of R&S procedures delivering finite-time Bayesian statistical guarantees, primarily the decision of when to terminate sampling. Checking stopping rules entails computing or approximating posterior quantities of interest perceived as being computationally intensive to evaluate. The main results of this paper show that these quantities can be efficiently computed via numerical integration and can yield substantial savings in sampling relative to the prevailing approach of using conservative bounds. In addition to enhancing the performance of Bayesian R&S procedures, the results have the potential to advance other research in this space, including the development of more efficient allocation rules.

Selecting a set of best stochastic inventory policies measured by opportunity cost

<abstract><p>In the present article, we consider the stochastic inventory model aiming at selecting a subset of best policies with minimum total cost. When the computational budget is limited, then the optimal computing budget allocation (OCBA) is used for allocating the available computational budget to the different policies in order to correctly select the best policies. To measure the quality of the selection, we use the expected opportunity cost (EOC) approach that measures the total difference means between the actual best policies and the selected policies. The proposed algorithm OCBA based on EOC is implemented on a stochastic inventory example. The results show that the EOC approaches zero as the total number of computational budgets increases and that using the EOC measure gives better results than using the probability of correct selection (PCS). Moreover, the numerical results indicate that the proposed algorithm is robust.</p></abstract>

Farmers Follow the Herd: A Theoretical Model on Social Norms and Payments for Environmental Services

The economic literature on Payments for Environmental Services (PES) has studied extensively the behavioural factors that prevent farmers from signing PES contracts, even when the payments exceed the expected opportunity costs. This article provides a theoretical model of the role played by the interplay of descriptive and injunctive social norms in farmers’ decisions. When they choose to contribute voluntarily to an environmental public good, farmers may be driven by descriptive norms akin to conformity (do as the majority of their peers) as well as by injunctive norms (in line with what society expects them to do), which are the equivalent of a social injunction to act in favour of the environment. The interactions between these two social norms can yield multiple equilibria, depending on the relative weight of the descriptive norm (sensitivity to conformism) and of the injunctive norm (sensitivity to moral pressure) in the utility functions of farmers. More generally, our model can explain why social groups are sometimes trapped in low public-good-contribution equilibria, even when public subsidies to contributors are high. We make policy recommendations to help reach higher contribution equilibria, with a specific focus on the farm policy context.

A Computing Budget Allocation Method for Minimizing EV Charging Cost Using Uncertain Wind Power

The idea of using wind power to charge electric vehicles (EVs) has attracted more and more attention nowadays due to the potential in significantly reducing air pollution. However, this problem is challenging on account of the uncertainty in the wind power generation and the charging demand from the EVs. Simulation-based policy improvement (SBPI) has been an important method for decision-making in stochastic dynamic programming and, in particular, for charging decisions of EVs in microgrids. However, the problem of allocating the limited computing budget for the best decision-making in online applications is less discussed. We consider this important problem in this work and make the following three major contributions. First, we show that the significant uncertainty in wind power generation forecasting could make the policy that is the outcome of an SBPI worse than the base policy. Second, we apply two existing methods to address this issue, namely, the optimal computing budget allocation (OCBA) for maximizing the probability of correct selection (OCBA_PCS) and the OCBA for minimizing the expected opportunity cost (OCBA_EOC). The asymptotic optimality is briefly reviewed. Third, we numerically compare the performance of OCBA_PCS and OCBA_EOC with the equal allocation (EA), a principle-based method, and a stochastic scenario-based method on small-scale and large-scale experiments. This work sheds light on the EV charging decision in general. Note to Practitioners-Together with the growing adoption of EVs in modern societies, there goes the challenge of how to satisfy the charging demand. Given the high uncertainty both in the wind power generation and in the charging demand, it is important to make decisions online using up-to-date estimation on the renewable power generation and the charging demand. Simulation-based policy improvement (SBPI) is shown both theoretically and practically to be useful to improve a given base policy in various applications, including this EV charging problem. However, the high uncertainty in forecasting could sometimes make the output of SBPI worse than that of the base policy. In this work, we first use numerical experiments to demonstrate the risk for such scenarios. Then, we propose to use two computing budget allocation procedures to address this issue. The asymptotic optimality of both algorithms is briefly reviewed. We demonstrate their performance on numerical experiments when there are only several EVs and when there are 100 EVs.

Information theory for ranking and selection

AbstractWe study the classical ranking and selection problem, where the ultimate goal is to find the unknown best alternative in terms of the probability of correct selection or expected opportunity cost. However, this paper adopts an alternative sampling approach to achieve this goal, where sampling decisions are made with the objective of maximizing information about the unknown best alternative, or equivalently, minimizing its Shannon entropy. This adaptive learning is formulated via a Bayesian stochastic dynamic programming problem, by which several properties of the learning problem are presented, including the monotonicity of the optimal value function in an information‐seeking setting. Since the state space of the stochastic dynamic program is unbounded in the Gaussian setting, a one‐step look‐ahead approach is used to develop a policy. The proposed policy seeks to maximize the one‐step information gain about the unknown best alternative, and therefore, it is called information gradient (IG). It is also proved that the IG policy is consistent, that is, as the sampling budget grows to infinity, the IG policy finds the true best alternative almost surely. Later, a computationally efficient estimate of the proposed policy, called approximated information gradient (AIG), is introduced and in the numerical experiments its performance is tested against recent benchmarks alongside several sensitivity analyses. Results show that AIG performs competitively against other algorithms from the literature.

On-Demand Service Platforms

An on-demand service platform connects waiting-time-sensitive customers with independent service providers (agents). This paper examines how two defining features of an on-demand service platform—delay sensitivity and agent independence—impact the platform’s optimal per-service price and wage. Delay sensitivity reduces expected utility for customers and agents, which suggests that the platform should respond by decreasing the price (to encourage participation of customers) and increasing the wage (to encourage participation of agents). These intuitive price and wage prescriptions are valid in a benchmark setting without uncertainty in the customers’ valuation or the agents’ opportunity costs. However, uncertainty in either dimension can reverse the prescriptions: Delay sensitivity increases the optimal price when customer valuation uncertainty is moderate. Delay sensitivity decreases the optimal wage when agent opportunity cost uncertainty is high and expected opportunity cost is moderate. Under agent opportunity cost uncertainty, agent independence decreases the price. Under customer valuation uncertainty, agent independence increases the price if and only if valuation uncertainty is sufficiently high. The online appendix is available at https://doi.org/10.1287/msom.2017.0678 .

Are the benefits of new health services greater than their opportunity costs?

The Australian health system performs well compared with other developed countries, but there is potential for improved health outcomes through the consideration of the opportunity costs of funding new health services. The opportunity costs of funding a new health service are the benefits forgone from the activities that would be funded if the new health service was not funded. When the forgone activity cannot be observed directly, the expected opportunity costs have been estimated as the expected gain in quality-adjusted life years (QALYs) associated with marginal increases in government expenditure on health. We have previously estimated that a gain of 1 QALY is expected for every additional A$28033 of government expenditure on health. This paper discusses the relevance and proposed use of this estimate of opportunity costs to inform decisions around the public funding of new health services in Australia.

Cost-effectiveness of Human Papilloma Virus (HPV) vaccination in Nigeria: a decision analysis using pragmatic parameter estimates for cost and programme coverage

BackgroundWorld Health Organisation recommends routine Human Papilloma Virus (HPV) vaccination for girls when its cost-effectiveness in the country or region has been duly considered. We therefore aimed to evaluate cost-effectiveness of HPV vaccination in Nigeria using pragmatic parameter estimates for cost and programme coverage, i.e. realistically achievable in the studied context.MethodsA microsimulation frame-work was used. The natural history for cervical cancer disease was remodelled from a previous Nigerian model-based study. Costing was based on health providers’ perspective. Disability adjusted life years attributable to cervical cancer mortality served as benefit estimate. Suitable policy option was obtained by calculating the incremental costs-effectiveness ratio. Probabilistic sensitivity analysis was used to assess parameter uncertainty. One-way sensitivity analysis was used to explore the robustness of the policy recommendation to key parameters alteration. Expected value of perfect information (EVPI) was calculated to determine the expected opportunity cost associated with choosing the optimal scenario or strategy at the maximum cost-effectiveness threshold.ResultsCombination of the current scenario of opportunistic screening and national HPV vaccination programme (CS + NV) was the only cost-effective and robust policy option. However, CS + NV scenario was only cost-effective so far the unit cost of HPV vaccine did not exceed $5. EVPI analysis showed that it may be worthwhile to conduct additional research to inform the decision to adopt CS + NV.ConclusionsNational HPV vaccination combined with opportunist cervical cancer screening is cost-effective in Nigeria. However, adoption of this strategy should depend on its relative efficiency when compared to other competing new vaccines and health interventions.

A Combined Statistical Selection Procedure Measured by the Expected Opportunity Cost

Selecting one of the best systems among finite but huge stochastic alternative systems is very important area of research since it has many applications in real life such as manufacturing systems, supply chain management and communication networks. Simulation is the main approach to estimate the performance values of these alternative systems. We propose a selection procedure which consists of two phases. In phase one, the ordinal optimization ( $${\textit{OO}}$$ ) technique is used to select a set K of k systems randomly. The probability that this set contains the actual best system can be measured using order statistics. In the second step of this phase, the optimal computing budget allocation ( $${\textit{OCBA}}_m$$ ) is used to select a smaller set of m systems from the set K. It is assumed that the computational budget is limited, the aim of $${\textit{OCBA}}_m$$ is to allocate these computational budget on the different systems to maximize the probability of correct selection P(CS). It gives the alternatives that have more influence on the solution, more computational budget; these two procedures are performed repeatedly until the available budget is consumed. In the second phase, the ranking and selection ( $$ R \& S$$ ) approach is applied on the smaller subset in order to select the best system. The algorithm is implemented on a generic example, and the expected opportunity cost is utilized to measure the potentially of incorrect selection. The numerical results show that the algorithm indeed selects a good enough system.

Optimal inventory control with sequential online auction in agriculture supply chain: an agent-based simulation optimisation approach

With the development of e-commerce, in agriculture supply chain, online auction is adopted as an inventory clearing tool. Comparing to mathematical models studying inventory control over online sequential auctions, our agent-based simulation model could systematically describe the complexities of bidders’ information interactions and behaviour preferences caused from financial and production perspectives, and by other supply chain members. In addition, we take into account the complex and dynamic market environment, which will impact the operation effect of auction policies. With identical auction items, the profit-maximising firm must decide auction lot-size, which is the number of units in each auction, minimum initial bid, and the time interval between auctions. To obtain the optimal solution, nested partitions framework and optimal expected opportunity cost algorithm are integrated to improve computation accuracy and efficiency. A case study based on real data is conducted to implement and validate the proposed approach. Furthermore, based on the model, the paper studies the sensitivities of the decision variables under different supply and demand scenarios.

A New Budget Allocation Framework for the Expected Opportunity Cost

In this paper, we present a new budget allocation framework for the problem of selecting the best simulated design from a finite set of alternatives. The new framework is developed on the basis of general underlying distributions and a finite simulation budget. It adopts the expected opportunity cost (EOC) quality measure, which, compared to the traditional probability of correct selection (PCS) measure, penalizes a particularly bad choice more than a slightly incorrect selection, and is thus preferred by risk-neutral practitioners and decision makers. To this end, we establish a closed-form approximation of EOC to formulate the budget allocation problem and derive the corresponding optimality conditions. A sequential budget allocation algorithm is then developed for implementation. The efficiency of the proposed method is illustrated via numerical experiments. We also link the EOC and PCS-based budget allocation problems by showing that the two are asymptotically equivalent. This result explains, to some extent, the similarity in performance between the EOC and PCS allocation procedures observed in the literature. The online appendix is available at https://doi.org/10.1287/opre.2016.1581 .

The International Decision Support Initiative Reference Case for Economic Evaluation: An Aid to Thought.

Policymakers in high-, low-, and middle-income countries alike face challenging choices about resource allocation in health. Economic evaluation can be useful in providing decision makers with the best evidence of the anticipated benefits of new investments, as well as their expected opportunity costs-the benefits forgone of the options not chosen. To guide the decisions of health systems effectively, it is important that the methods of economic evaluation are founded on clear principles, are applied systematically, and are appropriate to the decision problems they seek to inform. The Bill and Melinda Gates Foundation, a major funder of economic evaluations of health technologies in low- and middle-income countries (LMICs), commissioned a "reference case" through the International Decision Support Initiative (iDSI) to guide future evaluations, and improve both the consistency and usefulness to decision makers. The iDSI Reference Case draws on previous insights from the World Health Organization, the US Panel on Cost-Effectiveness in Health Care, and the UK National Institute for Health and Care Excellence. Comprising 11 key principles, each accompanied by methodological specifications and reporting standards, the iDSI Reference Case also serves as a means of identifying priorities for methods research, and can be used as a framework for capacity building and technical assistance in LMICs. The iDSI Reference Case is an aid to thought, not a substitute for it, and should not be followed slavishly without regard to context, culture, or history. This article presents the iDSI Reference Case and discusses the rationale, approach, components, and application in LMICs.

On-Demand Service Platforms

An on-demand service platform connects waiting-time sensitive customers with independent service providers (agents). This paper examines how two defining features of an on-demand service platform -- congestion-driven delay disutility and agent independence -- impact the platform's optimal per-service price and wage. Congestion reduces expected utility for customers and agents, which suggests that the platform respond by decreasing the price (to encourage participation of customers) and increasing the wage (to encourage participation of agents). These intuitive price and wage prescriptions are valid in a benchmark setting without uncertainty in the customers' valuation or the agents' opportunity costs. However, uncertainty in either dimension can reverse the prescriptions: Congestion increases the optimal price when customer valuation uncertainty is moderate. Congestion decreases the optimal wage when agent opportunity cost uncertainty is high and expected opportunity cost is moderate. Under agent opportunity cost uncertainty, agent independence decreases the price. Under customer valuation uncertainty, agent independence increases the price if and only if valuation uncertainty is sufficiently high.

Selecting the Best Simulated Design With the Expected Opportunity Cost Bound

In many applications, we wish to select the best simulated design among a set of design alternatives. While most work in the literature evaluates the quality of a selection procedure by the probability of correct selection of the best design, the expected opportunity cost of a potentially incorrect selection is also an important and useful measure, especially when the design performance reflects economic value. In this technical note, we consider the selection problem with an expected opportunity cost constraint. Based on some approximations, we derive for the selection problem an asymptotic closed-form allocation rule, which is easy to compute and implement. The numerical testing shows that the proposed selection procedure can enhance the simulation efficiency significantly.

Sequential Selection with Unknown Correlation Structures

We create the first computationally tractable Bayesian statistical model for learning unknown correlation structures in fully sequential simulation selection. Correlations represent similarities or differences between various design alternatives and can be exploited to extract much more information from each individual simulation. However, in most applications, the correlation structure is unknown, thus creating the additional challenge of simultaneously learning unknown mean performance values and unknown correlations. Based on our new statistical model, we derive a Bayesian procedure that seeks to optimize the expected opportunity cost of the final selection based on the value of information, thus anticipating future changes to our beliefs about the correlations. Our approach outperforms existing methods for known correlation structures in numerical experiments, including one motivated by the problem of optimal wind farm placement, where real data are used to calibrate the simulation model.