We propose an optimization framework to solve problems that involve parameters that are forecast to vary over a given time horizon. We model uncertainty in the forecast through the use of lower and upper bounds that can be seen as time-dependent uncertainty levels. Our framework is applicable in long-term budget planning or resource allocation settings. We propose a model to minimize the maximum deviation from a so-called “ideal function” that we then show can be reformulated as a narrowest path problem on an acyclic directed graph with weights determined by solving minimax regret problems. Given that constructing the graph might be computationally demanding, we devise an optimal path discovery iterative scheme that computes edge weights on an as-needed basis and that results in ε-optimal solutions in a finite number of steps. We conduct an extensive numerical analysis of the proposed procedure to determine average-case performance. We then apply our proposed framework in two real-life settings: (1) large-scale screening of populations for West Nile Virus and (2) the allocation of resources in blood donation centers. The results from both case studies indicate significant reductions in yearly societal costs. History: Accepted by J. Paul Brooks, Area Editor for Applications in Biology, Medicine, & Healthcare. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0048 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0048 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

In this paper, we analyze appointment systems involving heterogeneous customers, each requesting different services, with nonstationary arrival processes. The main goal is to identify server schedules that lead to good-performing systems, which we measure through the expected system time and the number of customer rejections. This decision problem arises in a number of applications and is especially relevant when certain service types dominate other service types. A key challenge in this analysis is the lack of closed-form analytical expressions that characterize the performance of the system. In this work, we construct a stylized optimization model based on a pointwise stationary approximation that emulates the original stochastic system. An analysis of the resulting stylized model comprised of a single customer type leads to key structural properties which we use to devise a globally convergent solution scheme that runs in polynomial time. This solution scheme is then generalized to the case of multiple customer types for two different formulations of the decision problem. To demonstrate the effectiveness of the proposed framework, we conduct a case study on Texas A&M University’s College and Psychological Services. Our results show that our optimal solutions substantially improve the performance of the system over current practices by reducing access time for critical mental health services by as much as 56%. Our analysis also identifies an easily implementable scheduling policy consisting of a single modification whose performance is within 10% of the more complex policies. History: Accepted by J. Paul Brooks, Area Editor for Applications in Biology, Medicine, & Healthcare. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0039 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0039 . The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

We study the problem of mass screening of heterogeneous populations under limited testing budget. Mass screening is an essential tool that arises in various settings, e.g., the COVID-19 pandemic. The objective of mass screening is to classify the entire population as positive or negative for a disease as efficiently and accurately as possible. Under limited budget, testing facilities need to allocate a portion of the budget to target sub-populations (i.e., proactive screening) while reserving the remaining budget to screen for symptomatic cases (i.e., reactive screening). This paper addresses this decision problem by taking advantage of accessible population-level risk information to identify the optimal set of sub-populations for proactive/reactive screening. The framework also incorporates two widely used testing schemes: Individual and Dorfman group testing. By leveraging the special structure of the resulting bilinear optimization problem, we identify key structural properties, which in turn enable us to develop efficient solution schemes. Furthermore, we extend the model to accommodate customized testing schemes across different sub-populations and introduce a highly efficient heuristic solution algorithm for the generalized model. We conduct a comprehensive case study on COVID-19 in the US, utilizing geographically-based data. Numerical results demonstrate a significant improvement of up to 52% in total misclassifications compared to conventional screening strategies. In addition, our case study offers valuable managerial insights regarding the allocation of proactive/reactive measures and budget across diverse geographic regions.

We study the design of large-scale group testing schemes under a heterogeneous population (i.e., subjects with potentially different risk) and with the availability of multiple tests. The objective is to classify the population as positive or negative for a given binary characteristic (e.g., the presence of an infectious disease) as efficiently and accurately as possible. Our approach examines components often neglected in the literature, such as the dependence of testing cost on the group size and the possibility of no testing, which are especially relevant within a heterogeneous setting. By developing key structural properties of the resulting optimization problem, we are able to reduce it to a network flow problem under a specific, yet not too restrictive, objective function. We then provide results that facilitate the construction of the resulting graph and finally provide a polynomial time algorithm. Our case study, on the screening of HIV in the United States, demonstrates the substantial benefits of the proposed approach over conventional screening methods. Summary of Contribution: This paper studies the problem of testing heterogeneous populations in groups in order to reduce costs and hence allow for the use of more efficient tests for high-risk groups. The resulting problem is a difficult combinatorial optimization problem that is NP-complete under a general objective. Using structural properties specific to our objective function, we show that the problem can be cast as a network flow problem and provide a polynomial time algorithm.

We provide a novel regret-based robust formulation of the Dorfman group size problem considering the realistic setting where the prevalence rate is uncertain, establish key structural properties of...