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In this work, we study the optimal design of two-armed clinical trials to maximize the accuracy of parameter estimation in a statistical model, where the interaction between patient covariates and treatment are explicitly incorporated to enable precision medication decisions. Such a modeling extension leads to significant complexities for the produced optimization problems because they include optimization over design and covariates concurrently. We take a min-max optimization model and minimize (over design) the maximum (over population) variance of the estimated interaction effect between treatment and patient covariates. This results in a min-max bilevel mixed integer nonlinear programming problem, which is notably challenging to solve. To address this challenge, we introduce a surrogate optimization model by approximating the objective function, for which we propose two solution approaches. The first approach provides an exact solution based on reformulation and decomposition techniques. In the second approach, we provide a lower bound for the inner optimization problem and solve the outer optimization problem over the lower bound. We test our proposed algorithms with synthetic and real-world data sets and compare them with standard (re)randomization methods. Our numerical analysis suggests that the proposed approaches provide higher-quality solutions in terms of the variance of estimators and probability of correct selection. We also show the value of covariate information in precision medicine clinical trials by comparing our proposed approaches to an alternative optimal design approach that does not consider the interaction terms between covariates and treatment. Summary of Contribution: Precision medicine is the future of healthcare where treatment is prescribed based on each patient information. Designing precision medicine clinical trials, which are the cornerstone of precision medicine, is extremely challenging because sample size is limited and patient information may be multidimensional. This work proposes a novel approach to optimally estimate the treatment effect for each patient type in a two-armed clinical trial by reducing the largest variance of personalized treatment effect. We use several statistical and optimization techniques to produce efficient solution methodologies. Results have the potential to save countless lives by transforming the design and implementation of future clinical trials to ensure the right treatments for the right patients. Doing so will reduce patient risks and reduce costs in the healthcare system. [ABSTRACT FROM AUTHOR]

In this paper, we consider service applications where drivers serve subscription customers at their homes on a regular basis and at known times. To build trust with customers, the company requires that subscription customers are consistently served by the same driver. In addition to subscription customers, on-demand customers request delivery on a daily basis. For the company, the challenge is to consistently serve the subscription customers while simultaneously maximizing the daily profit from the on-demand customers. We model the problem as a two-stage stochastic decision problem. The first stage determines the assignment of drivers to subscription customers. The second stage is a team-orienteering problem with time windows and mandatory visits by fixed drivers. We present an anticipatory consistent customer assignment policy (ACCA) based on the multiple scenario approach framework. Our computational study shows that ACCA significantly outperforms consistency concepts from the literature, while increasing costs less than 5%. [ABSTRACT FROM AUTHOR]

Two critical yet frequently conflicting objectives for logistics and transportation service companies are improving customer satisfaction and reducing transportation cost. In particular, given a network of customer requests with preferred service times, it is very challenging to find vehicle routes and service schedules simultaneously that respect all operating constraints and minimize the total transportation and customers' inconvenience costs. In this paper, we introduce the vehicle routing problem with time windows and convex node costs (VRPTW-CNC), in which we model each customer's inconvenience cost as a convex function of the service start time at that customer. The VRPTW-CNC combines and extends both the standard vehicle routing problem with time windows and some previous results on the optimal service scheduling problem over a fixed route. We propose a branch-and-cut-and-price algorithm to solve the VRPTW-CNC with general convex inconvenience cost functions. To solve the pricing problem, our labeling algorithm only generates labels that possibly lead to optimal schedule times over a route, which significantly improves the effectiveness of pricing. Extensive computational results demonstrate the effectiveness of our approach. [ABSTRACT FROM AUTHOR]