In this research, we focus on improving service-oriented routing by addressing the nuanced challenge of punctuality through the consideration of couriers' ability to ensure on-time deliveries. We utilize a comprehensive real-world data set from a cold chain logistics firm for analysis. Our empirical investigation indicates that relying solely on travel distance is inadequate for accurate delivery time prediction. We highlight critical elements, including couriers' fixed effects and workload, as key covariates to improve prediction performance. Distinguishing our work from existing literature, we integrate couriers' workload and location familiarity into our service-oriented routing model to enhance predictions of delivery times. We introduce the courier-assigned location mismatch (CALM) metric as a less intrusive approach to incorporating couriers' location familiarity into their delivery efficiency. We propose the novel service-oriented considerate routing (SOCR) model; by minimizing the CALM metric, couriers are assigned routes within familiar territories to the extent possible within the total routing distance constraint. The considerate routing strategies could potentially reduce the stress couriers face when delivering in unfamiliar areas. Additionally, we develop the connection of the SOCR model with a robust satisficing approach. This strategy guarantees timely deliveries by effectively mitigating the effects of predictive inaccuracies and potential model misspecifications. To solve the SOCR model, we apply Benders decomposition for an exact solution and tabu search for a heuristic approach, demonstrating their effectiveness and superior out-of-sample performance. Notably, our heuristic solutions significantly outperform exact solutions of classical vehicle routing problems with deadlines, resulting in substantial improvements in timely delivery performance.

In this paper, we propose a modified polyhedral method to elicit a decision maker's (DM's) nonlinear univariate utility function, which does not rely on explicit information about the shape structure, Lipschitz modulus, and the inflection point of the utility. The method is inspired by Toubia et al. (2004) for elicitation of the linear multi-variate utility and the success of the modification needs to overcome two main difficulties. First, we use the continuous piecewise linear function (PLF) to approximate the nonlinear utility and represent the PLF in terms of the vector of increments of linear pieces. Subsequently, elicitation of the nonlinear utility corresponds to reducing the polyhedral feasible set of the vectors of increments. Second, we reduce the size of the polyhedron by successive hyperplane cuts constructed by adaptively generating new queries (pairwise comparison lotteries) where the parameters of the lotteries are obtained by solving some optimization problems. In this reduction procedure, direction error of the cut hyperplane may occur due to the PLF approximation error. To tackle the issue, we develop a strategy by adding the support points of new lotteries to the set of breakpoints of the PLF. As an application, we use all the responses to the queries to construct an ambiguity set of utility functions which allows one to make decisions based on the worst-case utility and apply the modified polyhedral method in a preference robust optimization problem with proper conservatism reduction scheme. The preliminary numerical test results show that the proposed methods work very well.

In "Robust Actionable Prescriptive Analytics," Chen et al. present a significant advancement in prescriptive analytics. The authors propose a novel robust prescriptive analytics framework that bridges data-driven decision making and actionable policy optimization. Unlike traditional approaches that follow a “predict, then optimize” methodology, this framework directly maps side information to optimized decisions, ensuring both interpretability and implementability. Leveraging a robust satisficing approach, the model effectively mitigates overfitting to empirical data while maintaining computational tractability. The authors also introduce tree-based static and affine policies for enhanced interpretability, and they demonstrate the framework’s practical value through a portfolio optimization case study. This innovative approach provides a powerful tool for decision makers seeking robust, data-driven policies across various operational contexts.

We introduce a novel approach to prescriptive analytics that leverages robust satisficing techniques to determine optimal decisions in situations of distribution ambiguity and parameter estimation uncertainty. Our decision model relies on a reward function that incorporates uncertain parameters, which can be predicted using available side information. However, the accuracy of the linear prediction model depends on the quality of regression coefficient estimates derived from the available data. To achieve a desired level of fragility under distribution ambiguity, we begin by solving a residual-based robust satisficing model in which the residuals from the regression are used to construct an estimated empirical distribution and a target is established relative to the predict-then-optimize objective value. In the face of estimation uncertainty, we then solve an estimation-fortified robust satisficing model that minimizes the influence of estimation uncertainty while ensuring that the solution would maintain at most the same level of fragility in achieving a less ambitious guarding target. Our approach is supported by statistical justifications, and we propose tractable models for various scenarios, such as saddle functions, two-stage linear optimization problems, and decision-dependent predictions. We demonstrate the effectiveness of our approach through case studies involving a wine portfolio investment problem and a multiproduct pricing problem using real-world data. Our numerical studies show that our approach outperforms the predict-then-optimize approach in achieving higher expected rewards and at lower risks when evaluated on the actual distribution. Notably, we observe significant improvements over the benchmarks, particularly in cases of limited data availability.

Download This Paper Open PDF in Browser Add Paper to My Library Share: Permalink Using these links will ensure access to this page indefinitely Copy URL Copy DOI

We investigate how crowdsourced delivery platforms with both contracted and ad hoc couriers can effectively manage their workforce to meet delivery demands amidst uncertainties. Our objective is to minimize the hiring costs of contracted couriers and the crowdsourcing costs of ad hoc couriers, while considering the uncertain availability and behavior of the latter. Because of the complication of calibrating these uncertainties through data-driven approaches, we instead introduce a basic reduced information model to estimate the upper bound of the crowdsourcing cost and a generalized reduced information model to obtain a tighter bound. Subsequently, we formulate a robust satisficing model associated with the generalized reduced information model and show that a binary search algorithm can tackle the model exactly by solving a modest number of convex optimization problems. Our numerical tests using Solomon's data sets show that reduced information models provide decent approximations for practical delivery scenarios. Simulation tests further demonstrate that the robust satisficing model has better out-of-sample performance than the empirical optimization model that minimizes the total cost under historical scenarios.

Robust optimization presents a compelling methodology for optimization under uncertainty, providing a practical, ambiguity-averse evaluation of risk when the probability distribution is encapsulated by an ambiguity set. We introduce the moment-dispersion ambiguity set, an improvement on the moment-based set, enabling separate characterization of a random variable's location, dispersion, and support. To describe dispersion, we define the dispersion characteristic function, capturing complex attributes such as subGaussian and asymmetric dispersion, and its associated dispersion characteristic set, which serves as the input format for representing dispersion ambiguity in algebraic modeling tools. We devise a process for constructing and integrating ambiguity sets, showcasing their modeling flexibility. In particular, we introduce the independence propensity hyperparameter to foster joint ambiguity set creation for multiple random variables, enhancing our model's real-world applicability and facilitating varying interdependence characterization without needing a correlation matrix. For ambiguous risk assessment over momentdispersion ambiguity sets, we develop safe, tractable approximations for assessing entropic risks linked with affine and convex piecewise affine cost functions, accommodating varying risk tolerances. Lastly, we demonstrate the superior numerical performance of our model over other robust optimization models by adjusting the independence propensity hyperparameter when limited to marginal information. In data-driven experiments, we find that the moment-dispersion ambiguity sets yield less conservative decisions than classic moment-based sets and more robust decisions than Wasserstein ambiguity sets in datalimited scenarios.

Decision making under uncertainty involves both ambiguity and risk. In “Robust CARA Optimization,” Chen and Sim have developed innovative optimization models designed for ambiguity-averse decision makers whose risk preference is consistent with constant absolute risk aversion (CARA). The research delves into maximizing the worst-case expected exponential utility amid uncertainties from independent factors with ambiguous marginals. To enhance computational feasibility, the authors developed a series of approximations: starting with tractable concave functions in affinely perturbed cases, advancing to concave piecewise affinely perturbed scenarios, and culminating in novel multi-deflected linear decision rules for adaptive optimization. This comprehensive framework extends to a multi-period consumption model, ultimately forming an exponential conic optimization problem efficiently solvable with existing solvers. Practical applications demonstrated in project and multiperiod inventory management highlight the models’ potential to surpass existing stochastic optimization methods, especially under high risk aversion.

This study proposes a risk-adjusted version of bed occupancy rates (BORs) that can be used for patient admission control and bed capacity planning in hospitals. Simulations indicate a potential increase of 11% in elective patient admissions by planning using the proposed bed shortage index (BSI) as opposed to the traditional BOR. The BSI is also illustrated for purposes of bed capacity allocation between departments and across acute and nonacute hospitals.

We present a general framework for robust satisficing that favors solutions for which a risk-aware objective function would best attain an acceptable target even when the actual probability distribution deviates from the empirical distribution. The satisficing decision maker specifies an acceptable target, or loss of optimality compared with the empirical optimization model, as a trade-off for the model's ability to withstand greater uncertainty. We axiomatize the decision criterion associated with robust satisficing, termed as the fragility measure, and present its representation theorem. Focusing on Wasserstein distance measure, we present tractable robust satisficing models for risk-based linear optimization, combinatorial optimization, and linear optimization problems with recourse. Serendipitously, the insights to the approximation of the linear optimization problems with recourse also provide a recipe for approximating solutions for hard stochastic optimization problems without relatively complete recourse. We performnumerical studies on a portfolio optimization problem and a network lot-sizing problem. We show that the solutions to the robust satisficing models are more effective in improving the out-of-sample performance evaluated on a variety of metrics, hence alleviating the optimizer's curse.

We propose a new robust actionable prescriptive analytics framework that leverages past data and side information to minimize a risk-based objective function under distributional ambiguity. Our framework aims to find a policy that directly transforms the side information into implementable decisions. Specifically, we focus on developing actionable response policies that offer the benefits of interpretability and implementability. To address the potential issue of overfitting to empirical data, we adopt a data-driven robust satisficing approach that effectively handles uncertainty. We tackle the computational challenge for linear optimization models with recourse by developing a new tractable safe approximation for robust constraints, accommodating bilinear uncertainty and general norm-based uncertainty sets. Additionally, we introduce a biaffine recourse adaptation to enhance the quality of the approximation. Furthermore, we present a localized robust satisficing model that efficiently solves combinatorial optimization problems with tree-based static policies. Finally, we demonstrate the practical application of our framework through a simulation case study on risk-minimizing portfolio optimization using past returns as side information. We also provide a simulation case study on how the framework can be applied to obtain an interpretable policy for allocating taxis to different demand regions in response to weather information.

We study the problem of advance scheduling of ward admission requests in a public hospital, which affects the usage of critical resources such as operating theaters and hospital beds. Given the stochastic arrivals of patients and uncertain usage of resources, it is often infeasible for the planner to devise a risk‐free schedule to meet these requests without violating resource capacity constraints and creating adverse effects that include healthcare overtime, long patient waiting times, and bed shortages. The difficulty of quantifying these costs and the need to safeguard against resource overutilization lead us to propose a resource satisficing framework that renders the violation of resource constraints less likely and also diminishes its impact whenever it occurs. The risk of resource overutilization is captured by our resource satisficing index (RSI), which is calibrated to reflect a risk‐adjusted utilization rate for a better interpretation to the healthcare planner. Unlike the expected utilization rate, RSI is risk‐sensitive and serves to mitigate the risks of overutilization better whenever overutilization can be avoided in expectation. Our satisficing approach aims to balance out the overutilization risks by minimizing the maximal RSI among all resources and periods. Under our proposed partial adaptive scheduling policy, the resource satisficing model can be formulated and solved via a converging sequence of mixed‐integer linear optimization problems. A computational study establishes that our approach reduces resource overutilization risks to a greater extent than the benchmark methods.

A new study in the INFORMS journal Operations Research proposes a data-driven model for conducting strategic workforce planning in organizations. The model optimizes for recruitment and promotions by balancing the risks of not meeting headcount, budget, and productivity constraints, while keeping within a prescribed organizational structure. Analysis using the model indicates that there are increased workforce risks faced by organizations that are not in a state of growth or organizations that face limitations to organizational renewal (such as bureaucracies).

Satisficing, as an approach to decision making under uncertainty, aims at achieving solutions that satisfy the problem’s constraints as well as possible. Mathematical optimization problems that are related to this form of decision making include the P-model. In this paper, we propose a general framework of satisficing decision criteria and show a representation termed the S-model, of which the P-model and robust optimization models are special cases. We then focus on the linear optimization case and obtain a tractable probabilistic S-model, termed the T-model, whose objective is a lower bound of the P-model. We show that when probability densities of the uncertainties are log-concave, the T-model can admit a tractable concave objective function. In the case of discrete probability distributions, the T-model is a linear mixed integer optimization problem of moderate dimensions. Our computational experiments on a stochastic maximum coverage problem suggest that the T-model solutions can be highly competitive compared with standard sample average approximation models.

Many real-world optimization problems have input parameters estimated from data whose inherent imprecision can lead to fragile solutions that may impede desired objectives and/or render constraints infeasible. We propose a joint estimation and robustness optimization (JERO) framework to mitigate estimation uncertainty in optimization problems by seamlessly incorporating both the parameter estimation procedure and the optimization problem. Toward that end, we construct an uncertainty set that incorporates all of the data, and the size of the uncertainty set is based on how well the parameters are estimated from that data when using a particular estimation procedure: regressions, the least absolute shrinkage and selection operator, and maximum likelihood estimation (among others). The JERO model maximizes the uncertainty set’s size and so obtains solutions that—unlike those derived from models dedicated strictly to robust optimization—are immune to parameter perturbations that would violate constraints or lead to objective function values exceeding their desired levels. We describe several applications and provide explicit formulations of the JERO framework for a variety of estimation procedures. To solve the JERO models with exponential cones, we develop a second-order conic approximation that limits errors beyond an operating range; with this approach, we can use state-of-the-art second-order conic programming solvers to solve even large-scale convex optimization problems. This paper was accepted by J. George Shanthikumar, Management Science Special Section on Data-Driven Prescriptive Analytics.

At the heart of supervised learning is a minimization problem with an objective function that evaluates a set of training data over a loss function that penalizes poor fitting and a regularization function that penalizes over-fitting to the training data. More recently, data-driven robust optimization based learning models provide an intuitive robustness perspective of regularization. However, when the loss function is not Lipschitz continuous, solving the robust learning models exactly can be computationally challenging. We focus on providing tractable approximations for robust regression and classification problems for loss functions derived from Lipschitz continuous functions raised to the power of p . We also show the equivalence of the type-p robust learning models to the p th-root regularization problems when the underlying support sets are unbounded. Inspired by Long et al. (2021), we also propose tractable type-p robust satisficing learning models that are specified by target loss parameters. We illustrate that the robust satisficing regression and classification models can be tractably solved for a large class of problems, and we also establish finite sample probabilistic guarantees for limiting losses beyond the specified target. While the family of solutions generated by regularization and robust satisficing can be the same, from empirical studies on popular datasets, the relative targets for reasonably good out-of-sample performance can be found within a narrow range. We also demonstrate in the numerical study that the target-based hyper-parameter is easier to determine via cross-validation and can improve out-of-sample performance compared to standard regularization approaches.

On-time delivery is of utmost importance in today’s urban logistics. However, travel times are uncertain and classical deterministic routing solutions often fail to ensure timely delivery. In this paper, a robust solution that exploits travel times data to determine the best routes for maximal timely delivery is proposed. A new decision criterion is introduced, the service fulfillment risk index (sri), which accounts for both the late arrival probability and its magnitude. Together with Wasserstein distance–based ambiguity in travel times, sri can be evaluated efficiently in closed form. In addition, an exact branch-and-cut approach and a meta-heuristic algorithm are developed to minimize sri with a given travel cost. Simulation studies demonstrate that handling uncertainty improves service punctuality, and that incorporating ambiguity prevents overfitting. Most importantly, sri outperforms the canonical decision criteria of lateness probability and expected lateness duration.

Satisficers, in contrast to maximizers, are content with attaining the reasonable target that they set for themselves. Such behavior is prevalent in decision makers especially when they are facing complex situations under risks and uncertainty (Simon 1955). While there is an abundance of prescriptive analytics tools for maximizers, it is not the case for satisficers. To fill this gap, we develop a new prescriptive analytics tool called robust satisficing that uses data to help a satisficer achieve her target expected reward or consumption as well as possible under ambiguous risks and prediction uncertainty. It builds upon the robustness optimization framework recently proposed by Long et al. (2021), and we extend it to incorporate aspects of predictive analytics. We adopt linear regression as the underlying predictive model and propose a new estimator uncertainty and residual ambiguity set to characterize the relations between the underlying regression coefficients, which is uncertain but non-stochastic, and the stochastic random variables representing residuals that have ambiguous distributions. The robust satisficing model is also useful in allocating resources for multiple satisficing agents to meet their expected reward targets. We present some useful robust satisficing models that can be solved efficiently, and provide tractable approximations to tackle adaptive linear optimization problems. The simulation studies for multi-product pricing and newsvendor problems elucidate the benefits of the robust satisficing framework in helping the firm attain the target expected profits, mitigate shortfalls, and limit target surplus, if desired. The robust satisficing model can also improve solutions over one that is obtained by solving a baseline empirical optimization model using estimated parameters. The improvement is also more pronounced when data availability is limited. Paradoxically, maximizers can also benefit from the analytics of robust satisficing.

In practical optimization problems, we typically model uncertainty as a random variable though its true probability distribution is unobservable to the decision maker. Historical data provides some information of this distribution that we can use to approximately quantify the risk that depends on both the decision and the uncertainty. This empirical optimization approach is vulnerable to the issues of overfitting, which could be overcome by several data-driven robust optimization techniques. To tackle overfitting, Long et.al.(2022) propose a robust satisficing model, which is specified by a performance target and a penalty function that measures the deviation of the uncertainty from its nominal value, and yields solutions with superior out-of-sample performance. We generalize the robust satisficing framework to conic optimization problems with recourse, which has broad applications in predictive and prescriptive analytics. We derive an exact semidefinite optimization formulation for a biconvex quadratic evaluation function, with quadratic penalty and ellipsoidal support set. More importantly, under complete and bounded recourse, and a reasonably chosen polyhedral support set and penalty function, we propose safe approximations that are feasible for any reasonably chosen target. We then demonstrate that the assumption of complete and bounded recourse is not unimpeachable, and then introduce a novel perspective casting technique to derive an equivalent conic optimization problem satisfying the stated assumptions. Computationally, we showcase a study on data-driven portfolio optimization and demonstrate that the robust satisficing solutions can provide significant improvements over the solutions obtained by stochastic optimization models, including the celebrated Markowitz model, which is prone to overfitting.