Electronic Companion Research Articles

Interplay Between Servicizing and Remanufacturing: Economic and Environmental Implications

Problem definition: To investigate the interplay between servicizing and remanufacturing, two widely used strategies in the circular economy, and its impact on firms’ economic and environmental performance, we consider a profit-maximizing manufacturer who explores the possibility of jointly adopting the two strategies. Methodology and results: We develop optimization models that capture the main attributes for servicizing (pay-per-use, demand pooling) and remanufacturing (lower production costs, higher operating costs). We show that the presence of remanufacturing always makes servicizing less attractive to adopt, and having servicizing may discourage the adoption of remanufacturing if the remanufacturing cost reduction effect is not sufficiently large. The joint adoption of servicizing and remanufacturing is preferred when the remanufacturing cost is neither too high nor too low and the range of the remanufacturing cost that favors the joint adoption is further moderated by the firm’s pooling level and the operating cost of remanufactured products. Lastly, we find that when the firm adopts servicizing in the presence of remanufacturing with relatively high remanufacturing costs, it can reduce the number of remanufactured products with low environmental impact in the market and, thus, harm the environment, resulting in a misalignment between economic and environmental goals. Managerial implications: Our findings suggest that managers considering jointly adopting servicizing and remanufacturing must balance their competition on the low-usage end of the market with the potential complementarity due to remanufacturing cost reduction. Further, by showing the win-win conditions under which the joint adoption of servicizing and remanufacturing improves firms’ economic and environmental performance, we demonstrate that there are no one-size-fits-all circular economy strategies and call for caution when promoting these strategies across industries. Supplemental Material: The electronic companion is available at https://doi.org/10.1287/msom.2022.0379 .

Conditional Lead-Time Flexibility in an Assemble-to-Order System

Problem definition: We introduce and formalize a concept termed conditional lead-time flexibility (CLF), which refers to the industry practice where a manufacturer requests that its upstream suppliers dynamically adjust the pipeline orders’ remaining lead times. Over a finite horizon, an assemble-to-order manufacturer makes joint decisions on inventory replenishment and lead-time adjustment to minimize the total discounted expected cost. Methodology/results: The problem is formulated as a multiperiod dynamic programming with an enlarged state space to track the adjustable pipeline orders. The replenishment and lead-time adjustment decisions are made sequentially in each period. The analysis reveals that (i) the optimal cost-to-go function is both convex and additively separable, that (ii) both the optimal replenishment and lead-time adjustment decisions follow general base-stock policies, and that (iii) the convexity and additive separability allow us to perform a derivative analysis on the optimality equations and design an efficient algorithm. Managerial implications: Using real industry data, we numerically find that (i) CLF achieves notable cost savings over a wide range of parameters, that (ii) the value of CLF comes from both the order expediting and deferring, and that (iii) CLF outperforms dual sourcing when the unit adjustment cost is less than 40% of the unit ordering cost from the express source. Our findings underscore the importance of CLF. Funding: T. Deng acknowledges financial support from the National Key Research and Development Program of China [Grant 2022YFB3305602] and the National Natural Science Foundation of China (NSFC) [Grant 72188101]. Supplemental Material: The electronic companion is available at https://doi.org/10.1287/msom.2023.0520 .

Nonlinear Decision Rules Made Scalable by Nonparametric Liftings

Sequential decision making often requires dynamic policies, which are computationally not tractable in general. Decision rules provide approximate solutions by restricting decisions to simple functions of uncertainties. In this paper, we consider a nonparametric lifting framework where the uncertainty space is lifted to higher dimensions to obtain nonlinear decision rules. Current lifting-based approaches require predetermined functions and are parametric. We propose two nonparametric liftings, which derive the nonlinear functions by leveraging the uncertainty set structure and problem coefficients. Both methods integrate the benefits from lifting and nonparametric approaches, and hence provide scalable decision rules with performance bounds. More specifically, the set-driven lifting is constructed by finding polyhedrons within uncertainty sets, inducing piecewise-linear decision rules with performance bounds. The dynamics-driven lifting, on the other hand, is constructed by extracting geometric information and accounting for problem coefficients. This is achieved by using linear decision rules of the original problem, also enabling one to quantify lower bounds of objective improvements over linear decision rules. Numerical comparisons with competing methods demonstrate superior computational scalability and comparable performance in objectives. These observations are magnified in multistage problems with extended time horizons, suggesting practical applicability of the proposed nonparametric liftings in large-scale dynamic robust optimization. This paper was accepted by David Simchi-Levi, optimization. Supplemental Material: The electronic companion and data files are available at https://doi.org/10.1287/mnsc.2024.4988 .

Electronic Companion (E-Co)

Electronic Companion (E-Co)

Self-Adapting Network Relaxations for Weakly Coupled Markov Decision Processes

High-dimensional weakly coupled Markov decision processes (WDPs) arise in dynamic decision making and reinforcement learning, decomposing into smaller Markov decision processes (MDPs) when linking constraints are relaxed. The Lagrangian relaxation of WDPs (LAG) exploits this property to compute policies and (optimistic) bounds efficiently; however, dualizing linking constraints averages away combinatorial information. We introduce feasibility network relaxations (FNRs), a new class of linear programming relaxations that exactly represents the linking constraints. We develop a procedure to obtain the unique minimally sized relaxation, which we refer to as self-adapting FNR, as its size automatically adjusts to the structure of the linking constraints. Our analysis informs model selection: (i) the self-adapting FNR provides (weakly) stronger bounds than LAG, is polynomially sized when linking constraints admit a tractable network representation, and can even be smaller than LAG, and (ii) self-adapting FNR provides bounds and policies that match the approximate linear programming (ALP) approach but is substantially smaller in size than the ALP formulation and a recent alternative Lagrangian that is equivalent to ALP. We perform numerical experiments on constrained dynamic assortment and preemptive maintenance applications. Our results show that self-adapting FNR significantly improves upon LAG in terms of policy performance and/or bounds, while being an order of magnitude faster than an alternative Lagrangian and ALP, which are unsolvable in several instances. This paper was accepted by Baris Ata, stochastic models and simulation. Supplemental Material: The electronic companion and data files are available at https://doi.org/10.1287/mnsc.2022.01108 .

Dynamic Home Care Routing and Scheduling with Uncertain Number of Visits per Referral

Despite the rapid growth of the home care industry, research on the scheduling and routing of home care visits in the presence of uncertainty is still limited. This paper investigates a dynamic version of this problem in which the number of referrals and their required number of visits are uncertain. We develop a Markov decision process (MDP) model for the single-nurse problem to minimize the expected weighted sum of the rejection, diversion, overtime, and travel time costs. Because optimally solving the MDP is intractable, we employ an approximate linear program (ALP) to obtain a feasible policy. The typical ALP approach can only solve very small-scale instances of the problem. We derive an intuitively explainable closed-form solution for the optimal ALP parameters in a special case of the problem. Inspired by this form, we provide two heuristic reduction techniques for the ALP model in the general problem to solve large-scale instances in an acceptable time. Numerical results show that the ALP policy outperforms a myopic policy that reflects current practice, and is better than a scenario-based policy in most instances considered. Funding: This work was supported by the Natural Sciences and Engineering Research Council of Canada [Grants RGPIN-2018-05225 and RGPIN-2020-210524] and by the Telfer School of Management SMRG Postdoctoral Research Fellowship Support [Grant 2020]. Supplemental Material: The electronic companion is available at https://doi.org/10.1287/trsc.2023.0120 .

Code and Data Repository for Unified Framework for Choice-Based Facility Location Problem

The choice-based facility location (CBFL) problem arises in various industrial and business contexts. The problem is based on a decentralized perspective: Companies set up chains of facilities, and customers determine from which chain or facility to seek service according to their own preferences. Essentially, customer preferences or choices play a key role in characterizing various CBFL problems, which differ mainly in the models or rules employed to characterize the choice. Consequently, a large number of formulations appear and are often solved by dedicatedly designed approaches in the literature. Such a situation significantly complicates practitioners' decision-making process when they are facing practical problems but are unsure which ad hoc model is suitable for their cases. In this article, we address this dilemma by providing a unified modeling framework based on the concept of preference dominance. Specifically, we conceptualize the choice behavior as a sequential two-step procedure: Given a set of open facilities, each customer first forms a nondominated consideration set and then splits the buying power within the set. Such an interpretation renders practitioners high modeling flexibility, as they can tailor how preference dominance is constructed according to their specific contexts. In particular, we show that our model can represent several streams of CBFL problems. To support the applicability of our model, we design an efficient exact decomposition algorithm. Extensive computational studies reveal that although the algorithm is designed for a general purpose, it outperforms most approaches that are tailored for ad hoc problems by a large margin, which justifies both the effectiveness and the efficiency of the unified framework. This repository provides data for the problem and code for the algorthm. The main folders are 'data', 'src', and 'results'. 'data': four datasets generator (and instances) used in the paper. 'src': the source code for the decomposition algorithm. 'results': high-resoultion figures in our paper All experimental results can be found in the paper (manuscript and electronic companion).

Robust Combination Testing: Methods and Application to COVID-19 Detection

Simple and affordable testing tools are often not accurate enough to be operationally relevant. For coronavirus disease 2019 (COVID-19) detection, rapid point-of-care tests are cheap and provide results in minutes, but they largely fail policy makers’ accuracy requirements. We propose an analytical methodology, based on robust optimization, that identifies optimal combinations of results from cheap tests for increased predictive accuracy. This methodological tool allows policy makers to credibly quantify the benefits from combination testing and thus, break the trade-off between cost and accuracy. Our methodology is robust to noisy and partially missing input data and incorporates operational constraints—relevant considerations in practice. We apply our methodology to two data sets containing individual-level results of multiple COVID-19 rapid antibody and antigen tests, respectively, to generate Pareto-dominating receiver operating characteristic curves. We find that combining only three rapid tests increases out-of-sample area under the curve by 4% (6%) compared with the best-performing individual test for antibody (antigen) detection. We also find that a policy maker who requires a specificity of at least 0.95 can improve sensitivity by 8% and 2% for antibody and antigen testing, respectively, relative to available combination testing heuristics. Our numerical analysis demonstrates that robust optimization is a powerful tool to avoid overfitting, accommodate missing data, and improve out-of-sample performance. Based on our analytical and empirical results, policy makers should consider approving and deploying a curated combination of cheap point-of-care tests in settings where “gold standard” tests are too expensive or too slow. This paper was accepted by Stefan Scholtes, healthcare management. Supplemental Material: The data files and electronic companion are available at https://doi.org/10.1287/mnsc.2023.4826 .

The Electric Dial-a-Ride Problem on a Fixed Circuit

Shared mobility services involving electric autonomous shuttles have increasingly been implemented in recent years. Because of various restrictions, these services are currently offered on fixed circuits and operated with fixed schedules. This study introduces a service variant with flexible stopping patterns and schedules. Specifically, in the electric dial-a-ride problem on a fixed circuit (eDARP-FC), a fleet of capacitated electric shuttles operates on a given circuit consisting of a recharging depot and a sequence of stations where passengers can be picked up and dropped off. The shuttles may perform multiple laps, between which they may need to recharge. The goal of the problem is to determine the vehicles’ stopping sequences and schedules, including recharging plans, so as to minimize a weighted sum of the total passenger excess time and the total number of laps. The eDARP-FC is formulated as a nonstandard lap-based mixed integer linear programming and is shown to be NP-Hard. Efficient polynomial time algorithms are devised for two special scheduling subproblems. These algorithms and several heuristics are then applied as subroutines within a large neighborhood search metaheuristic. Experiments on instances derived from a real-life system demonstrate that the flexible service results in a 32%–75% decrease in the excess time at the same operational costs. Funding: This work was supported by the Fonds Wetenschappelijk Onderzoek [Project Data-Driven Logistics: Grant S007318N; Project Optimizing the Design of a Hybrid Urban Mobility System: Grant G020222N; and Grant OR4Logistics]. Y. Molenbruch is partially funded by the Fonds Wetenschappelijk Onderzoek [Grant 1202719N]. The computational resources and services used in this work were provided by the Flemish Supercomputer Center funded by the Fonds Wetenschappelijk Onderzoek and the Flemish Government. Supplemental Material: The electronic companion is available at https://doi.org/10.1287/trsc.2023.1208 .

Exponential-Size Neighborhoods for the Pickup-and-Delivery Traveling Salesman Problem

Neighborhood search is a cornerstone of state-of-the-art traveling salesman and vehicle routing metaheuristics. Whereas neighborhood exploration procedures are well-developed for problems with individual services, their counterparts for one-to-one pickup-and-delivery problems are more scarcely studied. A direct extension of classic neighborhoods is often inefficient or complex because of the necessity of jointly considering service pairs. To circumvent these issues, we introduce major improvements to existing neighborhood searches for the pickup-and-delivery traveling salesman problem and new large neighborhoods. We show that the classic Relocate Pair neighborhood can be fully explored in [Formula: see text] instead of [Formula: see text] time. We adapt the 4-Opt and Balas–Simonetti neighborhoods to consider precedence constraints. Moreover, we introduce an exponential-size neighborhood called 2k-Opt, which includes all solutions generated by multiple nested 2-Opts and can be searched in [Formula: see text] time using dynamic programming. We conduct extensive computational experiments, highlighting the significant contribution of these new neighborhoods and speedup strategies within two classical metaheuristics. Notably, our approach permits us to repeatedly solve small pickup-and-delivery problem instances to optimality or near-optimality within milliseconds, and therefore, it represents a valuable tool for time-critical applications, such as meal delivery or mobility on demand. Funding: This work was supported by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Conselho Nacional de Desenvolvimento Científico e Tecnológico [Grants 308528/2018-2, 315361/2020-4, 422470/2021-0], and Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro [Grants E-26/202.790/2019, E-26/201.417/2022, E-26/010.002232/2019]. Supplemental Material: The electronic companion is available at https://doi.org/10.1287/trsc.2022.1176 .

Branch-Cut-and-Price for the Time-Dependent Green Vehicle Routing Problem with Time Windows

Motivated by rising concerns regarding global warming and traffic congestion effects, we study the time-dependent green vehicle routing problem with time windows (TDGVRPTW), aiming to minimize carbon emissions. The TDGVRPTW is a variant of the time-dependent vehicle routing problem (TDVRP) in which, in addition to the time window constraints, the minimization of carbon emissions requires determination of the optimal departure times for vehicles, from both the depot and customer location(s). Accordingly, the first exact method based on a branch-cut-and-price (BCP) algorithm is proposed for solving the TDGVRPTW. We introduce the notation of a time-dependent (TD) arc and describe how to identify the nondominated TD arcs in terms of arc departure times. In this way, we reduce infinitely many TD arcs to a finite set of nondominated TD arcs. We design a state-of-the-art BCP algorithm for the TDGVRPTW with labeling and limited memory subset row cuts, together with effective dominance rules for eliminating dominated TD arcs. The exact method is tested on a set of test instances derived from benchmark instances proposed in the literature. The results show the effectiveness of the proposed exact method in solving TDGVRPTW instances involving up to 100 customers. Summary of Contribution: Due to the environmental situation, green vehicle routing problems (GVRPs) aim to consider greenhouse gas emissions reduction, while routing the vehicles, and play a key role in transportation and logistics. Vehicle greenhouse gas emissions strongly depend on the vehicle speeds and traffic conditions which in real life vary continuously over time. To tackle these challenges, we address the time-dependent green vehicle routing problem with time windows (TDGVRPTW) aimed at reducing total carbon emissions under time-dependent travel times and time window constraints. We design an effective exact method for the TDGVRPTW based on a state-of-the-art branch-cut-and-price algorithm. The paper is both of methodological value for researchers and of interest for practitioners. For researchers, the presented algorithm is amenable for various routing constraints and provides a ground for further studies and research. For practitioners, the paper suggests insights on how the carbon emissions change based on different vehicle speed profiles. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms—Discrete. Funding: This research is supported by the National Natural Science Foundation of China [Grants 71831003, 71831006, 72171043, and 71901180] and the Fundamental Research Funds for the Central Universities [Grants N170405005 and N180704015]. Supplemental Material: The electronic companion is available at https://doi.org/10.1287/ijoc.2022.1195 .

Herding in Probabilistic Forecasts

Decision makers often ask experts to forecast a future state. Experts, however, can be biased. In the economics and psychology literature, one extensively studied behavioral bias is called herding. Under strong levels of herding, disclosure of public information may lower forecasting accuracy. This result, however, is derived only for point forecasts. In this paper, we consider experts’ probabilistic forecasts under herding, find a closed-form expression for the first two moments of a unique equilibrium forecast, and show that the experts report too similar locations and inflate the variance of their forecasts because of herding. Furthermore, we show that the negative externality of public information no longer holds. In addition to reacting to new information as expected, probabilistic forecasts contain more information about the experts’ full beliefs and interpersonal structure. This facilitates model estimation. To this end, we consider a one-shot setting with one forecast per expert and show that our model is identifiable up to an infinite number of solutions based on point forecasts but up to two solutions based on probabilistic forecasts. We then provide a Bayesian estimation procedure for these two solutions and apply it to economic forecasting data collected by the European Central Bank and the Federal Reserve Bank of Philadelphia. We find that, on average, the experts invest around 19% of their efforts into making similar forecasts. The level of herding shows an increasing trend from 1999 to 2007 but drops sharply during the financial crisis of 2007–2009 and then rises again until 2019.This paper was accepted by Yan Chen, behavioral economics and decision analysis.Supplemental Material: The electronic companion and data are available at https://doi.org/10.1287/mnsc.2022.4487 .

Retailer Inventory Sharing in Two-Tier Supply Chains: An Experimental Investigation

When multiple retailers hold inventory to satisfy random demand, retailer inventory-sharing strategies can potentially reduce the supply-demand mismatch and increase overall supply chain performance. In this paper, we experimentally investigate alternative inventory-sharing strategies in a two-tier supply chain with an upstream manufacturer and two downstream retailers. In one setting, retailers act as if they are centralized and use a single quantity to fulfill joint demand. In the other, retailers are decentralized and face separate demands, but they can transfer inventory after demands are realized. In this latter decentralized scenario, we also consider whether the manufacturer or retailers have decision authority over the inventory transfer price. One key result is that when the retailers are decentralized and the manufacturer sets the transfer price, both retailers and the manufacturer earn higher profits than in the centralized retailer strategy, which runs counter to theory. We also find that when retailers are decentralized and set their own transfer price, the most equitable distribution of profits is achieved. In an effort to account for these results, we find that a model of fairness captures decisions well. Overall, by investigating how different inventory-sharing strategies affect the distribution of profits in a two-tier supply chain, our results provide guidance to firms considering how, if at all, they should enter such arrangements.This paper was accepted by Jay Swaminathan, operations management.Funding: The authors acknowledge financial support from Cornell University and the University of Virginia.Supplemental Material: The data files and electronic companion are available at https://doi.org/10.1287/mnsc.2022.4323 .

Dynamic Inventory Repositioning in On-Demand Rental Networks

We consider a rental service with a fixed number of rental units distributed across multiple locations. The units are accessed by customers without prior reservation and on an on-demand basis. Customers can decide on how long to keep a unit and where to return it. Because of the randomness in demand and in returns, there is a need to periodically reposition inventory away from some locations and into others. In deciding on how much inventory to reposition and where, the system manager balances potential lost sales with repositioning costs. Although the problem is increasingly common in applications involving on-demand rental services, not much is known about the nature of the optimal policy for systems with a general network structure or about effective approaches to solving the problem. In this paper, first, we show that the optimal policy in each period can be described in terms of a well-specified region over the state space. Within this region, it is optimal not to reposition any inventory, whereas, outside the region, it is optimal to reposition but only such that the system moves to a new state that is on the boundary of the no-repositioning region. We also provide a simple check for when a state is in the no-repositioning region. Second, we leverage the features of the optimal policy, along with properties of the optimal cost function, to propose a provably convergent approximate dynamic programming algorithm to tackle problems with a large number of dimensions. This paper was accepted by David Simchi-Levi, optimization. Funding: The research of S. Benjaafar is in part funded by the US National Science Foundation (NS) [Grant SCC-1831140]. The research of X. Li is in part funded by the SingaporeMinistry of Education [Grant R-266-000-128-133]. This work used the Extreme Science and Engineering Discovery Environment [NSF Grant ACI-1548562], the Bridges-2 system [NSF Grant ACI-1445606], and resources from the University of Pittsburgh Center for Research Computing. Supplemental Material: Data and the electronic companion are available at https://doi.org/10.1287/mnsc.2021.4286 .

Electronic Companion to Adaptivity and Confounding in Multi-Armed Bandit Experiments

Electronic Companion to Adaptivity and Confounding in Multi-Armed Bandit Experiments

Electronic companion- Adjustable and Distributionally Robust Chance-Constrained Optimization for Providing Flexibilities in an Active Distribution Network

Electronic companion- Adjustable and Distributionally Robust Chance-Constrained Optimization for Providing Flexibilities in an Active Distribution Network

Electronic Companion - A Clearing Mechanism for Joint Energy and Ancillary Services in Non-Convex Markets Considering High Penetration of Renewable Energy Sources

Electronic Companion - A Clearing Mechanism for Joint Energy and Ancillary Services in Non-Convex Markets Considering High Penetration of Renewable Energy Sources

Electronic companion - A Clearing Mechanism for Joint Energy and Ancillary Services in Non-Convex Markets Considering High Penetration of Renewable Energy Sources

Electronic companion - A Clearing Mechanism for Joint Energy and Ancillary Services in Non-Convex Markets Considering High Penetration of Renewable Energy Sources

Adaptive Distributionally Robust Optimization

We develop a modular and tractable framework for solving an adaptive distributionally robust linear optimization problem, where we minimize the worst-case expected cost over an ambiguity set of probability distributions. The adaptive distributionally robust optimization framework caters for dynamic decision making, where decisions adapt to the uncertain outcomes as they unfold in stages. For tractability considerations, we focus on a class of second-order conic (SOC) representable ambiguity set, though our results can easily be extended to more general conic representations. We show that the adaptive distributionally robust linear optimization problem can be formulated as a classical robust optimization problem. To obtain a tractable formulation, we approximate the adaptive distributionally robust optimization problem using linear decision rule (LDR) techniques. More interestingly, by incorporating the primary and auxiliary random variables of the lifted ambiguity set in the LDR approximation, we can significantly improve the solutions, and for a class of adaptive distributionally robust optimization problems, exact solutions can also be obtained. Using the new LDR approximation, we can transform the distributionally adaptive robust optimization problem to a classical robust optimization problem with an SOC representable uncertainty set. Finally, to demonstrate the potential for solving management decision problems, we develop an algebraic modeling package and illustrate how it can be used to facilitate modeling and obtain high-quality solutions for medical appointment scheduling and inventory management problems. The electronic companion is available at https://doi.org/10.1287/mnsc.2017.2952 . This paper was accepted by Noah Gans, optimization.

Technical Note—The Competitive Facility Location Problem in a Duopoly: Advances Beyond Trees

We consider a competitive facility location problem on a network where consumers located on vertices wish to connect to the nearest facility. Knowing this, each competitor locates a facility on a vertex, trying to maximize market share. We focus on the two-player case and study conditions that guarantee the existence of a pure-strategy Nash equilibrium for progressively more complicated classes of networks. For general graphs, we show that attention can be restricted to a subset of vertices referred to as the central block. By constructing trees of maximal bi-connected components, we obtain sufficient conditions for equilibrium existence. Moreover, when the central block is a vertex or a cycle (for example, in cactus graphs), this provides a complete and efficient characterization of equilibria. In that case, we show that both competitors locate their facilities in a solution to the 1-median problem, generalizing a well-known insight arising from Hotelling’s model. We further show that an equilibrium must solve the 1-median problem in other classes of graphs, including grids, which essentially capture the topology of urban networks. In addition, when both players select a 1-median, the solution must be at equilibrium for strongly-chordal graphs, generalizing a previously known result for trees. The electronic companion is available at https://doi.org/10.1287/opre.2017.1694 .