Knowledge that Transforms

Problem description: In many markets with demand uncertainties, competing retailers may share inventories for common products that they offer consumers. This paper examines how competitors’ product sharing affects their inventory and service-quality decisions. The existing literature has mainly focused on inventory sharing among independent retailers who do not compete with each other. Our research aims to fill the gap in this literature by investigating the tradeoffs of inventory sharing between retailers who directly compete for customers based on service quality. Methodology/results: We develop a game-theoretical model in which two retailers selling a common product from the same manufacturer compete for customers by offering differentiated services together with the product. Each retailer faces stochastic demand that increases in its service quality and decreases in the competitor’s service quality. When a retailer runs out of stock of the product, it may replenish its inventory directly from the manufacturer and/or request the competitor’s excess inventory if they have an inventory-sharing agreement. We find that inventory sharing may soften or intensify service competition, depending on the transfer price for the shared inventory. Specifically, when retailers agree to share inventory, their service levels decrease in the transfer price if their preseason inventory levels are exogenous, but are nonmonotone in the transfer price if the retailers endogenously choose inventory levels. Moreover, our analysis reveals that the retailers’ equilibrium inventory levels will increase in the transfer price and can be higher or lower than their levels in the case without inventory sharing. We also find that with exogenous inventory, the retailers prefer to share inventory at the highest nonmoot transfer price, whereas with endogenous inventory, the retailers may prefer not to share inventory, even at the optimal transfer price, when the level of competition and the preorder cost are high. Finally, we show that with service competition, inventory sharing cannot achieve full coordination under any transfer price. Managerial implications: When deciding whether to share inventory with competitors, managers should consider not only the benefits of inventory pooling, but also the strategic effect of sharing on the firms’ inventory choices and service levels.

Problem definition: Hospital-acquired conditions (HACs) represent undesirable complications that occur during a hospital stay. HACs can compromise patient safety and care outcomes and result in unnecessary socio-economic costs. Although hospitals are expected to reduce the incidence of HACs, few studies have examined the implications of HACs on other clinical outcomes and measures of hospital performance. This study contributes to the literature by exploring the relationship between exposure to a set of target HACs, length of stay (LOS) performance, and 30-day readmission risk. Methodology/results: To estimate the effects of HACs, we conduct econometric analyses using patient-visit-level data for heart attack, heart failure, and pneumonia patients hospitalized in the U.S. state of Florida during 2010–2014. We define LOS performance as the deviation of LOS from the Geometric Mean LOS (GMLOS), a standard LOS set by the Centers for Medicare and Medicaid Services. First, we find that exposure to HACs leads to a 37% increase in the odds of readmission and a 79% increase in LOS. Second, an increase in LOS is associated with a decrease in readmission risk, and this decrease is stronger for patients exposed to HACs. Third, LOS performance mediates the HACs-readmission risk relationship, such that the increase in the readmission risk of a HAC patient can be fully suppressed by the patient’s LOS. Fourth, we find that for patients exposed to HACs, the benefits of a longer LOS are almost entirely capitalized when the LOS becomes 65% longer than the GMLOS. Managerial implications: We demonstrate that, when addressing the consequences of HACs, clinicians also face indirectly a trade-off between reducing readmissions and controlling costs. We proffer LOS as a potential mechanism under hospitals’ control for mitigating the adverse effects of HACs on readmission risk. Thus, this study offers guidance to clinicians having to decide when to discharge patients with exposure to HACs.

Problem definition: Online retailers provide recommendations of ancillary services when a customer is making a purchase. Our goal is to predict the net present value (NPV) of these services, estimate the probability of a customer subscribing to each of them depending on what services are offered to them, and ultimately prescribe the optimal personalized service recommendation that maximizes the expected long-term revenue. Methodology/results: We propose a novel method called cluster-while-classify (CWC), which jointly groups observations into clusters (segments) and learns a distinct classification model within each of these segments to predict the sign-up propensity of services based on customer, product, and session-level features. This method is competitive with the industry state of the art and can be represented in a simple decision tree. This makes CWC interpretable and easily actionable. We then use double machine learning (DML) and causal forests to estimate the NPV for each service and, finally, propose an iterative optimization strategy—that is, scalable and efficient—to solve the personalized ancillary service recommendation problem. CWC achieves a competitive 74% out-of-sample accuracy over four possible outcomes and seven different combinations of services for the propensity predictions. This, alongside the rest of the personalized holistic optimization framework, can potentially result in an estimated 2.5%–3.5% uplift in the revenue based on our numerical study. Managerial implications: The proposed solution allows online retailers in general and Wayfair in particular to curate their service offerings and optimize and personalize their service recommendations for the stakeholders. This results in a simplified, streamlined process and a significant long-term revenue uplift. History: This paper has been accepted as part of the 2021 Manufacturing & Service Operations Management Practice-Based Research Competition.

Problem definition: We study the use of nonmonetary incentives based on reciprocity to facilitate capacity sharing between two service providers that have limited and substitutable service capacity. Academic/practical relevance: We propose a parsimonious game theory framework, in which two firms dynamically choose whether to accept each other’s customers without the capability to perfectly monitor each other’s capacity utilization state. Methodology: We solve the continuous-time imperfect-monitoring game by focusing on a class of public strategy, in which firms’ real-time capacity-sharing decision depends on an intuitive and easy-to-implement accounting device, namely the current net number of transferred customers. We refer to such an equilibrium as a trading-favors equilibrium. We characterize the condition in which capacity sharing takes place in such an equilibrium. Results: We find that some degree of efficiency loss (as compared with a central planner’s solution) is necessary to induce reciprocity. The efficiency loss is small when the two firms have similar traffic intensity even if they are different in service-capacity scale, whereas the efficiency loss can be considerably large when the two firms have significantly different traffic intensities. The trading-favors mechanism, surprisingly, can outperform the perfect-monitoring benchmark when the two firms exhibit high asymmetry in terms of service-capacity scale or traffic intensity because the smaller firm tends to deviate from collaboration. Managerial implications: Firms should consider engaging in nonmonetary reciprocal capacity sharing if regulations, transaction costs, or other market and operational frictions make it difficult to use a capacity-sharing contract based on monetary payments. The trading-favors collaboration can improve the firms’ payoff close to the centralized upper bound when the firms have similar traffic intensities. However, when their traffic intensities are highly different, firms are better off with a monetary-payment contract to induce more capacity sharing and are worse off investing in increasing their visibility to each other’s real-time available capacity, namely investing in perfect monitoring.

Problem definition: We study scheduling multi-class impatient customers in parallel server queueing systems. At the time of arrival, customers are identified as being one of many classes, and the class represents the service and patience time distributions as well as cost characteristics. From the system’s perspective, customers of the same class at time of arrival get differentiated on their residual patience time as they wait in queue. We leverage this property and propose two novel and easy-to-implement multi-class scheduling policies. Academic/practical relevance: Scheduling multi-class impatient customers is an important and challenging topic, especially when customers’ patience times are nonexponential. In these contexts, even for customers of the same class, processing them under the first-come, first-served (FCFS) policy is suboptimal. This is because, at time of arrival, the system only knows the overall patience distribution from which a customer’s patience value is drawn, and as time elapses, the estimate of the customer’s residual patience time can be further updated. For nonexponential patience distributions, such an update indeed reveals additional information, and using this information to implement within-class prioritization can lead to additional benefits relative to the FCFS policy. Methodology: We use fluid approximations to analyze the multi-class scheduling problem with ideas borrowed from convex optimization. These approximations are known to perform well for large systems, and we use simulations to validate our proposed policies for small systems. Results: We propose a multi-class time-in-queue policy that prioritizes both across customer classes and within each class using a simple rule and further show that most of the gains of such a policy can be achieved by deviating from within-class FCFS for at most one customer class. In addition, for systems with exponential patience times, our policy reduces to a simple priority-based policy, which we prove is asymptotically optimal for Markovian systems with an optimality gap that does not grow with system scale. Managerial implications: Our work provides managers ways of improving quality of service to manage parallel server queueing systems. We propose easy-to-implement policies that perform well relative to reasonable benchmarks. Our work also adds to the academic literature on multi-class queueing systems by demonstrating the joint benefits of cross- and within-class prioritization.

Problem definition: Consider consumers who prefer to consume a good later rather than earlier. If the price is constant, then we would expect consumers to wait to buy the good. That does not hold if consumers are concerned that others will buy the good early, so that a shortage will later occur. When will consumers arrive when they fear a shortage? What is the profit-maximizing policy of a monopolist? Might the firm lose profits by offering advance sales? The timing of consumer arrivals is much studied. Little consideration, however, has addressed how anticipated shortages affect arrival times. The application is important: managers want to know when consumers will arrive, when they should make the product available, and what price to charge to maximize profits. Methodology/results: We use game theory. We analyze analytically outcomes when a single item is for sale: we give closed solutions for the equilibrium customer behavior and profit-maximizing firm strategy and conduct sensitivity analysis. For generalization concerning more than one unit, we give some analytical results and provide many numerical solutions. When the price is constant over time, then even with no operating cost of doing so, offering advance sales reduces profits. If, however, the firm must offer both advance sales and later sales, then the profit-maximizing price induces all arrivals at the same time (either early or late, depending on the parameters). An increase in the number of units offered for sale increases the profit-maximizing price and increases the firm’s expected profit. The equilibrium strategy of consumers can generate some unexpected behavior. The arrival rate may increase with the price of the good. For a given price, an increase in the number of units for sale increases the number of consumers who arrive early. Managerial implications: The firm should offer the good only at the time consumers most desire it, and not earlier. Additionally, the profit-maximizing price can be derived from our analysis. This price is not the price which maximizes the expected number of arrivals.

Problem definition: Motivated by a platelet inventory management problem, we study a fixed lifetime perishable inventory management problem under a general demand process. Determining an optimal ordering policy for perishable inventory systems is particularly challenging because of the well-known “curse of dimensionality.” Approximation policies with worst-case performance bounds have been developed in the literature for perishable inventory systems. However, using real data, we observe that the existing policies tend to underorder when the unit shortage penalty is high, which is an important concern for critical perishable products, such as lifesaving blood products. We seek to address this problem in this paper. Methodology/results: We present a new approximation policy for perishable inventory systems, which we call a truncated balancing (TB) policy. In particular, we first define a new balancing ordering quantity and prove a novel lower bound on the optimal ordering quantity. We then define our TB policy such that the maximum between the balancing ordering quantity and the lower bound is ordered at each period. We prove that when first in, first out is an optimal issuing policy, (1) our proposed TB policy admits a worst-case performance bound of two, and (2) it is asymptotically optimal when the unit shortage penalty goes to infinity. Finally, we present a calibrated numerical study based on real data from our partner hospital and show that our proposed policy performs significantly better than the existing policies in practical scenarios with reasonably high shortage penalties. Managerial implications: Our analysis offers managerial insights for perishable inventory management, especially for systems with an imbalance in underage and overage cost parameters. When the unit shortage penalty is high, simply balancing the underage and overage costs can lead to underordering, whereas our proposed policy effectively addresses this drawback.

Problem definition: A blockchain payment system, such as Bitcoin or Ethereum, validates electronic transactions and stores them in a chain of blocks without a central authority. Miners with computing power compete for the rights to create blocks according to a preset protocol, referred to as hashing or mining, and, in return, earn fees paid by users who submit transactions. Because of security concerns caused by decentralization, a transaction is confirmed after a number of additional blocks are subsequently extended to the block containing it. This confirmation latency introduces an intricate interplay between miners and users. This paper provides approximate system equilibria and studies optimal designs of a blockchain. Methodology/results: The hashing process is essentially a single-server queue with batch services based on a fee-based priority discipline, and confirmation latency adds complexity to the equilibrium behavior and optimal design. We analyze how miners’ participation decisions interact with users’ participation and fee decisions and identify optimal designs when the goal is to maximize the throughput or social welfare. We validate our model and conduct numerical studies using data from Bitcoin. Managerial implications: By incorporating security issues, we uncover the interdependence of the decisions between users and miners and the driver for nonzero entrance fees in practice. We show that miners and users may end up in either a vicious or virtuous cycle, depending on the initial system state. By allowing the entrance fee to be a design parameter, we are able to establish that it is optimal to simply run a blockchain system at its full capacity and a block size as small as possible.

Problem definition: A significant percentage of online consumers place consecutive orders within a short duration. To reduce the total order arrangement cost, an online retailer may consolidate consecutive orders from the same consumer. We investigate how long the retailer should hold the consumer’s orders before sending them to a third-party logistics provider (3PL) for processing. In this order-holding problem, we optimize the holding time to balance the total order arrangement cost and the potential delay in delivery. Methodology/results: We model the order-holding problem as a Markov decision process. We show that the optimal order-holding decisions follow a threshold-type policy that is straightforward to implement: Hold any pending orders if the holding time is within a threshold or send them to the 3PL otherwise. Whenever the consumer places a new order, the holding time is reset, and the threshold is updated based on a cumulative set of the past consecutive orders in the consumer’s shopping journey. Using a consumer’s sequential decision model, we personalize the threshold by finding its closed-form expression in the consumer’s order features. We determine the model’s coefficients and evaluate the threshold-type policy using the data of the 2020 MSOM Data Driven Research Challenge. Extensive numerical experiments suggest that the personalized threshold-type policy outperforms two commonly used benchmarks by having fewer order arrangements or shorter holding times. Furthermore, personalizing the order-holding decisions is significantly more valuable for “enterprise” customers. Managerial implications: Our research suggests a higher threshold for consumers who are more likely to place consecutive orders within a short duration. The consumers’ demographic information has a significant effect on the threshold. Specifically, the threshold is higher for “plus” consumers, female consumers, and consumers in the age group of 16–25 years. The threshold for tier 1 cities is lower than that for tier 2 to tier 4 cities but higher than that for tier 5 cities. History: This paper has been accepted as part of the 2020 MSOM Data Driven Challenge.

Problem definition: Effective hypertension management is critical to reducing the consequences of atherosclerotic cardiovascular disease, a leading cause of death in the United States. Clinical guidelines for hypertension can be enhanced using decision-analytic approaches capable of capturing complexities in treatment planning. However, model-generated recommendations may be uninterpretable/unintuitive, limiting their clinical acceptability. We address this challenge by investigating interpretable treatment plans. Methodology/results: We formulate interpretable treatment plans as Markov decision processes (MDPs) and analyze the problems of optimizing monotone policies, which prohibit decreasing treatment intensity for sicker patients, and class-ordered monotone policies, which generalize monotone policies. We establish that both policies depend on initial state distributions and that optimal monotone policies can be generated tractably for many treatment planning problems. Next, we propose exact formulations for optimizing interpretable policies broadly. Then, we analyze the price of interpretability, proving that the class-ordered monotone policy’s price of interpretability does not exceed the monotone policy’s price of interpretability. Finally, we formulate and evaluate MDPs for hypertension treatment planning using a large nationally representative data set of the U.S. population. We compare the structure and performance of optimal monotone policies and class-ordered monotone policies with optimal MDP-based policies and current clinical guidelines. At the patient level, optimal MDP-based policies may be unintuitive, recommending more aggressive treatment for healthier patients than sicker patients. Conversely, monotone policies and class-ordered monotone policies never deescalate treatment, reflecting clinical intuition. Across 66.5 million patients, optimized monotone policies and class-ordered monotone policies outperform clinical guidelines, saving over 3,246 quality-adjusted life years per 100,000 patients, with both policies paying a low price of interpretability. Sensitivity analysis illustrates that monotone policies and class-ordered monotone policies are robust to various definitions of “interpretability.” Managerial implications: Interpretable policies can be tractably optimized, drastically outperform existing guidelines, and perform near optimally—potentially increasing the acceptability of decision-analytic approaches in practice.