Knowledge that Transforms

Motivated by algorithmic targeting and data management, we explore a scenario where the seller holds an advantage over consumers regarding match-related information about products. The seller optimizes a product line consisting of two vertically differentiated products alongside an opaque product resulting from their mixture, strategically recommending these products to potential consumers. We model algorithmic targeting using an information design framework, and our investigation revolves around understanding how algorithmic targeting shapes consumer purchasing behaviors and influences market equilibrium. Furthermore, we explore the potential orchestration between algorithmic targeting and opaque selling, facilitated by product-line design. These two closely related instruments coincide in ex-ante manipulating information while differing in their targeting objects. Interestingly, only when the basic products exhibit intermediate differentiation does the seller use both instruments. This is because, when the disparity between the two primary products is extreme (either too large or too small), algorithmic targeting makes opaque selling ineffective at increasing profits. However, when these differences are moderate, the two strategies can complement each other. Opaque selling enhances profitability by introducing intermediate product variety, enabling more nuanced market segmentation, while algorithmic targeting is more flexible in promoting the willingness-to-pay of a wider range of consumers. Furthermore, when conducting welfare analysis, the adoption of algorithmic targeting is found sometimes to reduce consumer surplus but can enhance overall social welfare, highlighting the need for careful regulatory oversight in this domain.

This article introduces the first joint shelf design and space planning problem that considers two placement options for items—hanging and shelving—on flexible shelves. These types of shelves are used in sectors such as do-it-yourself and toy retail, and for household goods in grocery stores. However, they have received limited attention in the literature, which typically focuses on regular shelves with a single placement option: placing items on shelf panels. The problem requires three interdependent decisions: (1) the placement option for each item (shelving or hanging), (2) the shelf design (number and vertical positioning of shelf panels), and (3) the shelf space planning (assignment of facings as well as the vertical and horizontal positioning of items). We formalize this problem as a mixed-integer linear program (MILP) and develop a greedy multi-start matheuristic to efficiently solve practical instances. Computational experiments demonstrate that our algorithm outperforms both a commercial solver and a benchmark method for two-dimensional shelf space planning in terms of runtime and solution quality. A comprehensive analysis of synthetic instances and a real-world case study provides several managerial insights. First, hanging items enables more flexible use of shelf space, which is especially beneficial when item variety is high. However, when large vertical grabbing gaps must be considered, stacking items on shelf panels may be more advantageous. In turn, there is a risk of wasted space due to height or width mismatches. Second, the number and size of the segments on the shelf significantly influence layout profitability, highlighting the need to jointly optimize shelf design and space allocation. Third, it is common practice to arrange hanging items in horizontal rows, which can be facilitated by segmenting the shelf space. While this improves visual appeal, increasing the number of segments tends to reduce overall space utilization and profitability. Finally, a real-world case study involving 237 products across six categories from a European grocery retailer confirms the practical applicability of our approach. It demonstrates significant potential for improving space utilization and layout efficiency.

We develop a practical optimization model for the management of a demand-side platform (DSP), which is applicable in static planning situations where the DSP acquires valuable impressions for high-volume advertiser clients in a real-time bidding environment. We propose a highly flexible model for the DSP to maximize its profit while maintaining acceptable levels of budget spending for its advertisers. Our model achieves flexibility and improved performance primarily through two different aspects: (i) we replace standard budget constraints with a more general budget utilization proxy function over budget spending levels, and (ii) we can accommodate arbitrary auction types by directly modeling the interactions between the DSP and the auctions. Our proposed formulation leads to a non-convex optimization problem due to the joint optimization over both impression allocation and bid price decisions. Using Fenchel duality theory, we obtain a convex dual problem that can be efficiently solved with subgradient based algorithms and from which a primal solution may be recovered efficiently. Under a natural and intuitive “increasing marginal cost” condition, as well as under a more general condition, we show that there is zero duality gap between the dual problem and the original non-convex primal problem. Under the same conditions, we also demonstrate convergence of our algorithm to an optimal solution of the non-convex formulation as the dual problem is solved to near optimality. We conduct experiments on both synthetic data as well as data from a real DSP, and our results demonstrate how our algorithm allows the DSP to better trade off between profitability and budget spending as compared to a widely used “greedy” heuristic approach.

Robotic mobile fulfillment (RMF) systems automate storage and transportation within fulfillment centers while still relying on human pickers. We focus on two key performance metrics in these systems, aiming to minimize overall completion time (OCT) as the primary objective and the number of required robots (NRR) as a secondary objective. We investigate two interrelated operational problems influencing these metrics: (i) Pod selection, which involves choosing the mobile racks for item picking, and (ii) pod scheduling, which entails assigning these racks to pickers and determining the picking sequence. We first explore the pod scheduling problem independently, providing theoretical results. This stand-alone problem is NP-hard with at least two pickers when minimizing OCT and remains NP-hard with even one picker when minimizing NRR. The NRR objective introduces a novel optimization problem structure, contributing to scheduling theory even beyond the RMF context. We demonstrate that a simple but effective scheduling rule is asymptotically optimal for minimizing OCT with multiple pickers. For NRR minimization with a single picker, we derive theoretical performance bounds for two sequencing rules. When incorporating the pod selection problem, we focus on two approaches: (i) Sequential and (ii) integrated pod selection and scheduling. The sequential approach handles pod selection first, then pod scheduling, while the integrated approach addresses both problems simultaneously within a single formulation to minimize OCT. Computational experiments using e-commerce order data reveal that the sequential approach achieves significantly faster and constant computation times, with a mean OCT similar to that of the integrated approach. We also find that our sequencing rules can reduce mean NRR by 13%–28% without affecting OCT, compared to the case where no such rules are used. The sequential approach for OCT minimization and the proposed sequencing rules for NRR minimization are scalable to large systems with any picker count. Our experiments also explore the changes in OCT and NRR values with varying numbers of pickers. These results guide managers in assigning the desired number of pickers for a target OCT and inform managers about the average NRR they can expect for the chosen picker count.

This article advances the literature on the optimality of the base-stock policy for a general demand distribution and a general prior belief, which we update as we observe realized demands, assumed to be continuous, independent and identically distributed, random variables. The value function depends on the belief, so the functional Bellman equation is infinite-dimensional. Significantly, in contrast with traditional approaches, we derive a functional equation for the derivative of the value function with respect to the inventory level, which provides a direct approach to computing the optimal base-stock policy. In two well-known cases, we characterize how the base-stock level depends on the belief, and we implement the approach to compute the optimal base-stock level. In the first case of conjugate probabilities, the infinite-dimensional state reduces to a finite-dimensional sufficient statistic. That allows us to solve two numerical examples of exponential and Weibull demands. Moreover, for the exponential demand example, we compare the optimal cost with the costs achieved by two myopic policies with three guesses of the initial belief. We find that the optimal policy improves upon the first myopic policy by 12.6%, 13.0%, and 9.2%, and upon the second myopic policy by 28.7%, 26.9%, and 27.7%. The second case considers the demand to come from one of two possible distributions, but we do not know which. Here, we derive a functional equation in one hyperparameter expressing the ratio of the weights assigned to the two distributions. We then develop an approximation scheme to solve it, show that it converges, and implement it numerically to obtain the optimal base-stock levels over time.

In reusable resources like vehicle sharing, city parking, and hotel services, resource units are used by consecutive customers for a stochastic usage time and are made available for future customers upon return. We model such reusable resources as Erlang loss systems, where customers who find all units occupied are blocked. Customers are rational decision-makers, and their willingness to join the system depends on factors such as price, time limits, service value, and resource availability. When each customer is charged a fixed price, we examine whether it is beneficial to install time limits, which increase availability at the expense of reduced usage time. We formulate and solve a two-dimensional revenue maximization problem to optimize both the usage price and the time limit. We differentiate between on-demand resources, which are immediately reusable upon return, and reserved resources, which can only be reused after the time limit expires. With on-demand resources, setting a time limit is proven to be detrimental, making the entry price the sole tool for maximizing revenue. This conclusion remains valid when the usage time increases with the entry price. In contrast, managing reserved resources involves an interplay between time limits and entry prices. Additionally, we show that loss systems (where customers do not wait) should be managed differently from systems where customers do wait. Specifically, in systems with waiting, we prove that only the time limit should be optimized, while the entry price should capture the full market share. We prove our results by analyzing the behavior of the equilibrium arrival rate and revenue, which necessitates establishing novel properties for the blocking probability. These properties yield new sharp bounds for the blocking probability and enable us to prove the convergence of the optimized model for on-demand resources to the quality-and-efficiency-drivenregime as the number of resource units grows.

Federal agencies use reverse auctions to procure cloud infrastructure services offered by major public cloud providers such as Amazon, Google, and Microsoft. Although recent research has examined operational issues in cloud computing, these papers have not analyzed the vendor base design decisions when these cloud capacity instances are procured through the reverse auction mechanism. Therefore, several important research questions are still unaddressed. For example, how should federal clients decide on the number of cloud providers for the multi-cloud strategy? How should clients decide on private cloud capacity investments along with sourcing requirements from multiple cloud providers? We find that the client’s capacity portfolio decision is determined by factors such as vendors’ cost heterogeneity and available capacity. Specifically, we find higher cost heterogeneity leads to a smaller vendor base. Interestingly and somewhat counter-intuitively, we find that higher cost heterogeneity may increase or decrease private cloud investments. We also study the client’s decision on the type of capacity instances to be procured via reverse auctions. We find federal clients should only utilize the on-demand instances mechanism (where capacity is procured after demand realization) to fulfill the cloud computing requirements. We further observe that if vendors experience capacity outages, then the client should upfront reserve capacity instances.

When a platform has limited inventory, it is important to have a variety of products available for each customer while managing the remaining stock. To maximize revenue over the long term, the assortment policy needs to take into account the complex purchasing behavior of customers whose arrival orders and preferences may be unknown. We propose a data-driven approach for dynamic assortment planning that utilizes historical customer arrivals and transaction data. To address the challenge of online assortment customization, we use a Markov decision process framework and employ a model-free deep reinforcement learning (DRL) approach to solve the online assortment policy because of the computational challenge. Our method uses a specially designed deep neural network (DNN) model to create assortments while observing the inventory constraints, and an advantage actor-critic algorithm to update the parameters of the DNN model, with the help of a simulator built from the historical transaction data. To evaluate the effectiveness of our approach, we conduct simulations using both a synthetic data set generated with a pre-determined customer type distribution and ground-truth choice model, as well as a real-world data set. Our extensive experiments demonstrate that our approach produces significantly higher long-term revenue compared to some existing methods and remains robust under various practical conditions. We also demonstrate that our approach can be easily adapted to a more general problem that includes reusable products, where customers might return purchased items. In this setting, we find that our approach performs well under various usage time distributions.

In business markets, sales from customers are often jointly determined by multiple roles, yet firms struggle to quantify individual contribution of each role and the synergies among them. This study applies a value-partitioning approach to separate the sales contributions of customer-focused outside (OS) representatives (reps) and operations-focused inside (IS) reps, and their synergistic effects. It leverages variations in OS–IS combinations to generate individual-level value-added metrics, as well as metrics for dyadic synergies. To address empirical challenges such as limited variations in OS–IS combinations, the study employs empirical Bayes estimation, which provides best linear unbiased prediction (BLUP) estimates. An application using data from a Fortune 500 firm operating in business markets, reveals that the value added by OS reps, IS reps, and their interface have substantial and differential impacts on customer sales. Specifically, an increase of one standard deviation in the effect of OS, IS, or interface synergy improves customer sales by 17.8%, 11.6%, or 14.3%, respectively. Simulations demonstrate the superiority of empirical Bayes over fixed effects estimation in reducing bias, and that the value-added metrics are predictive of future customer sales. This research also illustrates how value-added metrics can be applied to evaluate the impact of sales programs on different sales roles.

The attended home healthcare (AHH) industry is experiencing rapid growth due to the rising demand from an aging population and the potential benefits of alleviating pressures on traditional healthcare resources. However, ensuring timely one-on-one AHH services for homebound patients remains a challenge because of cascading delays arising from uncertainties in travel and service times. To address this issue in last-mile homecare delivery, we develop a systematic cascading delay mitigation strategy to ensure patients receive dependable homecare services. Specifically, we introduce a compound set reliability index ( CSRI ) that captures risk exposure by separately characterizing distinct travel and service time uncertainties, instead of approaching them as a single type of uncertainty in previous studies. The CSRI -based service-level constraints are then integrated into a set-partitioning formulation to mitigate the cascading delays. We devise an exact branch-price-and-cut framework and employ a variable neighborhood search metaheuristic to achieve fast-effective solutions. Numerical experiments with benchmark and real-world datasets validate the effectiveness of our methods, underscore the benefits of adopting a systematic cascading delay mitigation strategy, and provide insights to AHH service providers regarding the impact of crucial managerial parameters on delay manifestation. The CSRI constraints and dedicated solution methods can effectively support practical decision-making and enhance the punctuality of AHH services, leading to better service dependability and heightened stakeholder satisfaction.