Problem definition: Inventory management problems with periodic and controllable resets occur in the context of managing water storage in the developing world and dynamically optimizing endcap promotion duration in retail outlets. In this paper, we consider a set of sequential decision problems in which the decision maker must not only balance holding and shortage costs but discard all inventory before a fixed number of decision epochs with the option for an early inventory reset. Methodology/results: Finding optimal policies for these problems through dynamic programming presents unique challenges because of the nonconvex nature of the resulting value functions. Moreover, this structure cannot be readily analyzed even with extended convexity definitions, such as K-convexity. Managerial implications: Our key contribution is to present sufficient conditions that ensure the optimal policy has an easily interpretable structure, which generalizes the well-known (𝑠,𝑆) policy from the operations management literature. Furthermore, we demonstrate that, under these rather mild conditions, the optimal policy exhibits a four-threshold structure. We then conclude with computational experiments, thereby illustrating the policy structures that can be extracted in various inventory management scenarios.
KB 1040
Problem definition: We consider the dynamic pricing problem of multiple products under (asymmetric) reference effects over an infinite horizon. Unlike existing literature, which is mostly focused on the single-product setting, our multiproduct setting takes into account the cross-product effects among substitutes and incorporates the memory-based reference prices into the multinomial logit (MNL) demand model. Even with the single-product logit demand, the structure of the optimal pricing policy is intractable. Therefore, we focus on the long-run patterns of the optimal pricing policy and also discuss the performance of the myopic pricing policy. Methodology/results: We first provide a comprehensive characterization of the myopic pricing policy, including its solution, long-run convergence behavior, and optimality gap. For the optimal pricing policy, we show an intricate connection between its long-run dynamics and types of reference effects. We demonstrate that the presence of any gain-seeking product renders a long-run constant pricing policy suboptimal. Conversely, the constant policy (or optimal steady state) can exist in both loss-neutral and loss-averse scenarios, where we provide a sufficient condition for such existence and give the analytical expression for the optimal steady state. We further show that when pricing perfect substitutes, the true optimal policy under the multiproduct framework is more likely to yield a long-run cyclic pattern than the policy derived from the single-product framework, a phenomenon that aligns well with the periodic discounts in real-world markets. Managerial implications: This discrepancy in the long-run behaviors between multi- and single-product-based policies highlights the importance of employing the multiproduct framework and addressing the cross-product effects, as sticking to the single-product framework while managing multiple substitutes can misrepresent long-run dynamics and result in suboptimality. In the multiproduct domain, our model suggests that retailers are more likely to benefit from appropriate price variations than maintaining a constant pricing policy.
We study the data-integrated, price-setting newsvendor problem in which the price–demand relationship is described by some parametric model with unknown parameters. We develop the operational data analytics (ODA) formulation of this problem that features a data-integration model and a validation model. The data-integration model consists of a class of functions called the operational statistics. Each operational statistic maps the available data to the ordering decision. The validation model finds, among the set of candidate operational statistics, the ordering decision that leads to the highest actual profit, which is unknown because of the unknown demand parameters. This ODA framework leads to a consistent estimate of the profit function with which we optimize the pricing decision. The derived quantity and price decisions demonstrate robust profit performance even when the sample size is very small in relation to the demand variability. Compared with the conventional approach with which the unknown parameters are estimated and then the decisions are optimized, the ODA framework produces significantly superior performance in the mean, standard deviation, and minimum of the profit, suggesting the robustness of the ODA solution especially in the small-sample regime.
We study the reliable (uncapacitated) facility location (RFL) problem in a data-driven environment where historical observations of random demands and disruptions are available. Owing to the combinatorial optimization nature of the RFL problem and the mixed-binary randomness of parameters therein, the state-of-the-art RFL models applied to the data-driven setting either suggest overly conservative solutions or become computationally prohibitive for large- or even moderate-size problems. In this paper, we address the RFL problem by presenting an innovative prescriptive model aiming to balance solution conservatism with computational efficiency. In particular, our model selects facility locations to minimize the fixed costs plus the expected operating costs approximated by a tractable data-driven estimator, which equals to a probabilistic upper bound on the intractable Kolmogorov distributionally robust optimization estimator. The solution of our model is obtained by solving a mixed-integer linear program that does not scale in the training data size. Our approach is proved to be asymptotically optimal, and offers a theoretical guarantee for its out-of-sample performance in situations with limited data. In addition, we discuss the adaptation of our approach when facing data with covariate information. Numerical results demonstrate that our model significantly outperforms several important RFL models with respect to both in-sample and out-of-sample performances as well as computational efficiency.
This study investigates the operations of a novel service model, mobile charging, in which an e-commerce platform operator dispatches trucks equipped with charging piles to provide charging services for customers’ electric vehicles with low battery levels. We model the platform-customer interaction with a Stackelberg game and explicitly characterize customers’ optimal charging decisions under the platform’s various service plans. In a general scenario that involves charging requests within a transportation network, we develop a joint optimization model for the platform’s pricing and service fulfillment, utilizing an elaborately constructed augmented network. In addition, we explore a localized subproblem where multiple orders are concentrated within a specific region. With a simplified model structure, we propose an approximation algorithm with provable performance guarantees and further theoretically evaluate the resource consumption and associated platform benefits for serving the orders in each region. The results enable the batching of neighboring demands within the general scenario as a specialized node, resulting in a streamlined network with fewer nodes. Additionally, we can enhance the algorithm’s efficiency within the general framework through strategic prioritization of node visitations, leveraging the analytical findings. Furthermore, the insights derived can offer recommendations for the deployment of mobile charging and the selection of target areas in the initial stages. Overall, our study provides comprehensive guidelines and valuable insights for mobile charging operations.
Disturbances in production along with volatile demand have raised concerns over shortfalls in the global supply chain and prompted the need to build a more diversified supply chain with competitive suppliers. This research investigates the impact of disturbances on a two-tier supply chain network with asymmetric competing firms. We establish the equilibrium in a unique structure that represents the maximum set of profitable upstream supply paths achievable through competition and exhibits stability under specific conditions. We evaluate the efficiency of the supply chain configuration by a shortfall problem and solve it with an adapted pseudoflow algorithm that efficiently identifies the mismatches between shortfalls and capacity surpluses in the multitier network. The parametric analysis reveals that the disturbance loss can be significantly offset by supplier competition, although the marginal benefit of competition decreases rapidly with the number of suppliers. Furthermore, shortfalls could be magnified by network asymmetries that increase configuration inefficiency, and supply chain performance could be improved by pushing high-cost firms to cease production. Simulation results indicate that the supply chain with a moderate level of competition and a balanced configuration can be robust against disturbance and demand volatility.
Social scope group buying has emerged as an increasingly popular promotional strategy and has served as a new customer acquisition tool. In the service industry, companies use social group buying (SGB) to recruit new customers and promote full-price products. Through SGB activities, customers can trade their social capital to form buying groups, experience SGB-offered sample products, and further alleviate uncertainty regarding expensive full-price products before making a final purchase. We investigate this novel SGB phenomenon by examining customers’ decisions throughout the “experience-conversion” process. In collaboration with a leading online educational platform, we examine customers’ grouping behavior during SGB activities and analyze their subsequent purchases. Our analysis reveals an interesting pattern in which non-grouped customers have a higher proportion of full-price product purchases than grouped customers. We postulate that, in addition to observations from operational data, unobserved social information is important for gaining a deeper understanding of the customer behaviors underlying this pattern. Employing a Bayesian learning framework, we model customers’ three-stage discrete-choice decision-making processes and quantify two influential social information factors: social cost and social learning. By incorporating social information, our Bayesian learning model demonstrates improved effectiveness in assisting companies with accurately predicting final purchases in the conversion process. We provide actionable insights into how companies can employ our model to strategically tailor SGB designs by customer segments to increase overall purchase rates. Our study sheds light on the significance of social information in enhancing customer management and refining SGB design.
Revenue management decisions often involve both offline and online decisions. Offline decisions are made first and establish the broad and long-term operational context in which online decisions are frequently and repeatedly made, often in real time. We consider a joint optimization of offline and online decisions. Specifically, we examine a setting in which the offline decision concerns the selection of product-design characteristics (e.g., price, capacity, return eligibility, and other characteristics) and the online decision concerns the dynamic assortment optimization over a selling season. Our formulation has many applications, including optimizing products’ return eligibility and determining product discounts, and a key feature of our model is its explicit consideration of complex return dynamics and accompanying financial implications. We formulate an optimization problem that combines the impact of both offline and online decisions on the expected revenue. To determine the product design, we reformulate the choice-based deterministic linear program, solve its continuous relaxation, and round the resulting solution. Using value function approximations enables us to obtain a dynamic assortment policy whose expected revenue is at least a constant fraction of the choice-based deterministic linear program. Combining these two results, we show that our approach provides an approximate solution to the joint optimization problem with performance guarantees. Numerical experiments based on real transaction data from a major U.S. retailer show that our method achieves 95%–97% effectiveness, an advantage of up to 18% over methods that disregard the interplay between offline and online decisions. This framework also yields a systematic quantitative measure of the relative importance of both offline and online decisions. Based on this measure, numerical experiments highlight the crucial role of product design, accounting for 94% and 85% of the observed variation in effectiveness across various methods in applications involving volume discount and return eligibility, respectively.
Problem definition: Providing fast and reliable delivery services is key to running a successful online retail business. To achieve a better delivery time guarantee policy, we study how to estimate and promise delivery time for new customer orders in real time. Academic/practical relevance: Delivery time promising is critical to managing customer expectations and improving customer satisfaction. Simply overpromising or underpromising is undesirable because of the negative impacts on short-/long-term sales. To the best of our knowledge, we are the first to develop a data-driven framework to predict the distribution of order delivery time and set promised delivery time to customers in a cost-effective way. Methodology: We apply and extend tree-based models to generate distributional forecasts by exploiting the complicated relationship between delivery time and relevant operational predictors. To account for the cost-sensitive decision-making problem structure, we develop a new split rule for quantile regression forests that incorporates an asymmetric loss function in split point selection. We further propose a cost-sensitive decision rule to decide the promised delivery day from the predicted distribution. Results: Our decision rule is proven to be optimal given certain cost structures. Tested on a real-world data set shared from JD.com, our proposed machine learning–based models deliver superior forecasting performance. In addition, we demonstrate that our framework has the potential to provide better promised delivery time in terms of sales, cost, and accuracy as compared with the conventional promised time set by JD.com. Specifically, our simulation results indicate that the proposed delivery time promise policy can improve the sales volume by 6.1% over the current policy. Managerial implications: Through a more accurate estimation of the delivery time distribution, online retailers can strategically set the promised time to maximize customer satisfaction and boost sales. Our data-driven framework reveals the importance of modeling fulfillment operations in delivery time forecasting and integrating the decision-making problem structure with the forecasting model.