From Growth to Monetization: Managing Freemium Services

Wait Time Based Pricing for Queues with Customer-Chosen Service Times

Is there a role for governments in emerging countries to accelerate economic development by intervening in product and factor markets? To address this question, we study optimal dynamic Ramsey policies in a standard growth model with financial frictions. The optimal policy intervention involves pro-business policies like suppressed wages in early stages of the transition, resulting in higher entrepreneurial profits and faster wealth accumulation. This, in turn, relaxes borrowing constraints in the future, leading to higher labor productivity and wages. In the long run, optimal policy reverses sign and becomes pro-worker. In a multi-sector extension, optimal policy subsidizes sectors with a latent comparative advantage and, under certain circumstances, involves a depreciated real exchange rate. Our results provide an efficiency rationale, but also identify caveats, for many of the development policies actively pursued by dynamic emerging economies.

We consider a dynamic pricing model for selling a given stock of a perishable product over a finite time horizon. Customers, whose reservation price distribution changes over time, arrive according to a nonhomogeneous Poisson process. We show that at any given time, the optimal price decreases with inventory. We also identify a sufficient condition under which the optimal price decreases over time for a given inventory level. This sufficient condition requires that the willingness of a customer to pay a premium for the product does not increase over time. In addition to shedding managerial insight, these structural properties enable efficient computation of the optimal policy. Numerical studies are conducted to show the revenue impact of dynamic price policies. Price changes are set to compensate for statistical fluctuations of demand and to respond to shifts of the reservation price. For the former, our examples show that using optimal dynamic optimal policies achieves 2.4–7.3% revenue improvement over the optimal single price policy. For the latter, the revenue increase can be as high as 100%. These results explain why yield management has become so essential to fashion retailing and travel service industries.

Dynamic selling of quality-graded products under demand uncertainties

Optimal dynamic marketing-mix policies for frequently purchased products and services versus consumer durable goods: A generalized analytic approach

Motivated by the urgent demand for the electric vehicle (EV) fast refueling technologies, battery swapping and charging stations (BSCSs) are envisioned as a promising solution to provide timely EV refueling services. However, inappropriate battery charging operation in BSCSs cannot only incur unnecessary high charging cost but also threaten the reliability of the power grid. In this paper, we aim at obtaining an optimal charging operation policy for a single BSCS to minimize its charging cost while ensuring its quality-of-service. Leveraging the novel queueing network model, we propose to formulate the charging operation problem as a constrained Markov decision process and derive the optimal policy by the standard Lagrangian method and dynamic programming. To avoid the curse of dimensionality in practical large-scale systems, we further analyze the structure of the optimal policy and transform the dynamic programming procedure into an equivalent threshold optimization problem with a discrete separable convex objective function. Numerical results validate our theoretical analysis and the computational efficiency of our proposed algorithms. This paper also shows the impact of the system parameters (e.g., numbers of batteries and chargers) on the average cost under the optimal charging policy, which gives rich insights into the infrastructure planning of future BSCS networks.

Gaming disorder (GD) has been introduced as a new diagnosis in the International Classification of Disease 11 (ICD-11). Currently, there's limited understanding of how various video games may differentially contribute to the risk of developing GD. The main aim of this study was to examine the relationship between individuals' game genre preferences, their preferred games' monetization strategies, and GD Symptoms. A total of 85 patients undergoing treatment for GD at a child and youth psychiatric clinic were included in the study. Their preferred games were classified into five novel genres based on gameplay similarities and objectives, and further categorized based on their monetization strategy. Symptom burden of GD, measured with Game Addiction Scale for Adolescents (GASA), was highest for those playing Free-to-Play (F2P) games and lowest for Pay-to-Play (P2P) players. Players of Competitive Games endorsed higher GD symptom burden, whereas players of Story-driven games reported lower GD symptom burden. Symptoms of GD were associated with attention-deficit hyperactivity disorder (ADHD) diagnosis in males. This study reveals that game genre preference is influenced by sex, age, and certain psychiatric diagnoses. The categorizing of games into genres is increasingly complex and our research introduces a novel categorization in a developing research field. The result of this study suggests that the monetization model is important to consider while trying to understand the relationship between game characteristics and GD symptoms.

ABSTRACTUnlike the past work, the optimal operation policy, which minimizes the total batch time is derived for multivessel batch distillation (MVBD) for separation of binary components under constant total reflux. In this article, both the distribution of vessels along the MVBD column and the holdup in each vessel are optimized to minimize the total batch time. Furthermore, the time consumption of the optimal operation policy is also compared with that of the regular constant reflux operation theoretically and experimentally. The results show that the novel operation mode has great advantages in time saving and easy operation by adopting the optimal operation policy. Thus, for a given separation task, MVBD column reveals significant potential for separation with higher efficiency. © 2013 Curtin University of Technology and John Wiley & Sons, Ltd.

We consider an assembly system with multiple stages, multiple items, and multiple customer classes. The system consists of m production facilities, each producing a different item. Items are produced in variable batch sizes, one batch at a time, with exponentially distributed batch production times. Demand from each class takes place continuously over time according to a compound Poisson process. At each decision epoch, we must determine whether or not to produce an item and, should demand from a particular class arise, whether or not to satisfy it from existing inventory, if any is available. We formulate the problem as a Markov decision process and use it to characterize the structure of the optimal policy. In contrast to systems with exogenous and deterministic production lead times, we show that the optimal production policy for each item is a state-dependent base-stock policy with the base-stock level nonincreasing in the inventory level of items that are downstream and nondecreasing in the inventory level of all other items. For inventory allocation, we show that the optimal policy is a multilevel state-dependent rationing policy with the rationing level for each demand class nonincreasing in the inventory level of all nonend items. We also show how the optimal control problem can be reformulated in terms of echelon inventory and how the essential features of the optimal policy can be reinterpreted in terms of echelon inventory.

This paper investigates the robust optimal control problem of a class of continuous-time, partially linear, interconnected systems. In addition to the dynamic uncertainties resulted from the interconnected dynamic system, unknown bounded disturbances are taken into account throughout the learning process, wherein the system’s dynamics and the disturbances are assumed unknown. These challenges lead the collected online data to be imperfect. In this scenario, traditional data-driven control techniques, such as adaptive dynamic programming (ADP) and robust ADP, encounter a challenge in approximating the optimal control policy precisely due to imperfect data and computational errors. In this paper, a novel data-driven robust policy iteration method is proposed to simultaneously solve the robust optimal control problems. Without relying on the knowledge of the system’s dynamics, the external disturbances or the complete state, the implementation of the proposed method only needs to access the input and partial state information. Based on the small-gain theorem, the notions of strong unboundedness observability and input-to-output stability, it is guaranteed that the learned robust optimal control gain is stabilizing and that the solution of the closed-loop system is uniformly ultimately bounded despite the existence of dynamic uncertainties and unknown external disturbances. The simulation results reveal the efficiency and practicality of the proposed data-driven control method. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This work is motivated by the use of reinforcement learning to improve the quality of designing adaptive optimal controllers for engineering applications. Adaptive dynamic programming methods, in particular policy iteration (PI), are widely used in solving optimal control problems. However, due to the iterative nature of PI, the approximated optimal control policy may be inaccurate and imprecise. Especially, when using imperfect system’s measurements instead of the modelling information. This can result in causing the learned control policy to deviate from the actual optimal policy. This becomes more challenging in the existence of dynamic uncertainties and unknown external disturbances which corrupt the measurements and result in imperfect data. This work investigates the conditions on the uncertainties such that the proposed novel data-driven PI algorithm is robust to system’s uncertainties, unknown external disturbances and imperfect measurements. The approximated robust optimal control policy performs robustly in the existences of imperfect data and uncertainties, and at the same time is close enough to the optimal control policy.

Stochastic optimal control of agrochemical pollutant loads in reservoirs for irrigation

This paper analyzes the Ak model with anticipated future consumption. In the model with internal anticipation individual’s utility depends on current consumption and a forward-looking reference level which is formed from individual’s own future consumption. The global dynamics of the economy is characterized by means of a qualitative phase diagram analysis. In the model with external anticipation the consumption reference level is formed from economy-wide average future consumption, which is taken as given by individuals and causes the competitive equilibrium to be inefficient. Characterizing the global dynamics of the economy is required to characterize an optimal fiscal policy that corrects the inefficiency brought about by this external effect.

Industrial systems operating under severe mission environment are frequently confronted with intricate failure behaviors arising from system internal degradation and extrinsic stresses, posing an elevating challenge to system survivability and mission reliability. Mission termination strategies are attracting increasing attention as an intuitive and effective means to mitigating catastrophic mission-induced risk. However, how to manage coupled risk arising from competing fault processes, particularly when these modes are interdependent, has been rarely reported in existing works. To bridge this gap, this study delves into a dynamic risk control policy for continuously degrading systems operating under a random shock environment, which yields competing and dependent fault processes. An optimal mission termination policy is developed to minimize risk-centered losses throughout the mission execution, whose optimization problem constitutes a finite-time Markov decision process. Some critical structural properties associated with the optimal policy are derived, and by leveraging these structures, the alerting threshold for implementing mission termination procedure is formally established. Alternative risk control policies are introduced for comparison, and experimental evaluations substantiate the superior model capacity in risk mitigation.

Maximizing the throughput (or revenue generation) rate has become one of die most important criteria in die design and management of Flexible Manufacturing Systems (FMSs). This paper develops dynamic part-allocation policies for FMSs having finite storage capacity at each work station. Maximizing the throughput rate means that the resulting queueing network model has a state-dependent arrival process; therefore, product-form solutions do not hold. Consequently, several alternative modeling approaches are described and formulated for deriving die optimal part-routing policies. One of these optimal policies is based on a new initiated-suspension part-routing strategy. This strategy results in a reduced load on the material handling system while increasing die expected throughput (or revenue generation) rates of the manufacturing work stations. We also propose several efficient closed-loop heuristic policies that exploit die response structure of die optimal policies. These heuristic policies are of...

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