State-dependent Threshold Research Articles

Is there a state-dependent optimal interval for firms’ R&D investment? Evidence from China

ABSTRACT This study sheds light on the existence of a time-varying and state-dependent optimal interval of research and development (R&D) investment in which firms can maximize the positive effect of R&D on their performance. We develop a panel kink threshold regression model with multiple covariate-dependent thresholds to capture a time-varying optimal interval of R&D investment. Based on the data of A-share listed firms in Shanghai and Shenzhen in China from 2012 to 2020, we provide empirical evidence supporting a state-dependent optimal interval of R&D investment, above or below which R&D is significantly negatively associated with performance. Specifically, the lower bound of the optimal interval (R&D barrier point) is counter-cyclical, while the upper bound of the interval (R&D saturation point) is pro-cyclical. Our study provides a new approach to understand the time-varying and state-dependent threshold effect in the R&D investment, hence contributing to the research and practice of determining the optimal R&D investment.

How to optimize container withholding decisions for reuse in the hinterland?

This study investigates how a hinterland consignee (importer) makes decisions regarding the storage of empty containers for reuse by a shipper (exporter). The system is modeled as a double-ended queue with non-zero matching times, limited truck resources, and both consignee and shipper having fixed withholding capacities. The consignee’s withholding threshold is strategically set to minimize overall transport and detention costs. We derive closed-form expressions for performance measures in the case of a single storage facility at the shipper, utilizing a matrix-based approach. We extend this methodology numerically to the general case. Additionally, we present an accurate fixed-point approximation facilitating the determination of performance measures and optimal threshold. Our findings show the importance of withholding decisions in import and balanced areas for cost reduction. In export areas, a policy of full reuse proves nearly optimal. Analyzing dynamic state-dependent consignee decisions via a Markov decision process, we establish that the optimal policy involves withholding thresholds increasing with stored quantity at the shipper. While optimal, state-dependent thresholds yield limited cost savings compared to a fixed threshold, suggesting minimal impact from consignee-shipper information sharing. Additionally, we examine the influence of variability in matching and production times, observing decreased costs with reduced variability, particularly in export areas, but with minor impacts on withholding decisions.

Gauss chains: Quadratic to quintic

Gauss chains are one-dimensional nonperiodic lattices in which lattice sites are located at zj=jnd, with j∈W, n∈N, and d being the underlying lattice constant. They may potentially be realized in semiconductor superlattices or tailored chain molecules. In recent work, we have characterized the electronic delocalized states for the quadratic Gauss chain n=2 obtained using a one-dimensional transfer-matrix approach applied to the Kronig–Penney model. We here extend those results to cases of larger n, illustrating the approach for n=3, 4, and 5. Beginning with the structure factor, we find that the case n=2 has a visually evident structure lacking for n>2, and this structure (or lack thereof) is reflected in the statistics of the structure factor. Turning to the electronic structure, the delocalized-state spectrum for each n is singular-continuous with delocalized states at wavevectors k for all rational multiples rs of πd with r,s∈N coprime in the limit of weak onsite potential parameter λ. Most states, however, become localized at a state-dependent threshold value of |λ|. The case n=2 appears to exhibit delocalized-state spectra that most clearly reveal the hidden symmetry of these systems. Gauss chains with various n, therefore, provide a way (in principle) to realize a class of functions of number-theoretic importance.

Integrated optimisation of pricing, manufacturing, and procurement decisions of a make-to-stock system operating in a fluctuating environment

ABSTRACT Manufacturers experience random environmental fluctuations that influence their supply and demand processes directly. To cope with these environmental fluctuations, they typically utilise operational hedging strategies in terms of pricing, manufacturing, and procurement decisions. We focus on this challenging problem by proposing an analytical model. Specifically, we study an integrated problem of procurement, manufacturing, and pricing strategies for a continuous-review make-to-stock system operating in a randomly fluctuating environment with exponentially distributed processing times. The environmental changes are driven by a continuous-time discrete state-space Markov chain, and they directly affect the system's procurement price, raw material flow rate, and price-sensitive demand rate. We formulate the system as an infinite-horizon Markov decision process with a long-run average profit criterion and show that the optimal procurement and manufacturing strategies are of state-dependent threshold policies. Besides that, we provide several analytical results on the optimal pricing strategies. We introduce a linear programming formulation to numerically obtain the system's optimal decisions. We, particularly, investigate how production rate, holding cost, procurement price and demand variabilities, customers' price sensitivity, and interaction between supply and demand processes affect the system's performance measures through an extensive numerical study. Furthermore, our numerical results demonstrate the potential benefits of using dynamic pricing compared to that of static pricing. In particular, the profit enhancement being achieved with dynamic pricing can reach up to 15%, depending on the problem parameters.

Event-triggered based security consensus control for multi-agent systems with DoS attacks

This work devotes to the security consensus problems for time-varying multi-agent systems (MASs) based on event-triggered control method with denial-of-service (DoS) attacks and parameter uncertainties. During information transmission, DoS attacks exist in both control and measurement channels, regarded as a dwell-time switching scheme, and hence the augmented system can be transformed into a class of discrete-time switched system subject to dwell-time property which contains an unstable and a stable subsystem. To increase the utilization of communication resources, the control input signal can be updated by adopting a novel event-driven mechanism with state-dependent threshold over a given finite horizon. By utilizing multiple Lyapunov functions analysis strategy, two sufficient conditions are obtained to achieve the desired H∞ consensus performance. The cone complementary linearization algorithm is employed to cope with the nonlinear terms, and the desired controller gain matrices are calculated via resolving the corresponding linear matrix inequalities. Finally, the effectiveness of this proposed method is verified by providing a simulation example and the multi-automobile system.

Offering Free Upgrades Even Before Stocks Run Out: The Value of Proactive Upgrades

Problem definition: When selling multiple products with different feature combinations over a short selling season, a seller often adopts a “reactive” upgrade policy by offering a free upgrade to the next-price-level product only after a customer’s preferred product is out of stock. However, when customers’ preferences are heterogeneous for different feature combinations, some unyielding customers may reject free upgrades. In this paper, we consider a new “proactive” upgrade policy under which the seller may offer free upgrades even before a product is out of stock. Academic/practical relevance: The proactive upgrade policy enables the seller to strategically keep some units of a product in reserve to secure future sales of this product for those unyielding customers. However, the value of the proactive upgrade policy over the traditional reactive upgrade policy remains unclear. Methodology: Given the product choice probability the “upgrade acceptance probability” of each arriving customer, we formulate the problem of how to offer proactive upgrades as a finite horizon dynamic program with an embedded Markov decision process, and we determine the optimal proactive upgrade policy. Results: By exploiting the underlying mathematical structure, we prove that the optimal value function possesses the “anti-multimodularity” property such that the optimal upgrade strategy under the proactive upgrade policy is governed by two state-dependent thresholds: one threshold dictates when to offer proactive upgrades, and the other threshold dictates when to offer reactive upgrades. We also show that the proactive upgrade policy can create significant value over the reactive upgrade policy when the next-price-level product has similar consumer utility or when the price sensitivity is intermediate. Managerial implications: We identify the conditions under which the proactive upgrade policy provides significant value over the traditional reactive upgrade policy. These results can be useful for sellers who sell variants of similar products with different feature combinations to customers with heterogeneous feature preferences.

Delay-Optimal Scheduling for Integrated mmWave Sub-6 GHz Systems with Markovian Blockage Model

Millimeter wave (mmWave) communication has the potential to achieve very high data rates but is highly vulnerable to blockage. In this paper, we provision an integrated mmWavesub-6 GHz architecture to combat blockage and intermittent connectivity of the mmWave communications. To this end, we model the mmWave channel as a two-state Markov channel and investigate the problem of scheduling packets across the mmWave and sub-6 GHz interfaces such that the long-term average delay of system is minimized. We prove that the optimal policy is of a threshold-type with state-dependent thresholds, i.e., packets should always be routed to the mmWave interface as long as the number of packets in the system is smaller than the state-dependent threshold. Numerical results demonstrate that under heavy traffic, integrating sub-6 GHz with mmWave can reduce the average delay by over 70%. Moreover, considering the difficulty of tracking the mmWave channel state in practice, we develop heuristics of substituting a single fixed threshold (state-independent) for two state-dependent thresholds. Our simulation results indicate that the replacement only incurs a slight increase in average delay. Moreover, when system parameters are not known, we propose a certainty-equivalence threshold-based learning algorithm, and provide an upper bound on its regret.

A Gradient-Based Event-Driven MPC for Nonlinear Systems With Additive Disturbances Using State-Dependent Thresholds

In this article, we propose a gradient-based event-driven model predictive control (GEMPC) algorithm with a state-dependent threshold for nonlinear systems with additive disturbances and input and state constraints. Firstly, a novel gradient-based event-driven strategy is constructed in the light of the error gradient between the optimal prediction of the state and the real one, which could ensure the Zeno-free property via a positive triggering interval. Subsequently, the novel triggering mechanism and the dual-mode control are combined to establish a GEMPC framework, to further reduce the computing burden and communication transmission especially when the computational resources are limited. Additionally, the feasibility of the GEMPC algorithm and the input-to-state practical stability (ISpS) property of the considered system have been strictly proved in theory. Finally, the simulation comparison results on control of a perturbed nonlinear system are utilized to show the validity of the GEMPC algorithm.

Debt sustainability in a low interest rate world

Historic levels of public debt and conditions of r<g for advanced economies have prompted a reassessment of debt sustainability. Using a continuous-time model in which the debt-to-GDP ratio is stochastic and r<g on average, we find that theoretical conditions for sustainability are not closely tied to common metrics of sustainability: the level of debt or whether r<g. However, when the primary surplus is bounded, a state-dependent threshold level of public debt determines sustainability. Secular stagnation factors like slow population growth, low productivity growth, or higher output risk carry differing implications for debt sustainability.

Joint admission, production sequencing, and production rate control for a two-class make-to-order manufacturing system

Today's manufacturing industry faces a number of challenges related to the rapid delivery of products with a high degree of variety. Striking a balance between the effectiveness in capacity utilization and the rapidness in order-fulfillment is a substantial challenge for manufacturing companies. This work aims to provide a theoretical basis from which to address this practical question. To this end, we address the problem of coordinating the admission, production sequencing, and production rate controls for a two-class make-to-order manufacturing system. Formulating the problem as a Markov decision process model, we identify the structural properties of optimal control policies under both discounted and average profit criteria. We show that the cμ rule is optimal for production sequencing and the optimal admission and production rate control policies can be characterized by the state-dependent threshold levels, provided that the production times are not associated with customer class. We also show that the optimal production rates are monotone in the system state, as in the case of a single class queueing system, and that the lower priority class can be preferred to the higher priority class in order admission under a certain condition on the system parameters. Our numerical study demonstrates that a considerable economic benefit can be achieved if the production rate is dynamically controlled between the minimum and maximum rates rather than fixed to the mean rate of these values. Finally, we present a heuristic policy that is described by linear switching functions for the control of order admission and a selection rule for the control of production rate. We compare the performance of our heuristic to the optimal policy using a numerical experiment, revealing that the heuristic provides near optimal solutions to test example problems and is robust to the system parameters.

Offering Free Upgrades Even before Stocks Run Out: The Value of Proactive Upgrades

Problem Definition: When selling multiple products with different feature combinations over a short selling season, a seller often adopts a reactive'' policy by offering a free to the next-price-level product only after'' a customer's preferred product is out of stock. However, when customer preference is heterogeneous for different feature combinations, some unyielding customers may reject free upgrades. In this paper, we consider a new proactive'' policy under which the seller may offer free upgrades ``even before'' a product is out of stock. Academic/Practical Relevance: The proactive policy enables the seller to strategically keep some units of a product in reserve to secure future sales of this product for those unyielding customers. However, the value of proactive policy over the traditional reactive policy remains unclear. Methodology: We use the Multinomial Logistic Model to determine the upgrade acceptance probability'' of each arriving customer, so that we can formulate the proactive policy problem as a finite horizon dynamic program with an embedded Markov Decision Process, and we determine the optimal proactive policy. Results: By exploiting the underlying mathematical structure, we prove that the optimal value function possesses the anti-multimodularity'' property so that the optimal strategy under the proactive policy is governed by two state-dependent thresholds: one threshold dictates when to offer proactive upgrades, and the other threshold dictates when to offer reactive upgrades. We also show that the proactive policy can create significant value over the reactive policy when the next-price-level product has similar consumer utility or when the price sensitivity is intermediate. Managerial Implications: We identify the conditions under which the proactive policy provides significant value over the traditional reactive policy. These results can be useful for sellers who sell variants of similar products with different feature combinations to customers with heterogeneous feature preference.

A bi-objective manufacturing/remanufacturing system considering downward substitutions between three markets

An inventory control problem of a hybrid manufacturing/remanufacturing system under stochastic demand is studied. The paper proposes a successive substitution strategy between prime, budget and low budget segments of a market. Meaning a manufactured product may substitute for a remanufactured product at a discounted rate. The success of this proposal proportionally is dependent on the discount rate. Similarly, a once-remanufactured product may substitute for a twice-remanufactured product. In this proposal, a sales-dependent return is adopted to enhance returns prediction. This tactic utilizes a virtual stock of previous period sales instead of a used product stock. In such arrangements, only a fraction of customers accept keeping and returning their used product at the end of the product's lifetime. This is a push system because as soon as the company makes an order for remanufacturing, a core will be returned by a ready/potential customer and instantly will be pushed into the remanufacturing process. The system is formulated by a bi-objective Markov decision process considering profit and customer satisfaction criteria to provide optimal policy in the form of a lookup table. The heuristic policy is then characterized by utilizing five control parameters. This is a state-dependent threshold policy with a small deviation from the optimality. Then the effects of thresholds are investigated applying DOE and ANOVA. Finally, the performance of the successive substitution strategy using real data from the tire industry is examined. The results show that profitability, serviceability and core acquisition can be improved by using the proposed strategy.

An Optimal Flow Admission and Routing Control Policy for Resource Constrained Networks.

Overloaded network devices are becoming an increasing problem especially in resource limited networks with the continuous and rapid increase of wireless devices and the huge volume of data generated. Admission and routing control policy at a network device can be used to balance the goals of maximizing throughput and ensuring sufficient resources for high priority flows. In this paper we formulate the admission and routing control problem of two types of flows where one has a higher priority than the other as a Markov decision problem. We characterize the optimal admission and routing policy, and show that it is a state-dependent threshold type policy. Furthermore, we conduct extensive numerical experiments to gain more insight into the behavior of the optimal policy under different systems’ parameters. While dynamic programming can be used to solve such problems, the large size of the state space makes it untractable and too resource intensive to run on wireless devices. Therefore, we propose a fast heuristic that exploits the structure of the optimal policy. We empirically show that the heuristic performs very well with an average reward deviation of 1.4% from the optimal while being orders of magnitude faster than the optimal policy. We further generalize the heuristic for the general case of a system with n () types of flows.

Centrifugal effects in NΔ states

Recently it has been pointed out that in the two-baryon $N\Delta$ or $\Delta\Delta$ system the width of the state is greatly diminished due to the relative kinetic energy of the two baryons, since the internal energy of the particles, available for pionic decay, is smaller. For nonzero orbital angular momenta this effect becomes state dependent. Also the real part of the $N\Delta$ energy can get contribution from the centrifugal barrier leading to rotational series of diffuse states. Obviously, these states may have an interpretation as isospin one dibaryons. Direct and explicit calculations for this are presented with some details of the coupled state wave functions displayed. With finite expectation values of these repulsive effects it may be possible to define state dependent effective thresholds for $N\Delta$ states and these, in turn, can show resonant like behavior.

Optimal insertion of customers with waiting time targets

The insertion of randomly-arriving high-priority customers (HCs) into existing queues leads to longer waiting time of regular or scheduled customers. However, given their different levels of priority, not all HCs need to be served immediately. To reduce the waiting time for regular customers without affecting the service quality for HCs, this paper addresses the optimal insertion problem of HCs by considering their waiting time targets assigned based on their levels of priority. A finite-horizon Markov decision process model is proposed to minimize the total waiting cost incurred by both regular customers and HCs. The marginal waiting penalty is constant for regular customers and non-decreasing for HCs. Several properties are observed: the optimal control policy is proved to be a state-dependent threshold policy; the marginal effect of each state variable on the optimal action is bounded by 1; and, in some meaningful cases, the threshold proves to be state-independent. Based on these properties, several heuristic policies are proposed to solve large-size problems. Numerical experiments are performed to validate the structure of the optimal control policies and compare the performances of the heuristic policies. These results imply that the optimal control policy significantly outperforms the traditional HC-first policy. The best heuristic policy, characterized by a threshold policy derived through policy iteration, performs within 0.44% of an optimal policy for most cases, which offers insights into the near-optimal control for large-size problems.

Distributed Event-Triggered Consensus of General Linear Multiagent Systems Under Directed Graphs.

This article investigates the consensus problem of general linear multiagent systems under directed communication graphs with event-triggered mechanisms. First, a novel distributed static event-triggered mechanism with a state-dependent threshold is proposed to solve the consensus problem, both with a positive lower bound on the average time interval of the communication among agents and updates of controllers. Thus, the Zeno behavior is excluded for communication among agents and controller updates. Next, to further reduce the frequencies of communication among agents and updates of controllers, a distributed dynamic event-triggered mechanism is introduced. By applying the static and dynamic mechanisms, the problem can be addressed with the reduced use of system resources compared with that in most existing control algorithms. Finally, numerical simulations are presented to verify the effectiveness of the results.

Multi-Stage Supply Chain with Production Uncertainty

With supply chains becoming increasingly extended, the uncertainties in the upstream production process can greatly affect the material flows that aim toward meeting the uncertain demands at the downstream. We analyze a two-location system in which the upstream production facility experiences random capacities and the downstream store faces random demands. Different from the widely used approach that seeks the decomposition of the profit function based on the echelon inventories, our approach builds on the notions of stochastic functions, in particular, the stochastic linearity in midpoint and the directionally concave order. With these notions, we establish the concavity and submodularity of the profit functions in the transformed decision variables. In general, it is optimal to follow a two-level state-dependent threshold policy such that an order is issued at a location if and only if the inventory position of that location is below the corresponding threshold. In the special case where the salvage values are linear in the ending inventories, the profit function becomes separable in the inventory positions, and the optimal policy reduces to the echelon base-stock policy. The effect of the uncertain capacity and demand depends critically on whether the production capacity is limited or ample in relation to the demand. Only when the capacity and the demand do not differ much, the upstream facility carries positive inventory; otherwise, all units produced are shipped immediately toward the downstream. We further extend our analysis to systems with general stochastic production functions and with multiple locations.

Optimal control of production-inventory systems with correlated demand inter-arrival and processing times

We consider the production control problem of a production-inventory system with correlated demand inter-arrival and processing times that are modeled as Markovian Arrival Processes. The control problem is minimizing the expected average cost of the system in the steady-state by controlling when to produce an available part. We prove that the optimal control policy is the state-dependent threshold policy. We evaluate the performance of the system controlled by the state-dependent threshold policy by using the Matrix Geometric method. We determine the optimal threshold levels of the system by using policy iteration. We then investigate how the autocorrelation of the arrival and service processes impact the performance of the system. Finally, we compare the performance of the optimal policy with 3 benchmark policies: a state-dependent policy that uses the distribution of the inter-event times but assumes i.i.d.inter-event times, a single-threshold policy that uses both the distribution and also the autocorrelation, and a single-threshold policy that uses the distribution of the inter-event times but assumes they are not correlated. Our analysis demonstrates that ignoring autocorrelation in setting the parameters of the production policy causes significant errors in the expected inventory and backlog costs. A single-threshold policy that sets the threshold based on the distribution and also the autocorrelation performs satisfactorily for systems with negative autocorrelation. However, ignoring positive correlation yields high errors for the total cost. Our study shows that an effective production control policy must take correlations in service and demand processes into account.

The distributed output consensus control of linear heterogeneous multi-agent systems based on event-triggered transmission mechanism under directed topology

In this paper, the distributed output consensus control of linear heterogeneous multi-agent systems (LH_MASs) based on event-triggered transmission strategy under directed topology is addressed. Under the assumption that the state of each node is unmeasurable, the state observer is first designed. Then, in order to decrease the information interaction among agents, the event-triggered consensus protocol (ETCP) based on the designed state observer and dynamic compensator is proposed. Here, a novel triggering function is designed such that each agent does not need to monitor the states of its neighbors for event detection. In addition, on account of state-dependent threshold and time-dependent threshold, the combined threshold is presented to take both advantages into account at the same time. By selecting an appropriate Lyapunov function and regulation parameters, the output consensus of LH_MASs can be achieved and the Zeno behavior can be excluded. To avoid continuous monitoring of each agent’s state, we further propose the self-triggered consensus protocol (STCP). Furthermore, the novel event-triggered consensus protocol for mitigating external disturbances (ED_ETCP) is raised. Finally, several numerical examples are provided to illustrate the validity of the theoretical results.

Event-Triggered Consensus Control for Multi-Agent Systems Against False Data-Injection Attacks.

In this article, the event-triggered security consensus problem is studied for time-varying multiagent systems (MASs) against false data-injection attacks (FDIAs) and parameter uncertainties over a given finite horizon. In the process of information transmission, the malicious attacker tries to inject false signals to destroy consensus by compromising the integrity of measurements and control signals. The randomly occurring stealthy FDIAs on sensors and actuators are modeled by the Bernoulli processes. In order to reduce the unnecessary utilization of communication resources, an event-triggered control mechanism with state-dependent threshold is adopted to update the control input signal. The main objective of this article is to design a controller such that, under randomly occurring FDIAs and admissible parameter uncertainties, the MASs achieve consensus. By utilizing stochastic analysis method, two sufficient criteria are derived to ensure that the prescribed H∞ consensus performance can be achieved. Then, the desired controller gains are derived by solving recursive linear matrix inequalities. Simulation results are presented to illustrate the effectiveness and applicability of the proposed control method.