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For smooth running of business affairs, there needs to be a coordination among manufacturer, collector and retailer in forward and reverse supply chain. This paper handles the problem of making pricing, collecting and percentage sharing decisions in a closed-loop supply chain. The purpose of this paper is to examine the effect of responsibility sharing percentage on the profits of a manufacturer, a retailer and a collector. The paper further aims to understand the mutual interactions among decision variables and profit functions. It also determines the optimal selling price, optimal time, wholesale price, sharing percentage and optimal return rate in such a manner that the profit function is maximized.

The authors presented a three-echelon model consisting of a manufacturer, a retailer and a collector in the closed-loop supply chain and optimized the profits of each supply chain member. The authors introduced SRR models for the remanufacturing by providing some percentage of physical and financial support to the collector. Optimization techniques have been applied to obtain optimal solutions. Numerical examples and graphical representations of the optimal solutions are provided to illustrate the model.

This study stresses on profitable value retrieval from returned products, and it discusses how responsibility sharing can improve profitability and reduce the workload of an individual. In total, three main results are found. First, sharing and coordination among chain members can improve collector’s profit. Second, supply chain performance may also improve over time. Third, the profit of each member of the supply chain increases with an increase in sharing percentage up to a certain limit. So, the manufacturer can share the responsibility of the collector under a fixed limit.

The main limitation of this model is that there is no difference between manufactured and remanufactured products. There are many correlated issues that need to be further investigated. The future study in this direction may include multi-retailer, stochastic demand patterns.

It is directly utilized by supply chain industries in which coordination among chain members is still needed to maximize profits. This information enables the manufacturer to assist the collector financially or physically for the proper management of the three-layer supply chain. The present work will form a guideline to choose the appropriate parameter(s) and mathematical technique(s) in different situations for remanufacturable products.

From the management point of view, this study delivers the strongest result to remanufacturing companies and for whom effective and efficient coordination among chain members is vital to the overall performance of the supply chain.

There are very few studies that consider the remanufacturing of used products under a fixed time period. The authors considered selling price-sensitive and time-dependent exponentially declining demand. This model is developed by considering all possible help to a collector from manufacturer to collect used products from consumers. This research complements past research by showing coordination among supply chain members within a fixed time horizon.

Current reinforcement learning (RL) algorithms are facing issues such as low learning efficiency and poor generalization performance, which significantly limit their practical application in real robots. This paper aims to adopt a hybrid model-based and model-free policy search method with multi-timescale value function tuning, aiming to allow robots to learn complex motion planning skills in multi-goal and multi-constraint environments with a few interactions.

A goal-conditioned model-based and model-free search method with multi-timescale value function tuning is proposed in this paper. First, the authors construct a multi-goal, multi-constrained policy optimization approach that fuses model-based policy optimization with goal-conditioned, model-free learning. Soft constraints on states and controls are applied to ensure fast and stable policy iteration. Second, an uncertainty-aware multi-timescale value function learning method is proposed, which constructs a multi-timescale value function network and adaptively chooses the value function planning timescales according to the value prediction uncertainty. It implicitly reduces the value representation complexity and improves the generalization performance of the policy.

The algorithm enables physical robots to learn generalized skills in real-world environments through a handful of trials. The simulation and experimental results show that the algorithm outperforms other relevant model-based and model-free RL algorithms.

This paper combines goal-conditioned RL and the model predictive path integral method into a unified model-based policy search framework, which improves the learning efficiency and policy optimality of motor skill learning in multi-goal and multi-constrained environments. An uncertainty-aware multi-timescale value function learning and selection method is proposed to overcome long horizon problems, improve optimal policy resolution and therefore enhance the generalization ability of goal-conditioned RL.

Customer-intensive services refer to the service that a provider needs to invest in customers with high patience and experience. Within a certain rate range, the slower service rate and the longer service time, the higher customer’s utility; however, this may cause queue congestion. And the advertising of service provider will affect the revenue. The purpose of this paper is to investigate the effects of advertising on the optimal price, service rate and the optimal revenue of such service provider at different development stages.

This paper investigates the service strategies of service provider based on advertising effects. The authors first divide service provider into insufficient customers or sufficient customers according to the development stage, then analyze the impact of advertising at different stages. The authors focus on the formulation of the optimal price, service rate and the optimal revenue of service provider at different stages.

This paper finds that in the insufficient customers stage, the service provider’s strategy of “small profits but quick turnover” is conducive to quickly accumulating customers. With the development of service provider, the advertising indirectly increases the revenue of service provider by maintaining popularity. The result also shows that with the development of service provider, the initiative of such service market has gradually been mastered by service provider, from “buyer market” to “seller market.”

The finding provides an alternative explanation for the impact of advertising on service provider’s optimal strategies; it also solves the settings of service price and rate of customer-intensive service provider at different development stages. This study is essential to create the optimal revenue and solve supply–demand conflicts (such as doctor–patient conflict) between service provider and customers.

In a structural optimization design-based single-level response surface, the number of optimal variables is too much, which not only increases the number of experiment times, but also reduces the fitting accuracy of the response surface. In addition, the uncertainty of the optimal variables and their boundary conditions makes the optimal solution difficult to obtain. The purpose of this paper is to propose a method of fuzzy optimization design-based multi-level response surface to deal with the problem.

The main optimal variables are determined by Monte Carlo simulation, and are classified into four levels according to their sensitivity. The linear membership function and the optimal level cut set method are applied to deal with the uncertainties of optimal variables and their boundary conditions, as well as the non-fuzzy processing is carried out. Based on this, the response surface function of the first-level design variables is established based on the design of experiments. A combinatorial optimization algorithm is developed to compute the optimal solution of the response surface function and bring the optimal solution into the calculation of the next level response surface, and so on. The objective value of the fourth-level response surface is an optimal solution under the optimal design variables combination.

The results show that the proposed method is superior to the traditional method in computational efficiency and accuracy, and improves 50.7 and 5.3 percent, respectively.

Most of the previous work on optimization was based on single-level response surface and single optimization algorithm, without considering the uncertainty of design variables. There are very few studies which discuss the optimization efficiency and accuracy of multiple design variables. This research illustrates the importance of uncertainty factors and hierarchical surrogate models for multi-variable optimization design.

This paper seeks to develop and present a new mathematical formulation to determine the optimal preventive maintenance and replacement schedule of a system.

The paper divides the maintenance‐planning horizon into discrete and equally‐sized intervals and in each period decide on one of three possible actions: maintain the system, replace the system, or do nothing. Each decision carries a specific cost and affects the failure pattern of the system. The paper models the cases of minimizing total cost subject to a constraint on system reliability, and maximizing the system reliability subject to a budgetary constraint on total cost. The paper presents a new mathematical function to model an improvement factor based on the ratio of maintenance and repair costs, and show how it outperforms fixed improvement factor models by analyzing the effectiveness in terms of cost and reliability of the system.

Optimal decisions in each period over a planning horizon are sought such that the objectives and the requirements of the system can be achieved.

The developed mathematical models for this improvement factor can be used in theoretical and practical situations.

The presented models are effective decision tools that find the optimal solution of the preventive maintenance and replacement scheduling problem.

This study examines the potential of contracts as one of the supply chain coordination mechanisms under competitive conditions. It also investigates a two-echelon supply chain model with two manufacturers and two retailers to develop a competitive structure in grey stochastic demand.

Supply chain demand is considered as a stochastic phenomenon depending on the selling price of the product. Also, products can be replaced by market manufacturers. Each retailer faces the pricing of products from two manufacturers, leading to competition between downstream retailers. In the present study, the duopoly supply chain model was presented based on the wholesale price contract, revenue-sharing contract and quantity discount contract separately.

Grey optimization and analysis of their coordination were presented. The results showed the high performance of revenue-sharing contracts in the supply chain. Thus, manufacturers will give the next priority to quantity discount contracts.

Ordering is the main factor contributing to competitive decision-making. Meanwhile, decision-making along with ordering and pricing will be required due to the nature of the demand.

This research investigated the optimal structure of a discrete‐time Markov deterioration system monitored by multiple non‐independent monitors. The purpose is to obtain a sufficient condition with which the optimal policy is given by a control limit policy.

The model of this research is formulated as a partially observable Markov decision process. The problem is to obtain an optimal policy which can minimize the expected total discounted cost over an infinite horizon.

The research found that the expected optimal cost function over an infinite horizon has a property of control limit policy given the conditions that a transition probability having a property of totally positive of order 2 and a conditional probability of the monitors having a property of weak multivariate monotone likelihood ratio. Furthermore, we showed that the optimal policy has only four action regions at most.

If the optimum policy can be limited to a control limit policy, the tremendous amount of calculation time required to find the optimum procedure can be reduced. This enables the best decision to be identified in a much shorter period of time.

A deterioration system monitored incompletely by one monitor has been studied in the previous research. This research considered the case of a multiple number monitors whose observations were not independent.

The optimal payment in the whole operation and maintenance period of water environment treatment PPP projects has become the main approach to realize sustainable development of projects. This study is aimed at constructing an effective payment model for the whole life period of projects to achieve win-win among all stakeholders, so as to provide a theoretical reference and managerial implications for the public sector in the whole operation and maintenance period.

In the whole operation and maintenance period of water environment treatment PPP projects, this article investigates how the public sector optimizes the payment in the whole operation and maintenance period of projects. Firstly, the projects' whole operation and maintenance period is divided into several stages according to the performance appraisal period. And then, the multi-stage dynamic programming model is constructed to design the payment construct model for the public sector in each performance appraisal stage. The payment from the public sector is the decision variable, and the deduction from the private sector is a random variable.

The optimal payment model showed that the relatively less objective weight of public sector leaded to its relatively more total payment and vice versa. Therefore, the sustainable development of the projects can only be ensured when the objective weights both of them should be balanced. Additionally, the deduction from the performance appraisal of private sector plays an important role in the model construction. The larger deduction the private sector undertakes, the smaller profits private sector has. Since the deduction at each stage is a random variable, the deduction varies with the different probability distributions obeyed by the practical deduction in each stage.

The findings from this study have provided theoretical and application references, and some managerial implications are also given. First, the improvement of the pricing system of public sector should be accelerated. Second, the reasonable profit of the private sector must be guaranteed. While pursuing the maximization of social benefits, the public sector should make full use of the price sharing mechanism in the market and supervise the real income situation of the private sector. Third is increasing the public to participate in pricing. Additionally, it is a limitation that the deduction is assumed to conform to a uniform distribution in this study. Other probability distributions on deduction can be essentially further sought, so as to be more line with the actual situation of the projects.

The optimal payment in whole operation and maintenance period of the projects has become an important issue, which is a key to project success. This study constructs a multi-stage dynamic programming model to optimize payment in the whole period of projects. Additionally, this study adds its value through deeply developing the new theories of optimal payment to more suitable for the practical problems, so that to optimize the design of payment mechanism. Meanwhile, a valuable reference for public and private sectors is provided to ensure the sustainable development of the projects.

The purpose of this paper is to consider the general k level step-stress accelerated life test with the Rayleigh lifetime distribution for units subjected to stress under progressive Type-I censoring.

The parameter of this distribution is assumed to be a log-linear function of the stress, and a tampered failure rate model holds. The progressive Type-I censoring reduces the cost of testing. Due to constrained resources in practice, the test design must be optimized carefully. A numerical study is conducted to illustrate the optimum test design based on several four optimality criteria under the constraint that the total experimental cost does not exceed a pre-specified budget.

This paper compares unconstrained and constrained optimal k level step-stress test. Based on the results of the simulation study, the cost constraint reduces cost and time of the test and it also, in the most cases, increases the efficiency of the test. Also, the T-optimal design is lowest cost and time for testing and it is found more optimal in both conditions.

In this paper, various optimization criteria for selecting the stress durations have been used, and these criteria are compared together. Also, because of affecting the stress durations on the experimental cost, the author optimize under the constraint that the total experimental cost does not exceed a pre-specified budget. The efficiency of the unconstrained test in comparison with constrained test is discussed.

Although the wind power industry has been booming in China during the last decade, the development of wind turbine aftermarket service is still lagging behind, which seriously affects the operational efficiency of wind farms. If wind turbine manufacturers get involved in the aftermarket, the service pricing policy will impact the profits of both the manufacturer and the wind farm. Therefore, it is necessary to discuss an optimal service pricing strategy in the wind turbine aftermarket and design a method to improve electricity generation efficiency through service contract design. The paper aims to discuss these issues.

In order to decide the maintenance quantity and channel effort level, the authors design a normal Stackelberg game and an efficiency value-added revenue-sharing contract and discuss two kinds of revenue increment sharing models under situations, in which the supply chain’s leaders are the wind farm and the wind turbine manufacturer, respectively.

The results show that in either case, there exist optimal power generation revenue-sharing ratios that can maximize profit. At the same time, the authors outline an optimal service pricing policy, maintenance demand policy and channel service effort-level policy. The results summarize the influences of wind aftermarket services on wind farms’ and wind turbine manufacturers’ profit, which provides managerial insights into the process of manufacturing servitization.

The manufacturer’s channel effort level will influence the power generation increments very much, so the authors have developed a mechanism to stimulate the manufacturer improving the efficiency of aftermarket services.

Taking the power generation increment revenue as the profit increment function, the authors discuss the influence of service price on the profit increment of the wind farm and the wind turbine manufacturer and also consider the influence of service price on the wind farms maintenance quantity and wind turbine manufacturers channel effort level.