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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.

We address the problem of selecting a topological design for a network having a single traffic source and uncertain demand at the remaining nodes. Solving the associated fixed charge network flow (FCF) problem requires finding a network design that limits both the fixed costs of establishing links and the variable costs of sending flow to the destinations. In this paper, we discuss how to obtain a sequence of optimal solutions that arise as the demand intensity varies from low levels to high. One of the network design alternatives associated with these solutions will be chosen based upon the dominant selection criteria of the decision maker. We consider both probabilistic and non-probabilistic criteria and compare the network designs associated with each. We show that the entire sequence of optimal solutions can be identified with little more effort than solving a single FCF problem instance. We also provide solution approaches that are relatively efficient and suggest good design alternatives based upon approximations to the optimal sequence.

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.

A transfer from a richer individual to a poorer one seems to be the most intuitive and straightforward way of reducing income inequality in a society. However, can such a transfer reduce the welfare of the society? We show that a rich-to-poor transfer can induce a response in the individuals’ behaviors which actually exacerbates, rather than reduces, income inequality as measured by the Gini index. We use this result as an input in assessing the social welfare consequence of the transfer. Measuring social welfare by Sen’s social welfare function, we show that the transfer reduces social welfare. These two results are possible even for individuals whose utility functions are relatively simple (namely, at most quadratic in all terms) and incorporate a distaste for low relative income. We first present the two results for a population of two individuals. We subsequently provide several generalizations. We show that our argument holds for a population of any size, and that the choice of utility functions which trigger this response is not singular – the results obtain for an open set of the space of admissible utility functions. In addition, we show that a rich-to-poor transfer can exacerbate inequality when we employ Lorenz-domination, and that it can decrease social welfare when we draw on any increasing, Schur-concave welfare function.