In this modern era of dynamic reliability analysis, this paper introduces the dynamic circular multi-state sliding window system (DCMSWS), an innovative mathematical model that extends the concept of a circular sliding window system into dynamic scenarios. DCMSWS is considered to have failed when the combined performance of r consecutive multistate elements (MEs) falls below a predefined threshold, W. Each component type has a number of distinct individual components with variable states that change over time, making the state probabilities of those components time-dependent. By employing an algorithm grounded in Lz-transform, dynamic reliability measures comprising reliability, availability, mean expected performance, and expected profit are derived for the water supply system. This study represents a pioneering effort in dynamic circular multi-state sliding window systems and their evaluation using the Lz-transform, intimately connected with queuing theory.

In this paper, we consider the two-agent scheduling with time-dependent and position-dependent processing time in a two-machine flow-shop system. The objective is to minimize the makespan of agent A under the constraint that the objective of agent B cannot exceed a given upper bound. In the time-dependent processing time model, the constraint is the makespan of agent B . We first show that the problem is NP-hard in the ordinary sense. Then we prove that there exists an optimal schedule which is a permutation schedule, and there exists an optimal schedule in which the adapted version of Johnson’s rule do not hold for neither agent A nor agent B . Furthermore, we show that three special cases are polynomially solvable. In the position-dependent processing time model, if the constraint is the makespan of agent B , we show that the problem is NP-hard in the ordinary sense. If the constraint is the total completion times of agent B and jobs have different release dates, the problem is strongly NP-hard.

This paper investigates the impacts of information sharing on a green supply chain in which a capital-constrained manufacturer is endowed with private demand information. In different information sharing scenarios (no information sharing, partially sharing information with either the supplier or the bank, and public information sharing), the manufacturer invests in carbon emission reduction and determines the optimal output after gaining a loan from a bank by pledging carbon emission permits. Interestingly, we find that publicly sharing positive demand signals can either enhance or decrease the output and emission abatement level. Additionally, we find that the pledge rate becomes deterministic when sharing positive information. In contrast, it is variable and no larger than in the no-information-sharing scenario when sharing negative information. There is a case in which public information sharing benefits the manufacturer and supplier, regardless of sharing positive or negative information. Contrary to our intuition, we find that while the bank suffers from publicly sharing positive information, it can benefit from sharing negative information. Moreover, this study provides the specific conditions under which a manufacturer chooses a particular type of information sharing format.

Many e-marketplaces have introduced e-commerce brands (EBs) simultaneously displayed on the same platform with national brands (NBs), resulting in direct competition with NBs. This work uses game theory to study the underlying mechanisms of strategy interaction between the e-marketplace's brand promotion and the NB seller's sales channel strategies. We find that the e-marketplace should not blindly promote the EB since its optimal brand-promotion strategy depends on the market factors. Interestingly, when faced with the NB seller's agency channel or dual-channel strategy, the e-marketplace which engages in EB promotion attempts to mitigate NB seller's resistance and make up for the partial loss brought to the NB seller by reducing the commission fee. The NB seller should use the dual-channel regardless of the e-marketplace's brand-promotion strategy. Moreover, when the competition intensity between the two brands is moderate, the brand promotion conversion rate is relatively low, and consumers' recognition of the EB is relatively high, using the dual-channel and promoting the NB could lead to a ``win-win-win'' outcome for the NB seller, e-marketplace, and consumers, and further advance the sustainable development of the supply chain.

This paper addresses a single-machine parallel batch scheduling problem involving n jobs managed by two agents. The goal is to achieve simultaneous minimization of the makespan for agent A and the maximum cost for agent B. Both agents operate independently, with agents A and B handling nA and nB jobs respectively. The parallel batch machine has the capability to concurrently handle a maximum of b jobs grouped together as a batch. The processing time for the entire batch is determined by the longest processing time among the individual jobs assigned to that particular batch. For the unbounded version (b≥n) with either incompatible or compatible job groups, an O(nA+nB4)-time algorithm is presented. For the bounded version (b<n) with incompatible job groups, when all jobs of agent B share identical processing times, an O(nAlognA+nB2)-time algorithm is presented. For the bounded version with compatible job groups, when all jobs of agent B share identical processing times, an O(nAlognA+nAnB+nB3)-time algorithm is presented. The algorithms for the unbounded version with incompatible job groups and the bounded version with compatible job groups generalize or improve the previously known algorithms, while the algorithms for the unbounded version with compatible job groups and the bounded version with incompatible job groups are the first polynomial time algorithms for them.

This paper develops a metaheuristic, the Natural Selection Optimization Algorithm (NSOA), taking inspiration from the natural selection and the survival, growth, and reproduction of the fittest. The algorithm uses two instruments: Normal distribution and Sigmoid function. The Normal distribution generates random numbers such that the individuals in the initial population obey a Normal distribution, which can place search agents appropriately. The Sigmoid function controls the search process of the NSOA, aiding the convergence of the algorithm. To appreciate the global search ability of the NSOA, we test the NSOA against 52 benchmark functions, a hydrogeologic parameter estimation problem, and three engineering problems. Moreover, this paper compares the NSOA with six other algorithms under the same experimental configuration. Our results show that, for most functions, the NSOA converges and extracts the optimal value faster than the other established algorithms, pointing to the novelty and practical efficacy of the NSOA.

In countries around the world, whether developed or developing, there is increasing competition in the industry to strengthen their economies and waste. Managing the supply chain of many goods becomes an essential part of transportation. Along with this, in inventory management, products are most likely to require maintenance, and the production and transportation work necessitate different handling procedures. When a product is manufactured using raw materials in a production house, the manufacturer checks the inventory by producing for a certain time interval. Only some unusable products or products sent by the retailer that cannot be used are sent to the production house again for new products. This study develops an integrated green design production model for deteriorating items with reverse logistics and preservation technology investment under inflation. Firstly, the model is developed in a crisp environment, and then it is extended to a fuzzy environment. Optimal solutions are established numerically, and comparative analysis is performed to validate the result. A comparison study is provided. Finally, sensitivity analysis is done for some influential parameters. It is observed that in each part of the supply chain, the deterioration rate for perishable items is almost uncertain due to several reasons. For that, special methods are used here to reduce the total cost. Results show that the preservation model under a fuzzy environment provides 0.76% less cost than a crisp environment. The cycle time of the retailer and the production time of the producer is less in a fuzzy environment than in a crisp environment.

A non-green manufacturing process can destroy the environment rapidly and it creates global warming. On the other hand, green production processes and circular economic products can reduce environ mental pollution. Waste management through reuse, recycling, etc., is equally crucial for a healthy ecosystem and for saving natural resources. So, circular economic product based green manufacturing model development is very important in the current situation which can apply to the manufacturing industry. For this, a circular economic and green product based dual supply chain model is developed in this study. Here, three supply chain participants (manufacturer, online retailer and offline retailer) are considered where the manufacturer produces circular economic green products and fulfils the customers’ demand by retailers. For the online channel, the retailer purchases the products from the manufacturer and sales to the customers through online mode. But in the offline channel, the retailer completed the same tasks through offline mode. Also, it is assumed that the market demand is dependent on retailers’ selling price, product’s green level and circular economic index. Moreover, the retail price is influenced by the circular economic index. Then four different problems are proposed that maximizes the profits of manufacturer, retailers (online and offline) and integrated supply chain system and solved by centralized and decentralized methods. The objective of this study is to determine the optimal selling prices, product’s green level and circular economic index which maximizes the profits of the supply chain members. Finally, sensitivity analysis is carried out to determine the effects of model parameters on the optimal policy and draw a fruitful conclusion from this study.

Remanufacturing has attracted considerable attention because it significantly contributes to a sustainable supply chain where used parts/products can be recycled to reduce waste. Faced with the rise of the remanufacturing business, many original equipment manufacturers (OEMs) choose to authorize independent remanufacturers (IRs) for profit. In this paper, we consider a sustainable supply chain consisting of an OEM and an IR in a fuzzy environment where production cost and market demand are uncertain to study whether such an authorization decision would benefit both the economy and the environment. An unauthorized model (Nash game model) and two authorized models (Cooperative game and Stackelberg game models) are developed. Our results show that the cooperation between the OEM and the IR increases the selling price of the product, and therefore encourages authorization financially. However, a leader position of the OEM (i.e., in the Stackelberg game) helps achieve a win-win situation where profit maximization also improves the environment. Furthermore, our analysis illustrates that considering a fuzzy environment will boost the chances of authorization and help achieve the win-win situation.

Based on the competition in the recycling market, this paper investigates the technology licensing outsourcing strategy and the remanufacturing strategy of a closed-loop supply chain, and analyses the effect of the implementation of government subsidy policies. This paper considers a closed-loop supply chain consisting of a manufacturer, a retailer and two competing recyclers (one specializing in sorted recycling and the other in traditional recycling). Using the Stackelberg game model, eight decision-making models under different outsourcing modes, remanufacturing modes and government subsidies are constructed. Through the comparative analysis of the equilibrium results, the optimal outsourcing authorization and remanufacturing strategies for the closed-loop supply chain are proposed, and the facilitating effect of the government's double subsidy policy is verified. Our findings show that manufacturers tend to choose the unit-pay outsourcing model in outsourcing and remanufacturing decisions, although this may lead to profit inequality among other members. Meanwhile, increasing government subsidies for sorted recycling and remanufacturing favours the profitability of sorted recyclers, however, it is of concern that this is not conducive to increasing the profitability of traditional recyclers. Furthermore, at low recycling prices, an increase in dual subsidies is beneficial in boosting market demand and profits for all members, however, at high recycling prices, the equilibrium outcomes and member profits change in the opposite direction as under the fixed-pay outsourcing model. We also find that government inputs of double subsidies can increase member profits, promote recycling and remanufacturing, and maintain market stability, especially the fixed-pay outsourcing versus full remanufacturing model is more conducive to achieving these objectives. The research in this paper contributes to the construction and development of the remanufacturing cycle system in the market.