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Two-stage production systems including a processing shop and an assembly stage are widely used in various manufacturing industries. These two stages are usually studied independently which may not lead to ideal results. This paper aims to deal with a two-stage production system including a job shop and an assembly stage.

Some exact methods are proposed based on branch and bound (B&B) approach to minimize the total completion time of products. As B&B approaches are usually time-consuming, three efficient lower bounds are developed for the problem and variable neighborhood search is used to provide proper upper bound of the solution in each branch. In addition, to create branches and search new nodes, two strategies are applied including the best-first search and the depth-first search (DFS). Another feature of the proposed algorithms is that the search space is reduced by releasing the precedence constraint. In this case, the problem becomes equivalent to a parallel machine scheduling problem, and the redundant branches that do not consider the precedence constraint are removed. Therefore, the number of nodes and computational time are significantly reduced without eliminating the optimal solution.

Some numerical examples are used to evaluate the performance of the proposed methods. Comparison result to mathematical model (mixed-integer linear programming) validates the performance accuracy and efficiency of the proposed methods. In addition, computational results indicate the superiority of the DFS strategy with regard to CPU time.

Studies about the scheduling problems for two-stage production systems including job shop followed by an assembly stage traditionally present approximate method and metaheuristic algorithms to solve the problem. This is the first study that introduces exact methods based on (B&B) approach.

This study examines the scheduling problem for a two-stage flowshop. All jobs are immediately available for processing and job characteristics including the processing times and due dates are known and certain. The goals of the scheduling problem are (1) to minimize the total flowtime for all jobs, (2) to minimize the total number of tardy jobs, and (3) to minimize both the total flowtime and the total number of tardy jobs simultaneously. Lower bound performances with respect to the total flowtime and the total number of tardy jobs are presented. Subsequently, this study identifies the special structure of schedules with minimum flowtime and minimum number of tardy jobs and develops three sets of heuristics which generate a Pareto set of bicriteria schedules. For each heuristic procedure, there are four options available for schedule generation. In addition, we provide enhancements to a variety of lower bounds with respect to flowtime and number of tardy jobs in a flowshop environment. Proofs and discussions to lower bound results are also included.

The purpose of this paper is to forecast variability in mortgage rates by using interval measured data and interval computing method.

Variability (interval) forecasts generated by the interval computing are compared with lower‐ and upper‐bound forecasts based on the ordinary least squares (OLS) rolling regressions.

On average, 56 per cent of annual changes in mortgage rates may be predicted by OLS lower‐ and upper‐bound forecasts while the interval method improves forecasting accuracy to 72 per cent.

This paper uses the interval computing method to forecast variability in mortgage rates. Future studies may expand variability forecasting into more risk‐managing areas.

Results of this study may be interesting to executive officers of banks, mortgage companies, and insurance companies, builders, investors, and other financial decision makers with an interest in mortgage rates.

Although it is well‐known that changes in mortgage rates can significantly affect the housing market and economy, there is not much serious research that attempts to forecast variability in mortgage rates in the literature. This study is the first endeavor in variability forecasting for mortgage rates.

For the considered system, an enumeration method is applicable to evaluate the exact system reliability only for very small‐sized systems, because, when the size of system is large, it takes huge execution time. Therefore, the paper provides approximate values for the system reliability as useful for calculating the reliability of large systems in a reasonable execution time.

The paper provides upper and lower bounds of the system reliability, and limit theorem for the reliability of our considered system in i.i.d. case.

The paper experimentally finds that the proposed upper and lower bounds are effective when component reliabilities close to one or the value of k becomes larger. Next, it concludes approximate values for approximate equation derived from the limit theorem are always smaller than lower bound through numerical experiments.

The upper and lower bounds for the reliability of a system can be calculated by using the reliability of a small system by the same idea as previous study for two‐dimensional system.

Up to now some researchers studied multi‐dimensional consecutive‐k‐out‐of‐n:F systems, and showed promising applications of such multi‐dimensional models, e.g. diagnosis of a disease diagnosed by reading an X‐ray. As another examples, three‐dimensional system can be applied for the mathematical model of a three‐dimensional flash memory cell failure model, and so on.

The paper considers a kind of three‐dimensional k‐within‐consecutive‐r‐out‐of‐n:F system. It proposes upper and lower bounds of the system reliability and limit theorem.

The safety assessment of engineering structures under repeated variable dynamic loads such as seismic and wind loads can be considered as a dynamic shakedown problem. This paper aims to extend the stress compensation method (SCM) to perform lower bound dynamic shakedown analysis of engineering structures and a double-closed-loop iterative algorithm is proposed to solve the shakedown load.

The construction of the dynamic load vertexes is carried out to represent the loading domain of a structure under both dynamic and quasi-static load. The SCM is extended to perform lower bound dynamic shakedown analysis of engineering structures, which constructs the self-equilibrium stress field by a series of direct iteration computations. The self-equilibrium stress field is not only related to the amplitude of the repeated variable load but also related to its frequency. A novel double-closed-loop iterative algorithm is presented to calculate the dynamic shakedown load multiplier. The inner-loop iteration is to construct the self-equilibrated residual stress field based on the certain shakedown load multiplier. The outer-loop iteration is to update the dynamic shakedown load multiplier. With different combinations of dynamic load vertexes, a dynamic shakedown load domain could be obtained.

Three-dimensional examples are presented to verify the applicability and accuracy of the SCM in dynamic shakedown analysis. The example of cantilever beam under harmonic dynamic load with different frequency shows the validity of the dynamic load vertex construction method. The shakedown domain of the elbow structure varies with the frequency under the dynamic approach. When the frequency is around the resonance frequency of the structure, the area of shakedown domain would be significantly reduced.

In this study, the dynamical response of structure is treated as perfect elastoplastic. The current analysis does not account for effects such as large deformation, stochastic external load and nonlinear vibration conditions which will inevitably be encountered and affect the load capacity.

This study provides a direct method for the dynamical shakedown analysis of engineering structures under repeated variable dynamic load.

Adopting the circular economy (CE) notion in the supply chain perspective is necessary for the sustainability viewpoint. However, such practices are deficient, especially in developing countries like India, because of several obstacles. The purpose of this study was to create an approach for circular supply chain management (CSCM) adaption in Indian rubber industries by identifying and evaluating its associated obstacles.

A hybrid approach of analytic hierarchy process (AHP) and the grey-based ELECTRE method had been employed in this research to obtain the mutual rankings of the identified obstacles based on their impressions on the CSCM prosperity criteria through a case study and involving diverse expert's opinions.

Presented study's findings illustrate that “Lack of consumer knowledge and consciousness towards environmental sustainability” was found to be the top-ranked obstacle followed by “Unwillingness towards supply chain re-structuring”.

The obstacles' prioritized rankings could help leaders to create sequential strategies for adapting a resilient CSCM structure by systematically eliminating these obstacles. Moreover, the pinpointed critical obstacles could be investigated further in separate studies and generate future studies' scope.

During the extensive literature survey, it had been found that the CSCM practices are in the fledgling stage in the developing country's context. Moreover, studies related to CSCM adaption in rubber-based manufacturing industries were much lacking. Presented work is peculiar, aiming to accelerate the CSCM adaption in the industrial rubber sector in developing countries like India.

Cycle time reduction is important for order fulling process but often subject to resource constraints. This study considers an unrelated parallel machine environment where orders with random demands arrive dynamically. Processing speeds are controlled by resource allocation and subject to diminishing marginal returns. The objective is to minimize long-run expected order cycle time via order schedule and resource allocation decisions.

A stochastic optimization algorithm named CAP is proposed based on particle swarm optimization framework. It takes advantage of derived bound information to improve local search efficiency. Parameter impacts including demand variance, product type number, machine speed and resource coefficient are also analyzed through theoretic studies. The algorithm is evaluated and benchmarked with four well-known algorithms via extensive numerical experiments.

First, cycle time can be significantly improved when demand randomness is reduced via better forecasting. Second, achieving processing balance should be of top priority when considering resource allocation. Third, given marginal returns on resource consumption, it is advisable to allocate more resources to resource-sensitive machines.

A novel PSO-based optimization algorithm is proposed to jointly optimize order schedule and resource allocation decisions in a dynamic environment with random demands and stochastic arrivals. A general quadratic resource consumption function is adopted to better capture diminishing marginal returns.

Cassimon et al. (2007) propose a pricing formula of American call options under the multiple dividends by extending Roll (1977). However, because these studies investigate the option pricing formula under the escrow model, there is inconsistency for the assumption of the stock prices. This paper proposes pricing formulas of American call options under the multiple dividends and piecewise geometric Brownian motion. For the formulas, I approximate the log prices of ex-dividend dates to follow a multivariate normal distribution, and decompose the option price as a function of payoffs and exercise boundaries. Then, I obtain an upper bound of the American call options by substituting approximated log prices into the both of the payoffs and the exercise boundaries. Besides, I obtain a lower bound of the price by substituting approximated price only into the exercise boundaries. These upper and lower bounds are exact prices when the amounts of dividends are linear to the stock prices. According to the numerical study, the lower bound produces relatively small errors. Especially, it produces small errors when the dividends are more sensitive to the stock price changes.

The purpose of this paper is to acquire strict upper and lower bounds on quantities of slender beams on Winkler foundation in finite element analysis.

It leans on the dual analysis wherein the constitutive relation error (CRE) is used to perform goal-oriented error estimation. Due to the coupling of the displacement field and the stress field in the equilibrium equations of the beam, the prolongation condition for the stress field which is the key ingredient of CRE estimation is not directly applicable. To circumvent this difficulty, an approximate problem and the solution thereof are introduced, enabling the CRE estimation to proceed. It is shown that the strict bounding property for CRE estimation is preserved and strict bounds of quantities of the beam are obtainable thereafter.

Numerical examples are presented to validate the strict upper and lower bounds for quantities of beams on elastic foundation by dual analysis.

This paper deals with one-dimensional (1D) beams on Winkler foundation. Nevertheless, the present work can be naturally extended to analysis of shells and 2D and 3D reaction-diffusion problems for future research.

CRE estimation is extended to analysis of beams on elastic foundation by a decoupling strategy; strict upper bounds of global energy norm error for beams on elastic foundation are obtained; strict bounds of quantities for beams on elastic foundation are also obtained; unified representation and corresponding dual analysis of various quantities of the beam are presented; rigorous derivation of admissible stresses for beams is given.

Suggests that, in recent years, remarkable progress has been made in the development of the topological design of logistics networks, especially in the warehouse location problem. Extends the standard warehouse location problem to a generalization of multiproduct capacitated warehouse location problem, as opposed to differentiated variations of a single‐product warehouse location problem, where each warehouse has a given capacity for carrying each product. Presents an algorithm based on cross‐decomposition, to reduce the computational difficulty by incorporating Benders decomposition and Lagrangean relaxation. Computational results of this algorithm are encouraging.