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Assembly is the last step in manufacturing processes. The two-sided assembly line balancing problem (TALBP) is a typical research focus in the field of combinatorial optimization. This paper aims to study a multi-constraint TALBP-I (MC-TALBP-I) that involves positional constraints, zoning constraints and synchronism constraints to make TALBP more in line with real production. For enhancing quality of assembly solution, an improved imperialist competitive algorithm (ICA) is designed for solving the problem.

A mathematical model for minimizing the weighted sum of the number of mated-stations and stations is established. An improved ICA is designed based on a priority value encoding structure for solving MC-TALBP-I.

The proposed ICA was tested by several benchmarks involving positional constraints, zoning constraints and synchronism constraints. This algorithm was compared with the late acceptance hill-climbing (LAHC) algorithm in several instances. The results demonstrated that the ICA provides much better performance than the LAHC algorithm.

The best solution obtained by solving MC-TALBP-I is more feasible for determining the real assembly solution than the best solution obtained by solving based TALBP-I only.

A novel ICA based on priority value encoding is proposed in this paper. Initial countries are generated by a heuristic method. An imperialist development strategy is designed to improve the qualities of countries. The effectiveness of the ICA is indicated through a set of benchmarks.

This paper aims to review and discuss four aspects of mixed-model assembly line balancing (MMALB) problem mainly on the optimization angle. MMALB is a non-deterministic polynomial-time hard problem which requires an effective algorithm for solution. This problem has attracted a number of research fields: manufacturing, mathematics and computer science.

This paper review 59 published research works on MMALB from indexed journal. The review includes MMALB problem varieties, optimization algorithm, objective function and constraints in the problem.

Based on research trend, this topic is still growing with the highest publication number observed in 2016 and 2017. The review indicated that the future research direction should focus on human factors and sustainable issues in the problem modeling. As the assembly cost becomes crucial, resource utilization in the assembly line should also be considered. Apart from that, the growth of new optimization algorithms is predicted to influence the MMALB optimization, which currently relies on well-established algorithms.

The originality of this paper is on the research trend in MMALB. It provides the future direction for the researchers in this field.

A method for balancing a single‐model assembly line is described which incorporates various constraining features such as fixed position, positive and negative zoning, multiple parallel stations, etc. It can easily be extended for multiple manning of stations. First a priority list of the elements is formed. For each element, its elemental time is added to those of its total number of successors. The list is then rearranged in non‐increasing order. The method has been tested by solving a large number of randomly generated problems. A computer program has been developed for the generalised method.

Various approaches and algorithms have been proposed since the 1950s to solve the assembly line (AL) balancing problem. These methods have established an AL configuration from the beginning. However, a prebalanced AL may have to be rebalanced in real life for many reasons, such as changes in the cycle time, production demand, product features or task operation times. This problem has increasingly attracted the interest of scientists in recent years. This study aims to offer a detailed review of the assembly line rebalancing problems (ALRBPs) to provide a better insight into the theoretical and practical applications of ALRBPs.

A structured database search was conducted, and 41 ALRBP papers published between 2005 and 2022 were classified based on the problem structure, objective functions, problem constraints, reasons for rebalancing, solution approaches and type of data used for solution evaluation. Finally, future research directions were identified and recommended.

Single model, straight lines with deterministic task times were the most studied type of the ALRBPs. Eighteen percent of the studies solved worker assignment problems together with ALRBP. Product demand and cycle time changes were the leading causes of the rebalancing need. Furthermore, seven future research opportunities were suggested.

Although there are many review studies on AL balancing problems, to the best of the authors’ knowledge, there have been no attempts to review the studies on ALRBPs.

Cycle time fluctuations in assembly lines are one of the important reasons of re‐balancing. As a result of re‐balancing of assembly lines, it will be necessary to change task sequences or equipment locations. The purpose of this paper is to find the task sequence which enables assembly line balancing (ALB) with minimum number of stations (NS) for different cycle times such that tasks and equipment or fixture locations remain unchanged.

In this paper a heuristic which consist of two stages is proposed to find a common task sequence for different cycle times in assembly lines.

It is shown that optimal NS for different cycle times can be achieved with a fixed task sequence.

The approach is limited to a single model case. Model variety together with cycle time variety can be investigated in further studies.

Assembly lines which require less time and cost for re‐balancing can be easily designed by the proposed approach.

ALB problem is handled with a new viewpoint. Also, it is observed that the proposed approach serves as a bridge between assembly line design and balancing. In this regard, it is thought to have an important place in the ALB literature.

This paper aims to build a mathematical model to determine the price of an acre of developable land, whether it is part of a large open tract (farm) or a smaller residential parcel that can legally be subdivided. The primary purpose of the model is to explore the effect of various minimum lot‐size regulations on the price of these two types of vacant land. The study also attempts to explain apparently conflicting findings that have recently appeared in empirical studies of “down‐zoning” in the states of Maryland and New Jersey.

The mathematical model of land value is based on principles of asset valuation under uncertainty at various locations within a metropolitan area. The price of an acre of land is modeled as the present value of a stream of indirect utility to homeowners, and economic rents to farmers, developers or landlords, depending on an endogenous date of development. The cases of New Jersey and Maryland are compared using parameterized simulations, with minimum lot size allowed to vary.

The simulations reconcile earlier empirical studies on Maryland and New Jersey. The observed absence of any price effect of down‐zoning in rural Maryland appears to be caused by the fact that development is not imminent there. In New Jersey, development is imminent virtually everywhere, and a high proportion of today's vacant land value is due to its development potential. This means that down‐zoning will typically lead to dramatic declines in vacant land value in New Jersey.

The study relies on state averages, so its results should not be applied to particular parcels in Maryland or New Jersey. The study incorporates uncertainty in expected developer profits, but not in future political decisions.

By clarifying the context in which zoning changes will or will not lead to decline in a landowner's asset value, the study can inform legal and political debates over re‐zonings in the USA. Included in these debates is the claim that some re‐zonings violate the “takings” clause of the USA constitution.

The majority of papers on this subject are empirical, using a hedonic or an appraisal methodology. This paper provides a coherent theoretical model of per‐acre land prices under different levels of zoning restriction. It can be used for simulation or prediction with relatively few input parameters.

This paper aims to develop a novel trajectory optimization algorithm which is capable of producing high accuracy optimal solution with superior computational efficiency for the hypersonic entry problem.

A two-stage trajectory optimization framework is constructed by combining a convex-optimization-based algorithm and the pseudospectral-nonlinear programming (NLP) method. With a warm-start strategy, the initial-guess-sensitive issue of the general NLP method is significantly alleviated, and an accurate optimal solution can be obtained rapidly. Specifically, a successive convexification algorithm is developed, and it serves as an initial trajectory generator in the first stage. This algorithm is initial-guess-insensitive and efficient. However, approximation error would be brought by the convexification procedure as the hypersonic entry problem is highly nonlinear. Then, the classic pseudospectral-NLP solver is adopted in the second stage to obtain an accurate solution. Provided with high-quality initial guesses, the NLP solver would converge efficiently.

Numerical experiments show that the overall computation time of the two-stage algorithm is much less than that of the single pseudospectral-NLP algorithm; meanwhile, the solution accuracy is satisfactory.

Due to its high computational efficiency and solution accuracy, the algorithm developed in this paper provides an option for rapid trajectory designing, and it has the potential to evolve into an online algorithm.

The paper provides a novel strategy for rapid hypersonic entry trajectory optimization applications.

The border control becomes challenging when a protected region is large and there is a limited number of border patrols. This research paper proposes a novel heuristic-based patrol path planning scheme in order to efficiently patrol with resource scarcity.

The trespasser influencing score, which is determined from the environmental characteristics and trespassing statistic of the region, is used as a heuristic for measuring a chance of approaching a trespasser. The patrol plan is occasionally updated with a new trespassing statistic during a border operation. The performance of the proposed patrol path planning scheme was evaluated and compared with other patrol path planning schemes by the empirical experiment under different scenarios.

The result from the experiment indicates that the proposed patrol planning outperforms other patrol path planning schemes in terms of the trespasser detection rate, when more environment-aware trespassers are in the region.

The experiment was conducted through simulated agents in simulated environment, which were assumed to mimic real behavior and environment.

This research paper contributes a heuristic-based patrol path planning scheme that applies the environmental characteristics and dynamic statistic of the region, as well as a border surveillance problem model that would be useful for mobile sensor planning in a border surveillance application.

Parallel two-sided assembly lines are usually designed to produce large-sized products such as trucks and buses. In parallel two-sided assembly lines, both left and right sides of the line are used for manufacturing one or more products on two or more assembly lines located parallel to each other. The purpose of this paper is to develop a new mathematical model for the parallel two-sided assembly line balancing problem that helps to evaluate and validate the balancing operations of the machines such as removal of tools and fixtures and reallocating the operators.

The proposed approach is explained with the help of an example problem. In all, 22 test problems are formed using the benchmark problems P9, P12, P16 and P24. The results obtained are compared among approaches of the task(s) shared, tool(s) shared and both tool(s) and task(s) shared for effect on efficiency as the performance measure. The solution presented here follows the exact solution procedure that is solved by Lingo 16 solver.

Based on the experiments, line efficiency decreases when only tools are shared and increases when only tasks are shared. Results indicate that by sharing tasks and tools together, better line efficiency is obtained with less cost of tools and fixtures.

According to the industrial aspect, the result of the study can be beneficial for assembly of the products, where tools and tasks are shared between parallel workstations of two or more parallel lines.

According to the author’s best knowledge, this paper is the first to address the tools and tasks sharing between any pair of parallel workstations.