An effective hybrid honey bee mating optimization algorithm for balancing mixed-model two-sided assembly lines

Mixed-model two-sided assembly lines are widely used in a range of industries for their abilities of increasing the flexibility to meet a high variety of customer demands. Balancing assembly lines is a vital design issue for industries. However, the mixed-model two-sided assembly line balancing (MTALB) problem is NP-hard and difficult to solve in a reasonable computational time. So it is necessary for researchers to find some efficient approaches to address this problem. Honey bee mating optimization (HBMO) algorithm is a population-based algorithm inspired by the mating process in the real colony and has been applied to solve many combinatorial optimization problems successfully. In this paper, a hybrid HBMO algorithm is presented to solve the MTALB problem with the objective of minimizing the number of mated-stations and total number of stations for a given cycle time. Compared with the conventional HBMO algorithm, the proposed algorithm employs the simulated annealing (SA) algorithm with three different neighborhood structures as workers to improve broods, which could achieve a good balance between intensification and diversification during the search. In addition, a new encoding and decoding scheme, including the adjustment of the final mated-station, is devised to fit the MTALB problem. The proposed algorithm is tested on several sets of instances and compared with Mixed Integer Programming (MIP) and SA. The superior results of these instances validate the effectiveness of the proposed algorithm.     

A simulated annealing algorithm based approach for balancing and sequencing of mixed-model U-lines

It is known that two interrelated problems called as line balancing and model sequencing should be solved simultaneously for an efficient implementation of a mixed-model U-shape assembly line in a JIT (Just in Time) environment. On the other hand, three versions of assembly line balancing problem can be identified: Type I, Type II, and Type E. There are only two articles ( Kara, Ozcan, & Peker, 2007a and Hamzadayi & Yildiz, 2012) related to simultaneous balancing and sequencing of mixed-model U-lines for minimizing the number of stations (Type 1 problem) by ignoring the fixed model sequence in the current literature. In this paper, a simulated annealing algorithm is proposed for solving a problem of type 1 by ignoring the fixed model sequence. Accordingly, simulated annealing based fitness evaluation approach proposed by Hamzadayi and Yildiz (2012) is enhanced by adding the tabu list, and inserted into the proposed algorithm. Implementation difficulties experienced in meta-heuristics based on solution modification for solving these types of problems are demonstrated. ‘Absolute deviation of workloads’ (ADW) is quite frequently used as performance criteria in the literature. It is found that ADW is an insufficient performance criterion for evaluating the performance of the solutions, and this is showed by means of an illustrative example. The parameters of the proposed algorithm are reviewed for calibrating the algorithm by means of Taguchi design of experiments. Performance of the proposed approach is tested through a set of test problems. The results of computational experiments indicate that the proposed approach is an effective method in solving simultaneous line balancing/model sequencing problems for mixed-model U-lines for minimizing the number of stations.     

Modeling and solving mixed-model assembly line balancing problem with setups. Part I: A mixed integer linear programming model

This paper is the first one of the two papers entitled “modeling and solving mixed-model assembly line balancing problem with setups”, which has the aim of developing the mathematical programming formulation of the problem and solving it with a hybrid meta-heuristic approach. In this current part, a mixed-integer linear mathematical programming (MILP) model for mixed-model assembly line balancing problem with setups is developed. The proposed MILP model considers some particular features of the real world problems such as parallel workstations, zoning constraints, and sequence dependent setup times between tasks, which is an actual framework in assembly line balancing problems. The main endeavor of Part-I is to formulate the sequence dependent setup times between tasks in type-I mixed-model assembly line balancing problem. The proposed model considers the setups between the tasks of the same model and the setups because of the model switches in any workstation. The capability of our MILP is tested through a set of computational experiments. Part-II tackles the problem with a multiple colony hybrid bees algorithm. A set of computational experiments is also carried out for the proposed approach in Part-II.     

A genetic algorithm based approach for simultaneously balancing and sequencing of mixed-model U-lines with parallel workstations and zoning constraints

This paper presents a Priority-Based Genetic Algorithm (PGA) based method for the simultaneously tackling of the mixed-model U-shape assembly line (MMUL) line balancing/model sequencing problems (MMUL/BS) with parallel workstations and zoning constraints and allows the decision maker to control the process to create parallel workstations and to work in different scenarios. In the presented method, simulated annealing based fitness evaluation approach (SABFEA) is developed to be able to make fitness function calculations easily and effectively. A new fitness function is adapted to MMULs for aiming at minimizing the number of workstations as primary goal and smoothing the workload between-within workstations by taking all cycles into consideration. A numerical example to clarify the solution methodology is presented. Performance of the proposed approach is tested through sets of test problem with randomly generated minimum part sets. The results of the computational experiments indicate that SABFEA works with PGA very concordantly; and it is an effective method in solving MMUL/BS with parallel workstations and zoning constraints.     

A multi-objective genetic algorithm for mixed-model assembly line rebalancing

When demand structure or production technology changes, a mixed-model assembly line (MAL) may have to be reconfigured to improve its efficiency in the new production environment. In this paper, we address the rebalancing problem for a MAL with seasonal demands. The rebalancing problem concerns how to reassign assembly tasks and operators to candidate stations under the constraint of a given cycle time. The objectives are to minimize the number of stations, workload variation at each station for different models, and rebalancing cost. A multi-objective genetic algorithm (moGA) is proposed to solve this problem. The genetic algorithm (GA) uses a partial representation technique, where only a part of the decision information about a candidate solution is expressed in the chromosome and the rest is computed optimally. A non-dominated ranking method is used to evaluate the fitness of each chromosome. A local search procedure is developed to enhance the search ability of moGA. The performance of moGA is tested on 23 reprehensive problems and the obtained results are compared with those by other authors.     

Optimisation of mixed-model assembly line balancing problem under uncertain demand

Assembly lines play a crucial role in determining the profitability of a company. Market conditions have increased the importance of mixed-model assembly lines. Variations in the demand are frequent in real industrial environments and often leads to failure of the mixed-model assembly line balancing scheme. Decision makers have to take into account this uncertainty. In an assembly line balancing problem, there is a massive amount of research in the literature assuming deterministic environment, and many other works consider uncertain task times. This research utilises the uncertainty theory to model uncertain demand and introduces complexity theory to measure the uncertainty of assembly lines. Scenario probability and triangular fuzzy number are used to describe the uncertain demand. The station complexity was measured based on information entropy and fuzzy entropy to assist in balancing systems with robust performances, considering the influence of multi-model products in the station on the assembly line. Taking minimum station complexity, minimum workload difference within station, maximum productivity as objective functions, a new optimization model for mixed-model assembly line balancing under uncertain demand was established. Then an improved genetic algorithm was applied to solve the model. Finally, the effectiveness of the model was verified by several instances of mixed-model assembly line for automobile engine.     

A multi-objective scatter search for a mixed-model assembly line sequencing problem

A mixed-model assembly line (MMAL) is a type of production line where a variety of product models similar to product characteristics are assembled. There is a set of criteria on which to judge sequences of product models in terms of the effective utilization of this line. In this paper, we consider three objectives, simultaneously: minimizing total utility work, total production rate variation, and total setup cost. A multi-objective sequencing problem and its mathematical formulation are described. Since this type of problem is NP-hard, a new multi-objective scatter search (MOSS) is designed for searching locally Pareto-optimal frontier for the problem. To validate the performance of the proposed algorithm, in terms of solution quality and diversity level, various test problems are made and the reliability of the proposed algorithm, based on some comparison metrics, is compared with three prominent multi-objective genetic algorithms, i.e. PS-NC GA, NSGA-II, and SPEA-II. The computational results show that the proposed MOSS outperforms the existing genetic algorithms, especially for the large-sized problems.     

Multi-objective two-sided mixed-model assembly line balancing using particle swarm optimisation with negative knowledge

Particle swarm optimisation (PSO) is an evolutionary metaheuristic inspired by the swarming behaviour observed in flocks of birds. The applications of PSO to solve multi-objective discrete optimisation problems are not widespread. This paper presents a PSO algorithm with negative knowledge (PSONK) to solve multi-objective two-sided mixed-model assembly line balancing problems. Instead of modelling the positions of particles in an absolute manner as in traditional PSO, PSONK employs the knowledge of the relative positions of different particles in generating new solutions. The knowledge of the poor solutions is also utilised to avoid the pairs of adjacent tasks appearing in the poor solutions from being selected as part of new solution strings in the next generation. Much of the effective concept of Pareto optimality is exercised to allow the conflicting objectives to be optimised simultaneously. Experimental results clearly show that PSONK is a competitive and promising algorithm. In addition, when a local search scheme (2-Opt) is embedded into PSONK (called M-PSONK), improved Pareto frontiers (compared to those of PSONK) are attained, but longer computation times are required.     

A simulated annealing algorithm for multi-manned assembly line balancing problem

Assembly line balancing problems with multi-manned workstations usually occur in plants producing high volume products (e.g. automotive industry) in which the size of the product is reasonably large to utilize the multi-manned assembly line configuration. In these kinds of assembly lines, usually there are multi-manned workstations where a group of workers simultaneously performs different operations on the same individual product. However, owing to the high computational complexity, it is quite difficult to achieve an optimal solution to the balancing problem of multi-manned assembly lines with traditional optimization approaches. In this study, a simulated annealing heuristic is proposed for solving assembly line balancing problems with multi-manned workstations. The line efficiency, line length and the smoothness index are considered as the performance criteria. The proposed algorithm is illustrated with a numerical example problem, and its performance is tested on a set of test problems taken from literature. The performance of the proposed algorithm is compared to the existing approaches. Results show that the proposed algorithm performs well.     

An imperialist competitive algorithm for a mixed-model assembly line sequencing problem

This paper presents a novel imperialist competitive algorithm (ICA) to a just-in-time (JIT) sequencing problem where variations of production rate are to be minimized. This type of problem is NP-hard. Up to now, some heuristic and meta-heuristic approaches are proposed to minimize the production rates variation. This paper presents a novel algorithm for optimization which inspired by imperialistic competition in real world. Sequences of products where minimize the production rates variation is desired. Performance of the proposed ICA was compared against a genetic algorithm (GA) in small, medium and large problems. Experimental results show the ICA performance against GA.     

A genetic algorithm based approach to the mixed-model assembly line balancing problem of type II

Mixed-model assembly lines allow for the simultaneous assembly of a set of similar models of a product, which may be launched in the assembly line in any order and mix. As current markets are characterized by a growing trend for higher product variability, mixed-model assembly lines are preferred over the traditional single-model assembly lines.

This paper presents a mathematical programming model and an iterative genetic algorithm-based procedure for the mixed-model assembly line balancing problem (MALBP) with parallel workstations, in which the goal is to maximise the production rate of the line for a pre-determined number of operators.

The addressed problem accounts for some relevant issues that reflect the operating conditions of real-world assembly lines, like zoning constraints and workload balancing and also allows the decision maker to control the generation of parallel workstations.     

Modeling and solving mixed-model assembly line balancing problem with setups. Part II: A multiple colony hybrid bees algorithm

This paper is the second one of the two papers entitled “Modeling and Solving Mixed-Model Assembly Line Balancing Problem with Setups”, which deals with the mixed-model assembly line balancing problem of type I (MMALBP-I) with some particular features of the real world problems such as parallel workstations, zoning constraints and sequence dependent setup times between tasks. Due to the complex nature of the problem, we tackled the problem with bees algorithm (BA), which is a relatively new member of swarm intelligence based meta-heuristics and tries to simulate the group behavior of real honey bees. However, the basic BA simulates the group behavior of real honey bees in a single colony; we aim at developing a new BA, which simulates the group behavior of honey bees in a single colony and between multiple colonies. The multiple colony type of BA is more realistic than the single colony type because of the multiple colony structure of the real honey bees; each colony represents the honey bees living in a different hive and is generated with a different heuristic rule. The performance of the proposed multiple colony algorithm is tested on 36 representatives MMALBP-I extended by adding low, medium and high variability of setup times. The results are compared with single colony algorithms in terms of solution quality and computational times. Computational results indicate that the proposed multiple colony algorithm has superior performance. Part II of the paper also presents optimal solutions of some problems provided by MILP model developed in Part I.     

A robust design of simulated annealing approach for mixed-model sequencing

The effectiveness of the solution method based on simulated annealing (SA) mainly depends on how to determine the SA-related parameters. A scheme as well as parameter values for defining an annealing schedule should be appropriately determined, since various schemes and their corresponding parameter values have a significant impact on the performance of SA algorithms. In this paper, based on robust design we propose a new annealing parameter design method for the mixed-model sequencing problem which is known to be NP-hard. To show the effectiveness of the proposed method, extensive computation experiments are conducted. It was found that the robust designed method outperforms the SA algorithm by McMullen and Frazier [McMullen, P.R., & Frazier, G.V. (2000). A simulated annealing approach to mixed-model sequencing with multiple objectives on a just-in-time line. IIE Transactions, 32, 679–686].     

A new particle swarm algorithm for a multi-objective mixed-model assembly line sequencing problem

The sequencing of products for mixed-model assembly line in Just-in-Time manufacturing systems is sometimes based on multiple criteria. In this paper, three major goals are to be simultaneously minimized: total utility work, total production rate variation, and total setup cost. A multi-objective sequencing problem and its mathematical formulation are described. Due to the NP-hardness of the problem, a new multi-objective particle swarm (MOPS) is designed to search locally Pareto-optimal frontier for the problem. To validate the performance of the proposed algorithm, various test problems are solved and the reliability of the proposed algorithm, based on some comparison metrics, is compared with three distinguished multi-objective genetic algorithms (MOGAs), i.e. PS-NC GA, NSGA-II, and SPEA-II. Comparison shows that MOPS provides superior results to MOGAs.     

A hybrid multi-objective shuffled frog-leaping algorithm for a mixed-model assembly line sequencing problem

In this paper, a mixed-model assembly line (MMAL) sequencing problem is studied. This type of production system is used to manufacture multiple products along a single assembly line while maintaining the least possible inventories. With the growth in customers’ demand diversification, mixed-model assembly lines have gained increasing importance in the field of management. Among the available criteria used to judge a sequence in MMAL, the following three are taken into account: the minimization of total utility work, total production rate variation, and total setup cost. Due to the complexity of the problem, it is very difficult to obtain optimum solution for this kind of problems by means of traditional approaches. Therefore, a hybrid multi-objective algorithm based on shuffled frog-leaping algorithm (SFLA) and bacteria optimization (BO) are deployed. The performance of the proposed hybrid algorithm is then compared with three well-known genetic algorithms, i.e. PS-NC GA, NSGA-II, and SPEA-II. The computational results show that the proposed hybrid algorithm outperforms the existing genetic algorithms, significantly in large-sized problems.     

A multi-objective mixed-model assembly line sequencing problem in order to minimize total costs in a Make-To-Order environment,considering order priority

Nowadays, mixed-model assembly line is used increasingly as a result of customers’ demand diversification. An important problem in this field is determining the sequence of products for entering the line. Before determining the best sequence of products, a new procedure is introduced to choose important orders for entering the shop floor. Thus the orders are sorted using an analytical hierarchy process (AHP) approach based on three criteria: critical ratio of each order (CR_o), Significance degree of customer and innovation in a product, while the last one is presented for the first time. In this research, six objective functions are presented: minimizing total utility work cost, total setup cost and total production rate variation cost are the objectives which were presented previously, another objective is minimizing total idle cost, meanwhile two other new objectives regarding minimizing total operator error cost and total tardiness cost are presented for the first time. The total tardiness cost tries to choose a sequence of products that minimizes the tardiness cost for customers with high priority. First, to check the feasibility of the model, GAMS software is used. In this case, GAMS software could not search all of the solution space, so it is tried in two stages and because this problem is NP-hard, particle swarm optimization (PSO) and simulated annealing (SA) algorithms are used. For small sized problems, to compare exact method with proposed algorithms, the problem must be solved using meta-heuristic algorithms in two stages as GAMS software, whereas for large sized problems, the problem can be solved in two ways (one stage and two stages) by using proposed algorithms; the computational results and pairwise comparisons (based on sign test) show GAMS is a proper software to solve small sized problems, whereas for a large sized problem the objective function is better when solved in one stage than two stages; therefore it is proposed to solve the problem in one stage for large sized problems. Also PSO algorithm is better than SA algorithm based on objective function and pairwise comparisons.     

Genetic algorithms for sequencing problems in mixed model assembly lines

Mixed model assembly lines are a type of production line where a variety of product models similar in product characteristics are assembled. The effective utilisation of these lines requires that a schedule for assembling the different products be determined. In this paper, the performance of genetic algorithms for sequencing problems in mixed model assembly lines is investigated. The problem first considered is a comparison between a existing heuristic and the proposed genetic algorithm to get the constant usage of every part used by the line considering variation at multi levels (Number of levels fixed as four. level 1—product, level 2—subassembly, level 3—component, level 4—raw-materials) for various test-bed problems. The algorithms proposed by Miltenburg and Sinnamon hereafter referred to as MS 1992 [IIE Trans. 24 (1992) 121] and the proposed genetic algorithm (GA) applied to mixed model assembly line are compared. Results of evaluation indicate that the GA performs better over MS1992 on 25 of the 40 problems investigated.

The other problem solved is a multiple objective sequencing problem in mixed model assembly lines. Three practically important objectives are minimizing total utility work keeping a constant rate of part-usage, minimizing the variability in parts usage and minimizing total setup cost. In this paper, the performance of the selection mechanisms, the Pareto stratum-niche cubicle and the selection based on scalar fitness function value are compared with respect to the objective of minimising variation in part-usage, minimising total utility work and minimising the setup cost. Results of evaluation indicate that the genetic algorithm that uses the Pareto stratum-niche cubicle performs better than the genetic algorithm with the other selection mechanisms.     

Two-sided assembly line balancing considering the relationships between tasks

Previous studies of the two-sided assembly line balancing problem assumed equal relationships between each two tasks assignable to a side of the line. In practice, however, this relationship may be related to such factors as the distance between the implementation place and the tools required for implementation. We know that the more relationships exist between the tasks assigned to each station, the more efficient will be the assembly line. In this paper, we suggest an index for calculating the value of the relationship between each two tasks, and define a performance criterion called ‘assembly line tasks consistency’ for calculating the average relationship between the tasks assigned to the stations of each solution. We propose a simulated annealing algorithm for solving the two-sided assembly line balancing problem considering the three performance criteria of number of stations, number of mated-stations, and assembly line tasks consistency. Also, the simulated annealing algorithm is modified for solving the two-sided assembly line balancing problem without considering the relationships between tasks. This modification finds five new best solutions for the number of stations performance criterion and ten new best solutions for the number of mated-stations performance criterion for benchmark instances.     

A hybrid genetic algorithm for mixed model assembly line balancing problem with parallel workstations and zoning constraints

In this paper, we propose a hybrid genetic algorithm to solve mixed model assembly line balancing problem of type I (MMALBP-I). There are three objectives to be achieved: to minimize the number of workstations, maximize the workload smoothness between workstations, and maximize the workload smoothness within workstations. The proposed approach is able to address some particular features of the problem such as parallel workstations and zoning constraints. The genetic algorithm may lack the capability of exploring the solution space effectively. We aim to improve its exploring capability by sequentially hybridizing the three well known heuristics, Kilbridge & Wester Heuristic, Phase-I of Moodie & Young Method, and Ranked Positional Weight Technique, with genetic algorithm. The proposed hybrid genetic algorithm is tested on 20 representatives MMALBP-I and the results are compared with those of other algorithms.     

Two-machine robotic cell scheduling problem with sequence-dependent setup times

In this paper, we introduce a new and practical two-machine robotic cell scheduling problem with sequence-dependent setup times (2RCSDST) along with different loading/unloading times for each part. Our objective is to simultaneously determine the sequence of robot moves and the sequence of parts that minimize the total cycle time. The proposed problem is proven to be strongly NP-hard. Using the Gilmore and Gomory (GnG) algorithm, a polynomial-time computable lower bound is provided.