An enumeration procedure for the assembly line balancing problem based on branching by non-decreasing idle time

In this article, we present a new exact algorithm for solving the simple assembly line balancing problem given a determined cycle time (SALBP-1). The algorithm is a station-oriented bidirectional branch-and-bound procedure based on a new enumeration strategy that explores the feasible solutions tree in a non-decreasing idle time order. The procedure uses several well-known lower bounds, dominance rules and a new logical test based on the assimilation of the feasibility problem for a given cycle time and number of stations (SALBP-F) to a maximum-flow problem.     

Heuristics and lower bounds for the simple assembly line balancing problem type 1: Overview,computational tests and improvements

Assigning tasks to work stations is an essential problem which needs to be addressed in an assembly line design. The most basic model is called simple assembly line balancing problem type 1 (SALBP-1). We provide a survey on 12 heuristics and 9 lower bounds for this model and test them on a traditional and a lately-published benchmark dataset. The present paper focuses on algorithms published before 2011.     

Simple and U-type assembly line balancing problems with a learning effect

In this paper, we introduced learning effect into assembly line balancing problems. In many realistic settings, the produced worker(s) (or machine(s)) develops continuously by repeated the same or similar activities. Therefore, the production time of product shortens if it is processed later. We show that polynomial solutions can be obtained for both simple assembly line balancing problem (SALBP) and U-type line balancing problem (ULBP) with learning effect.     

An imperialist competitive algorithm for multi-objective U-type assembly line design

Many assembly lines are now being designed as U-type assembly lines rather than straight lines because of the pressure of the just-in-time (JIT) manufacturing concept. Since any type of an assembly line balancing problem is known to be NP-hard, there has been a growing tendency toward using evolutionary algorithms to solve such a hard problem. This paper proposes a new population-based evolutionary algorithm, namely imperialist competitive algorithm (ICA) inspired by the process of socio-political evolution, to address the multi-objective U-type assembly line balancing problem (UALBP). Two considered objectives are to minimize the line efficiency and minimize the variation of workload. Furthermore, the Taguchi design is applied to tune the effective parameters of the proposed ICA. To demonstrate the efficiency of the proposed algorithm, the associated results are compared against an efficient genetic algorithm (GA) in the literature over a large group of benchmarks taken from the literature. The computational results show that the proposed ICA outperforms GA.     

Rules-based heuristic approach for the U-shaped assembly line balancing problem

The type-2 U-shaped assembly line balancing problem is important for many just-in-time manufactures, but an efficient algorithm is not available at present. Thus, in this study, a novel heuristic approach based on multiple rules and an integer programming model is proposed to address this problem. In the proposed approach, three rules are systematically grouped together, i.e., task selection, task assignment, and task exchange rules. The sufficient conditions for implementing the exchange rules are proposed and proved. Thirteen small or medium scale benchmark issues comprising 63 instances were solved, where the computational results demonstrate the efficiency and effectiveness of the proposed method compared with integer programming. The computational results obtained for 18 examples comprising 121 instances demonstrate that the task exchange rules significantly improve the computational accuracy compared with the traditional heuristic. Finally, 30 new standard instances produced by a systematic data generation process were also solved effectively by the proposed approach. The proposed heuristic approach with multiple rules can provide a theoretical basis for other local search algorithms, especially for addressing issues such as the U-Shaped assembly line balancing problem.     

A classification of assembly line balancing problems

Assembly lines are special flow-line production systems which are of great importance in the industrial production of high quantity standardized commodities. Recently, assembly lines even gained importance in low volume production of customized products (mass-customization). Due to high capital requirements when installing or redesigning a line, its configuration planning is of great relevance for practitioners. Accordingly, this attracted attention of many researchers, who tried to support real-world configuration planning by suited optimization models (assembly line balancing problems). In spite of the enormous academic effort in assembly line balancing, there remains a considerable gap between requirements of real configuration problems and the status of research. To ease communication between researchers and practitioners, we provide a classification scheme of assembly line balancing. This is a valuable step in identifying remaining research challenges which might contribute to closing the gap.     

Simple heuristics for the assembly line worker assignment and balancing problem

We propose simple heuristics for the assembly line worker assignment and balancing problem. This problem typically occurs in assembly lines in sheltered work centers for the disabled. Different from the well-known simple assembly line balancing problem, the task execution times vary according to the assigned worker. We develop a constructive heuristic framework based on task and worker priority rules defining the order in which the tasks and workers should be assigned to the workstations. We present a number of such rules and compare their performance across three possible uses: as a stand-alone method, as an initial solution generator for meta-heuristics, and as a decoder for a hybrid genetic algorithm. Our results show that the heuristics are fast, they obtain good results as a stand-alone method and are efficient when used as a initial solution generator or as a solution decoder within more elaborate approaches.     

A dynamic programming based heuristic for the assembly line balancing problem

The simple assembly line balancing problem is the simplification of a real problem associated to the assignment of the elementary tasks required for assembly of a product in an assembly line. This problem has been extensively studied in the literature for more than half a century. The present work proposes a new procedure to solve the problem we call Bounded Dynamic Programming. This use of the term Bounded is associated not only with the use of bounds to reduce the state space but also to the reduction of such space based on heuristics. This procedure is capable of obtaining an optimal solution rate of 267 out of 269 instances, which have been used in previous works, thus obtaining the best-known performance for the problem. These results are an improvement from any previous procedure found in the literature even when using smaller computing times.     

Assembly line balancing as generalized bin packing

Bin packing heuristics are generalized and adapted to solve the assembly line balancing problem. Worst-case analysis is provided. The results are compared to those for a resource constrained scheduling problem considered by Garey, Graham, Johnson and Yao.     

A new diversity induction mechanism for a multi-objective ant colony algorithm to solve a real-world time and space assembly line balancing problem

Time and space assembly line balancing considers realistic multi-objective versions of the classical assembly line balancing industrial problems. It involves the joint optimisation of conflicting criteria such as the cycle time, the number of stations, and/or the area of these stations. The different problems included in this area also inherit the precedence constraints and the cycle time limitations from assembly line balancing problems. The presence of these hard constraints and their multi-criteria nature make these problems very hard to solve. Multi-objective constructive metaheuristics (in particular, multi-objective ant colony optimisation) have demonstrated to be suitable approaches to solve time and space assembly line balancing problems. The aim of this contribution is to present a new mechanism to induce diversity in an existing multi-objective ant colony optimisation algorithm for the 1/3 variant of the time and space assembly line balancing problem. This variant is quite realistic in the automative industry as it involves the joint minimisation of the number and the area of the stations given a fixed cycle time limit. The performance of our proposal is validated considering ten real-like problem instances. Moreover, the diversity induction mechanism is also tested on a real-world instance from the Nissan plant in Barcelona (Spain).     

Balancing stochastic two-sided assembly lines: A chance-constrained,piecewise-linear,mixed integer program and a simulated annealing algorithm

Two-sided assembly lines are often designed to produce large-sized products, such as automobiles, trucks and buses. In this type of a production line, both left-side and right-side of the line are used in parallel. In all studies on two-sided assembly lines, the task times are assumed to be deterministic. However, in real life applications, especially in manual assembly lines, the tasks may have varying execution times defined as a probability distribution. The task time variation may result from machine breakdowns, loss of motivation, lack of training, non-qualified operators, complex tasks, environment, etc. In this paper, the problem of balancing two-sided assembly lines with stochastic task times (STALBP) is considered. A chance-constrained, piecewise-linear, mixed integer program (CPMIP) is proposed to model and solve the problem. As a solution approach a simulated annealing (SA) algorithm is proposed. To assess the effectiveness of CPMIP and SA algorithm, a set of test problems are solved. Finally, computational results indicating the effectiveness of CPMIP and SA algorithm are reported.     

Absalom: Balancing assembly lines with assignment restrictions

Assembly line balancing problems (ALBPs) arise whenever an assembly line is configured, redesigned or adjusted. An ALBP consists of distributing the total workload for manufacturing products among the work stations along the line. On the one hand, research has focussed on developing effective and fast solution methods for exactly solving the simple assembly line balancing problem (SALBP). On the other hand, a number of real-world extensions of SALBP have been introduced but solved with straight-forward and simple heuristics in many cases. Therefore, there is a lack of procedures for exactly solving such generalized ALBP.In this paper, we show how to extend the well-known solution procedure Salome [Scholl, A., Klein, R., 1997. Salome: A bidirectional branch-and-bound procedure for assembly line balancing. Informs J. Comput. 9 319–334], which is able to solve even large SALBP instances in a very effective manner, to a problem extension with different types of assignment restrictions (called ARALBP). The extended procedure, referred to as Absalom, employs a favorable branching scheme, an arsenal of bounding rules and a variety of logical tests using ideas from constraint programming.Computational experiments show that Absalom is a very promising exact solution approach although the additional assignment restrictions complicate the problem considerably and necessitate a relaxation of some components of Salome.     

Binary fuzzy goal programming approach to single model straight and U-shaped assembly line balancing

Assembly line balancing generally requires a set of acceptable solutions to the several conflicting objectives. In this study, a binary fuzzy goal programming approach is applied to assembly line balancing. Models for balancing straight and U-shaped assembly lines with fuzzy goals (the number of workstations and cycle time goals) are proposed. The binary fuzzy goal programming models are solved using the methodology introduced by Chang [Chang, C.T., 2007. Binary fuzzy goal programming. European Journal of Operational Research 180 (1), 29–37]. An illustrative example is presented to demonstrate the validity of the proposed models and to compare the performance of straight and U-shaped line configurations.     

A station-oriented enumerative algorithm for two-sided assembly line balancing

In this paper, a station-oriented enumerative algorithm for two-sided assembly lines balancing (TALB) is proposed. First, the time transfer function is defined and combined with the precedence relation to compute the earliest and the latest start time of tasks. With the direction and cycle time constraints, a station-oriented procedure based on the start time is designed to assign tasks, starting from the left station to the rightstation of the position. Some unsuitable position assignments would be finally removed by checking the precedence constraints among the assigned tasks. The proposed algorithm is integrated with the Hoffmann heuristic to develop a system for solving TALB problems. The test is performed on the well-known benchmark set of problem instances. Experimental results demonstrate that the proposed procedure is efficient.     

An application of the branch,bound, and remember algorithm to a new simple assembly line balancing dataset

The simple assembly line balancing problem (SALBP) is a well-studied NP-complete problem for which a new problem database of generated instances was published in 2013. This paper describes the application of a branch, bound, and remember (BB&R) algorithm using the cyclic best-first search strategy to this new database to produce provably exact solutions for 86% of the unsolved problems in this database. A new backtracking rule to save memory is employed to allow the BB&R algorithm to solve many of the largest problems in the database.     

Balancing two-sided U-type assembly lines using modified particle swarm optimization algorithm

In this paper, a new two-sided U-type assembly line balancing (TUALB) procedure and a new algorithm based on the particle swarm optimization algorithm to solve the TUALB problem are proposed. The proposed approach minimizes the number of stations for a given cycle time as the primary objective and it minimizes the number of positions as a secondary objective. The proposed approach is illustrated with an example problem. In order to evaluate the efficiency of the proposed algorithm, the test problems available in the literature are used. The experimental results show that the proposed approach performs well.     

A shortest route formulation of simple U-type assembly line balancing problem

In this paper, a shortest route formulation of simple U-type assembly line balancing (SULB) problem is presented and illustrated on a numerical example. This model is based on the shortest route model developed in [Manage. Sci. 11 (2) (1964) 308.] for the traditional single model assembly line balancing problem.     

A survey on problems and methods in generalized assembly line balancing

Assembly lines are traditional and still attractive means of mass and large-scale series production. Since the early times of Henry Ford several developments took place which changed assembly lines from strictly paced and straight single-model lines to more flexible systems including, among others, lines with parallel work stations or tasks, customer-oriented mixed-model and multi-model lines, U-shaped lines as well as unpaced lines with intermediate buffers.In any case, an important decision problem, called assembly line balancing problem, arises and has to be solved when (re-) configuring an assembly line. It consists of distributing the total workload for manufacturing any unit of the product to be assembled among the work stations along the line.Assembly line balancing research has traditionally focused on the simple assembly line balancing problem (SALBP) which has some restricting assumptions. Recently, a lot of research work has been done in order to describe and solve more realistic generalized problems (GALBP). In this paper, we survey the developments in GALBP research.     

An optimal procedure for the single-model deterministic assembly line balancing problem

The purpose of this paper is to develop an optimal solution method for the single-model assembly line balancing problem with deterministic work element durations. The procedure we present is a branch-and-bound algorithm which concentrates on the special structure of the problem. The method is equipped with dominance rules, bounding arguments and reliable branching heuristics. Computational results are given, indicating the method to be more than competitive to ones previously reported.     

Branch and bound algorithm for a transfer line design problem: Stations with sequentially activated multi-spindle heads

In this paper, a new transfer line balancing problem is considered. The main difference from the simple assembly line balancing problem is that the operations are grouped into blocks (batches). All the operations of the same block are carried out simultaneously by one piece of equipment (multi-spindle head). Nevertheless, the blocks assigned to the same workstation are executed in series. The line cost consists of the sum of block and workstation costs. At the considered line design stage, the set of all available blocks is given. The aim is to find a subset from the given set of available blocks and to find a partition of this subset to workstations such that each operation is executed once and the line cost is minimal while all the precedence, cycle time, and compatibility (operation inclusion and block exclusion) constraints are respected. A new lower bound based on solving a special set partitioning problem is presented and a branch and bound algorithm is developed. The experimental results prove the quality of the lower bound and applicability of the suggested branch and bound algorithm for medium sized industrial cases.