Simple Assembly Line Balancing Problem Research Articles

Optimisation of Simple Assembly Line Balancing Problem Type E: A Systematic Literature Review

Abstract Numerous research studies have focused on the Simple Assembly Line Balancing Problem (SALBP). Although many of these studies have attempted to minimise the number of workstations for a given cycle time (SALBP-1) or min-imise the cycle time for a given number of workstations (SALBP-2), few have focused on the E-type of the SALBP, which is a general NP-hard problem. Therefore, a Systematic Literature Review (SLR) in this area is extremely important. The SALB-E problem involves scheduling a given set of tasks in an orderly sequence of workstations, where task precedence relations are satisfied, and finding the optimal pair of number of workstations and cycle time that maximises line efficiency. The aim of this systematic review was to examine existing research on SALB-E issues and predict future directions for studies on this topic. A systematic methodology was used to review papers published between 1995 and 2023, selected from the Scopus, ScienceDirect, and Google Scholar data-bases. The review showed that future studies should focus on multi- and mixed-model U-shaped and two-sided lines in the SALBP-E. In addition, it may be important to evaluate multiple objective functions rather than just a single one. To solve this problem, it is preferable to develop and refine genetic algorithms and investigate new approaches within the metaheuristic framework.

An exact constraint programming based procedure for the multi-manned assembly line balancing problem

Unlike the Simple Assembly Line Balancing Problem (SALBP), the Multi-manned Assembly Line Balancing Problem (MALBP) allows the assignment of multiple workers at the same station. This study proposes a novel Constraint Programming (CP) model to evaluate the satisfiability of a type-F MALBP. Given a cycle time limit, the number of workers and the number of stations are set as parameters in each iteration. We adopt an exact lexicographical procedure as the solution method for this multi-objective optimization problem, performing a lower-bound search to minimize the number of workers as the primary objective. Such an assumption is common for real-world applications, in which the total cost of a worker is usually several orders of magnitude higher than the cost of a station. When dealing with hard instances, we adopt the task–worker assignment solution for SALBP as input to an auxiliary Mixed-Integer Linear Programming (MILP) model, which provides an initial condition for the task scheduling portion of the CP model. Strong tasks’ scheduling bounds are also provided to tighten the search space, and mathematical similarities with SALBP are exploited to support our solution method. The integrated MILP-CP procedure yielded 126 optimal solutions from a 140-instance dataset, including nine new optimality proofs. Moreover, twelve additional instances were improved compared to the literature, enhancing the solution quality. Considering the best-found primal bounds, the maximum gap for the still-open instances is just 0.32%. These results demonstrated the effectiveness of the proposed procedure in solving MALBP when combined with solid bounds.

An artificial bee colony based-hyper heuristic algorithm with local search for the assembly line balancing problems

PurposeAssembly lines are widely employed in manufacturing processes to produce final products in a flow efficiently. The simple assembly line balancing problem is a basic version of the general problem and has still attracted the attention of researchers. The type-I simple assembly line balancing problems (SALBP-I) aim to minimise the number of workstations on an assembly line by keeping the cycle time constant.Design/methodology/approachThis paper focuses on solving multi-objective SALBP-I problems by utilising an artificial bee colony based-hyper heuristic (ABC-HH) algorithm. The algorithm optimises the efficiency and idleness percentage of the assembly line and concurrently minimises the number of workstations. The proposed ABC-HH algorithm is improved by adding new modifications to each phase of the artificial bee colony framework. Parameter control and calibration are also achieved using the irace method. The proposed model has undergone testing on benchmark problems, and the results obtained have been compared with state-of-the-art algorithms.FindingsThe experimental results of the computational study on the benchmark dataset unequivocally establish the superior performance of the ABC-HH algorithm across 61 problem instances, outperforming the state-of-the-art approach.Originality/valueThis research proposes the ABC-HH algorithm with local search to solve the SALBP-I problems more efficiently.

Assessing by Simulation the Effect of Process Variability in the SALB-1 Problem

The simple assembly line balancing (SALB) problem is a significant challenge faced by industries across various sectors aiming to optimise production line efficiency and resource allocation. One important issue when the decision-maker balances a line is how to keep the cycle time under a given time across all cells, even though there is variability in some parameters. When there are stochastic elements, some approaches use constraint relaxation, intervals for the stochastic parameters, and fuzzy numbers. In this paper, a three-part algorithm is proposed that first solves the balancing problem without considering stochastic parameters; then, using simulation, it measures the effect of some parameters (in this case, the inter-arrival time, processing times, speed of the material handling system which is manually performed by the workers in the cell, and the number of workers who perform the tasks on the machines); finally, the add-on OptQuest in SIMIO solves an optimisation problem to constrain the cycle time using the stochastic parameters as decision variables. A Gearbox instance from literature is solved with 15 tasks and 14 precedence rules to test the proposed approach. The deterministic balancing problem is solved optimally using the open solver GLPK and the Pyomo programming language, and, with simulation, the proposed algorithm keeps the cycle time less than or equal to 70 s in the presence of variability and deterministic inter-arrival time. Meanwhile, with stochastic inter-arrival time, the maximum cell cycle is 72.04 s. The reader can download the source code and the simulation models from the GitHub page of the authors.

An exact method to incorporate ergonomic risks in Assembly Line Balancing Problems

Since ergonomic risks related to the tasks performed by each worker are generally neglected when solving the Simple Assembly Line Balancing Problem (SALBP) or partially treated in post-processing, this paper aims to incorporate ergonomic issues natively in the decision process (ErgoSALBP). For such a problem, we present a novel Mixed-Integer Linear Programming (MILP) model that linearizes and incorporates into the SALBP the Occupational Repetitive Action (OCRA). This well-known method gives ergonomic risk indicators for musculoskeletal disorders. A lexicographical approach to address the problem is proposed, where the minimum number of stations is obtained for SALBP and used as a starting point to solve a type-F ErgoSALBP (feasibility problem) focused on satisfying the maximum ergonomic risk workload. Once the exact solution is found, we establish an objective function to smooth the ergonomic risk distribution among stations. We tested a total of 2160 instances with up to 297 tasks. Our method was able to solve 94% of all instances optimally. The share of solutions found with only green stations (the ideal ergonomic condition) was 87%, surpassing the state of the art. For the instances where the model did not converge to a solution within the time limit, we present a procedure to assess the optimality gap. Furthermore, the model can be embedded as a building block for other assembly line configurations. Finally, the results provide trade-off insights for managers: the average OCRA for the line improves as the cycle time increases, which may positively impact workers’ satisfaction and product quality in the long run.

Analysis of the simple assembly line balancing problem complexity

The simple assembly line balancing problem (SALBP) involves the determination of the assignment of elementary assembly operations to the workstations of the assembly line for the manufacture of a final product, with the objective of maximising assembly efficiency. In addition to its practicality, the SALBP can be considered as an extension of the bin packing problem (BPP) to account for the precedence relations between items. These constraints introduce an ordering component to the problem, which increases the complexity of SALBP resolution. However, previous studies indicated that precedence constraints do not play an important role in the capacity of state-of-the-art procedures to solve benchmark instances to optimality.In this study, we analysed the influences of different features of an SALBP instance on the performance of state-of-the-art solution methods for the abovementioned problem. First, we provide an alternative proof of complexity for the SALBP that uses precedence constraints to demonstrate its non-deterministic polynomial time (NP)-complete status, followed by a new set of benchmark instances directed towards an empirical analysis of the different features of SALBP instances. The experimental results revealed that the packing features of the SALBP are a major source of the perceived difficulty for any instance; however, precedence constraints play a role in the performance of these solution procedures. Specifically, the number of precedence constraints plays an important role in the results obtained from state-of-the-art methods. In addition to the analysis, certain issues that were identified in the publicly available implementations of the state-of-the-art method for resolving this problem were addressed in this study.

Assembly and Production Line Designing, Balancing and Scheduling with Inaccurate Data: A Survey and Perspectives

Assembly lines (conveyors) are traditional means of large-scale and mass-scale productions. An assembly line balancing problem is needed for optimizing the assembly process by configuring and designing an assembly line for the same or similar types of final products. This problem consists of designing the assembly line and distributing the total workload for manufacturing each unit of the fixed product to be assembled among the ordered workstations along the constructed assembly line. The assembly line balancing research is focused mainly on simple assembly line balancing problems, which are restricted by a set of conditions making a considered assembly line ideal for research. A lot of published research has been carried out in order to describe and solve (usually heuristically) more realistic generalized assembly line balancing problems. Assembly line designing, balancing and scheduling problems with not deterministic (stochastic, fuzzy or uncertain) parameters have been investigated in many published research works. This paper is about the design and optimization methods for assembly and disassembly lines. We survey the recent developments for designing, balancing and scheduling assembly (disassembly) lines. New formulations of simple assembly line balancing problems are presented in order to take into account modifications and uncertainties characterized by real assembly productions.

A New Multi-Objective Genetic Algorithm for Assembly Line Balancing

Abstract The aim of this work is to enable a step towards a self-adapting digital toolset for manufacturing planning focusing on minimally constrained assembly line balancing. The approach includes the simultaneous definition of the optimum number of workstations, the optimum cycle time and the assignment of tasks to workstations. A bespoke genetic algorithm (GENALSAS) is proposed and demonstrated which focuses on examining the simple assembly line balancing problem (SALBP). The proposed genetic algorithm (GA) has been shown to consistently deliver detailed production plans for SALBP problem forms with minimum inputs. Neither the number of workstations nor the system cycle time is assumed/fixed as in previous work in the field. The work simultaneously attains better performing solutions compared with previous studies both in terms of time to converge and the quality of the solution.

Stability factor for robust balancing of simple assembly lines under uncertainty

This paper deals with an optimization problem, which arises when a new simple assembly line has to be designed subject to a fixed number of available workstations, cycle time constraint, and precedence relations between necessary assembly tasks. The studied problem consists in assigning a given set of tasks to workstations so as to find the most robust line configuration, which can withstand processing time uncertainty as much as possible. The line robustness is measured by a new indicator, called stability factor . In this work, the studied problem is proven to be strongly NP-hard, upper bounds are proposed, and the relation of the stability factor with another robustness indicator, known as stability radius , is investigated. A mixed-integer linear program (MILP) is proposed for maximizing the stability factor in the general case, and an alternative formulation is also derived when uncertainty originates in workstations only. Computational results are reported on a collection of instances derived from classic benchmark data used in the literature for the Simple Assembly Line Balancing Problem (SALBP).

Variable-depth local search heuristic for assembly line balancing problems

ABSTRACT Assembly lines are production flow systems wherein activities are organised around a line consisting of various workstations through which the product flows. At each station, the product is assembled through a subset of operations. The assembly line balancing problem (ALBP) consists of allocating operations between stations to maximise the system efficiency. In this study, a variable-depth local search algorithm is proposed for solving simple assembly line balancing problems (SALBPs), which are the most widely studied versions of the ALBP. Although the state-of-the-art techniques for solving the SALBP consist of exact enumeration-based methods or heuristics, this paper proposes a local search-based heuristic using variable-length sequences that allow the solution space to be efficiently explored. The proposed algorithm improves the best solution known for multiple instances reported in the literature, indicating that its efficiency is comparable to those of the state-of-the-art method for solving the SALBP. Moreover, the characteristics of the instances for which the proposed procedure provides a better solution than previously reported construction procedures are investigated.

A survey on Benders Decomposition methods applied to Assembly Line Balancing Problems

The assembly line balancing problem (ALBP) assigns tasks to (work)stations to manufacture products. It divides the station loads as evenly as possible since any bottleneck defines the production rate of a flow shop system. The sum of task processing times represents the station load in the classical Simple Assembly Line Balancing Problem (SALBP). Thus, the most loaded station imposes a lower bound on the line's cycle time. However, the simple sum of processing times is only valid under several assumptions. For instance, more realistic ALBPs may contain stochastic data, multiple workers per station, or depend on the production sequence. Hence, the station load computation involves further scheduling decisions for this latter class of problems. In order to tackle these ALBPs with practical extensions, several literature contributions have recently employed Benders decomposition (BD) algorithms. The BD structure allows a division of the formulation into two or more levels. More specifically, this framework permits the decoupling of task assignment decisions and cycle time assessments. In the field of ALBPs, various stochastic and sequence-dependent problems have successfully applied this approach. This paper provides a literature review of these methods, the different formulations, implementation details, and improvement ideas.

An assembling line balancing problem: Lead-acid batteries case study

This paper presents an application of a simple assembly line balancing problem (SALB) in a lead-acid battery factory in Colombia. SALBP-1 was the selected approach to carry out the research. In this type of SALBP, there is a fixed cycle time, and the purpose is to minimize the number of workstations. To this aim, a process characterization was conducted, and a mixed-integer linear model was formulated. Then, an exact solution was found using GAMS® software. The main findings included reducing the number of workstations from 10 to 4. This change impacted the line efficiency and the idle time achieving a 150% and a 94% improvement, respectively. This research demonstrated the impact of dealing with SALBP on production companies over the line performance in terms of idle time minimization and productivity increase.

Approximation algorithms for simple assembly line balancing problems

Approximation algorithms for simple assembly line balancing problems

A mixed-integer linear programming formulation for assembly line balancing problem with human-robot shared tasks

Human-robot collaboration (HRC) has arisen as a promising technology to improve the productivity of assembly processes. This paper discusses an assembly line balancing problem (ALBP) where manual, robotic, or HRC operations may be considered decision alternatives. Each assembly process task may be operated either by a human operator, a robot operator, or an HRC. This possibility of shared functions between humans and robots may result in a hybrid manual-robotic assembly line. This problem’s mathematical model is developed based on the simple ALBP and modifying the idea of two-sided ALBP, with additional aspects related to resource alternatives of human, robot, or HRC, and robot’s tool-type for the operations. The problem is formulated analytically in a mixed-integer linear programming model with a cost-oriented objective function. The exact method can be applied to obtain an optimal solution.

Assembly line balancing with parallel workstations

ABSTRACT The simple assembly line balancing problem (SALBP) considers work division among different workstations of a serially arranged assembly process to maximise its efficiency under workload (cumulative) and technological (precedence) constraints. In this work, we consider a variant of the SALBP which allows parallel workstations. To study the effect of parallel stations, we propose a new problem (the parallel station assembly line balancing problem or PSALBP) in which the objective is to minimise the number of parallel stations required to obtain the maximum theoretical efficiency of the assembly process. We study the complexity of the problem and identify a polynomially solvable case. This result is then used as a building block for the development of a heuristic solution procedure. Finally, we carry out a computational experiment to identify the characteristics of assembly lines that may benefit from station paralleling and to evaluate the performance of the proposed heuristic.

Heuristics based on Slope Indices for Simple Type I Assembly Line Balancing Problems and Analyzing for a Few Performance Measures

In any mechanical manufacturing industry, raw materials’ cost is the major cost component which constitutes up to 40% of the total cost. Other major cost is the processing cost to convert the raw materials in to a finished product that takes place in an assembly line. Optimizing the available resources including the number of work benches and operators is important to meet the timely delivery of finished goods with optimum cost. In an assembly line, the manufacturing processes on any material are sub-divided into many tasks which may include sub-assemblies and machining. These tasks are carried out in several work stations which are responsible for a single or a set of operations carried out on the materials. Assembly lines need to be balanced to have even distribution of work for both men and machines. Type 1 simple assembly line balancing problems (SALBP-1) refer to minimization of number of work stations by keeping the cycle time constant. If the number of work stations is fixed, minimizing the cycle time falls under Type II problems. To solve these types of NP-hard problems, heuristics are used by researchers. The heuristics use different parameters to assign a particular task to a work station. This paper proposes and analyses a few heuristics that can be used to solve SALBP-1. They use slope indices to order the jobs and assign them to different work stations. The slope indices are the ratios of any two parameters taken suitably

Problema de balanceo de una línea del tipo SALBP: caso de una línea de confección de prendas

This paper presents a SALBP ( simple assembly line balancing problem ) problem, where n tasks are performed on manual workstations, located along a production line. The problem is studied using the variations SALBP-1, SALBP-2 and SALBP-F; the latter is treated as a bi-objective model, in order to evaluate possible feasible solutions of the combination of stations and process times. The three variations are solved with the use of heuristic methods and analytical methods, to conclude on the complexity of the problem and the efficiency of the proposed solutions.

Simple assembly line balancing problem of Type 1 with grey demand and grey task durations

PurposeThe purpose of this paper is to present a mixed integer programming model for simple assembly line balancing problems (SALBP) with Type 1 when the annual demand and task durations are uncertain and encoded with grey numbers.Design/methodology/approachGrey theory and grey numbers are used for illustrating the uncertainty of parameters in an SALBP, where the objective is to minimize the total number of workstations. The paper proposes a 0-1 mathematical model for SALBP of Type 1 with grey demand and grey task durations.FindingsThe uncertainty of the demand and task durations are encoded with grey numbers and a well-known 0-1 mathematical model for SALBP of Type 1 is modified to find the minimum number of workstations in order to meet both the lower and upper bounds of the uncertain demand. The results obtained from the proposed mathematical model show a task-workstation assignment that does not distribute precedence relations among tasks and workstations and the sum of task durations in each single workstation is less than or equal to the grey cycle time.Originality/valueThe grey theory and grey numbers have not been previously used to identify uncertainties in assembly line balancing problems. Therefore, this study provides an important contribution to the literature.

Estimating the Stability Radius of an Optimal Solution to the Simple Assembly Line Balancing Problem

The simple assembly line balancing problem (SALBP) is considered. We describe the special class of problems with an infinitely large stability radius of the optimal balance. For other tasks we received the lower and the upper reachable estimates of the stability radius of optimal balances in the case of an independent perturbation of the parameters of the problem.

Assembly Line Balancing Based on Beam Ant Colony Optimisation

We use a hybrid approach which executes ant colony algorithm in combination with beam search (ACO-BS) to solve the Simple Assembly Line Balancing Problem (SALBP). The objective is to minimise the number of workstations for a given fixed cycle time, in order to improve the solution quality and speed up the searching process. The results of 269 benchmark instances show that 95.54% of the problems can reach their optimal solutions within 360 CPU time seconds. In addition, we choose order strength and time variability as indicators to measure the complexity of the SALBP instances and then generate 27 instances with a total of 400 tasks (the problem size being much larger than that of the largest benchmark instance) randomly, with the order strength at 0.2, 0.6 and 0.9 three levels and the time variability at 5-15, 65-75, and 135-145 levels. However, the processing times are generated following a unimodal or a bimodal distribution. The comparison results with solutions obtained by priority rule show that ACO-BS makes significant improvements on the quality of the best solutions.