Monolithic vs. hierarchical balancing and scheduling of a flexible assembly line

A monolithic and a hierarchical approach are presented for balancing and scheduling of a flexible assembly line (FAL). The system is made up of a set of assembly stations in series, each with limited work space and is capable of simultaneously producing a mix of product types. The objective is to determine an assignment of assembly tasks to stations and an assembly schedule for all products so as to complete the products in minimum time. In the monolithic approach balancing and scheduling decisions are made simultaneously. In the hierarchical approach, however, first the station workloads are balanced, and then detailed assembly schedule is determined for prefixed task assignments and assembly routes by solving a permutation flowshop problem. Mixed integer programming formulations are presented for the two approaches. Numerical examples are included to illustrate and compare the approaches and some computational results are reported.     

A genetic algorithm for robotic assembly line balancing

Flexibility and automation in assembly lines can be achieved by the use of robots. The robotic assembly line balancing (RALB) problem is defined for robotic assembly line, where different robots may be assigned to the assembly tasks, and each robot needs different assembly times to perform a given task, because of its capabilities and specialization. The solution to the RALB problem includes an attempt for optimal assignment of robots to line stations and a balanced distribution of work between different stations. It aims at maximizing the production rate of the line. A genetic algorithm (GA) is used to find a solution to this problem. Two different procedures for adapting the GA to the RALB problem, by assigning robots with different capabilities to workstations are introduced: a recursive assignment procedure and a consecutive assignment procedure. The results of the GA are improved by a local optimization (hill climbing) work-piece exchange procedure. Tests conducted on a set of randomly generated problems, show that the Consecutive Assignment procedure achieves, in general, better solution quality (measured by average cycle time). Further tests are conducted to determine the best combination of parameters for the GA procedure. Comparison of the GA algorithm results with a truncated Branch and Bound algorithm for the RALB problem, demonstrates that the GA gives consistently better results.     

A lexicographic approach to bi-objective loading of a flexible assembly system

The paper presents a bi-objective integer program and an approximative lexicographic approach for a bicriterion loading and routing problem in a flexible assembly system. The problem objective is to determine an allocation of tasks among the assembly stations for a set of products so as to balance station workloads and minimize total interstation transfer time. In the approach proposed, first the station workloads are balanced using a linear relaxation-based heuristic and then assembly routes are selected based on a network flow model. An illustrative example is provided and some results of computational experiments are reported.     

混合型装配线平衡问题求解方法研究

对混合型装配线平衡问题进行了描述和数学建模,提出一种启发式求解算法,求解目标是最小化工作站数目.为进一步优化求解结果,对启发式算法求解的结果进行仿真研究,分析各工作站的工作率、等待率和阻塞率,并以此为依据调整部分作业任务的分配,允许不同品种产品的相同作业任务安排在不同的工作站中,以对求解结果进行修正,进一步均衡各工作站的作业量.该求解方法既简化了求解过程,又兼顾到了系统的瞬时特性和作业任务的不可拆分性对求解结果的影响,实例分析验证了方法的有效性.     

On a learning precedence graph concept for the automotive industry

Assembly line balancing problems (ALBP) consist in assigning the total workload for manufacturing a product to stations of an assembly line as typically applied in automotive industry. The assignment of tasks to stations is due to restrictions which can be expressed in a precedence graph. However, (automotive) manufacturers usually do not have sufficient information on their precedence graphs. As a consequence, the elaborate solution procedures for different versions of ALBP developed by more than 50 years of intensive research are often not applicable in practice.Unfortunately, the known approaches for precedence graph generation are not suitable for the conditions in the automotive industry. Therefore, we describe a new graph generation approach that is based on learning from past feasible production sequences and forms a sufficient precedence graph that guarantees feasible line balances. Computational experiments indicate that the proposed procedure is able to approximate the real precedence graph sufficiently well to detect optimal or nearly optimal solutions for a well-known benchmark data set. Even for additional large instances with up to 1,000 tasks, considerable improvements of line balances are possible. Thus, the new approach seems to be a major step to close the gap between theoretical line balancing research and practice of assembly line planning.     

Maximizing the production rate in simple assembly line balancing — A branch and bound procedure

In this paper, a branch and bound procedure for the Simple Assembly Line Balancing Problem Type 2 (SALBP-2) is described. This NP-hard problem consists of assigning tasks to a given number of work stations of a paced assembly line so that the production rate is maximized. Besides, possible precedence constraints between the tasks have to be considered. Existing solution procedures for SALBP-2 are mainly based on repeatedly solving instances of the closely related SALBP-1, which is to minimize the number of stations for a given production rate. The proposed branch and bound procedure directly solves SALBP-2 by using a new enumeration technique, the Local Lower Bound Method, which is complemented by a number of bounding and dominance rules. Computational results indicate that the new procedure is very efficient.     

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.     

A heuristic multi-start decomposition approach for optimal design of serial machining lines

We study an optimal design problem for serial machining lines. Such lines consist of a sequence of stations. At every station, the operations to manufacture a product are grouped into blocks. The operations within each block are performed simultaneously by the same spindle head and the blocks of the same station are executed sequentially. The inclusion and exclusion constraints for combining operations into blocks and stations as well as the precedence constraints on the set of operations are given. The problem is to group the operations into blocks and stations minimizing the total line cost. A feasible solution must respect the given cycle time and all given constraints. In this paper, a heuristic multi-start decomposition approach is proposed. It utilizes a decomposition of the initial problem into several sub-problems on the basis of a heuristic solution. Then each obtained sub-problem is solved by an exact algorithm. This procedure is repeated many times, each time it starts with a new heuristic solution. Computational tests show that the proposed approach outperforms simple heuristic algorithms for large-scale problems.     

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.     

Cost-oriented assembly line balancing: Model formulations,solution difficulty,upper and lower bounds

This paper deals with cost-oriented assembly line balancing. First we focus on the special objective function and a formal problem statement. Then we concentrate on general model formulations that can be solved by standard optimisation tools and introduce several improvements to existent models. These models are designed for either general branch-and-bound techniques with LP-relaxation or general implicit enumeration techniques. Further we discuss the solution difficulty of the problem and show that the “maximally-loaded-station-rule” has to be replaced by the “two-stations-rule”. Compared to the time-oriented version, this causes an enormous increase in solution difficulty. We introduce improved and new bounds for the number of stations and for the relevant costs per product unit. These are used in the general model formulations as well as in specially designed optimisation methods. Finally we give a brief overview of these specially designed methods that are discussed in detail in Amen (2000a,b, 2001).     

An Operational Strategy for Throughput Maximization and Bottleneck Control in an Assembly Line System: By Selection of the Processing Rates

In this paper, an optimal operational strategy is developed to optimize the system utilization while controlling the bottleneck problem in a finite capacity integrated assembly line system (consisting of a set of tandem workstations, a set of inspection stations, a loading station and an unloading station, linked by a set of transporter stations). To develop the proposed operational strategy, a stochastic optimization model is developed for selecting the optimal processing rates of the workstations and the transporter stations, such that the total throughput rate from the system is maximized while the resulting probability of finding either a workstation or a transporter station blocked is sufficiently close to zero.     

Improving the computational efficiency in a global formulation (GLIDE) for interactive multiobjective optimization

In this paper, we present a new general formulation for multiobjective optimization that can accommodate several interactive methods of different types (regarding various types of preference information required from the decision maker). This formulation provides a comfortable implementation framework for a general interactive system and allows the decision maker to conveniently apply several interactive methods in one solution process. In other words, the decision maker can at each iteration of the solution process choose how to give preference information to direct the interactive solution process, and the formulation enables changing the type of preferences, that is, the method used, whenever desired. The first general formulation, GLIDE, included eight interactive methods utilizing four types of preferences. Here we present an improved version where we pay special attention to the computational efficiency (especially significant for large and complex problems), by eliminating some constraints and parameters of the original formulation. To be more specific, we propose two new formulations, depending on whether the multiobjective optimization problem to be considered is differentiable or not. Some computational tests are reported showing improvements in all cases. The generality of the new improved formulations is supported by the fact that they can accommodate six interactive methods more, that is, a total of fourteen interactive methods, just by adjusting parameter values.     

R-SALSA: A branch,bound, and remember algorithm for the workload smoothing problem on simple assembly lines

We consider a simple assembly line balancing problem with given cycle time and number of stations. A quadratic objective function based on a so-called smoothness index SX levels the workloads of the stations. For this problem, called SALBP-SX, only a few solution procedures have been proposed in literature so far. In this paper, we extend and improve the branch-and-bound procedure SALSA (Simple Assembly Line Smoothing Algorithm) of Walter et al. (2021) to a bidirectional branch, bound, and remember algorithm called R-SALSA (R for remember). Like SALSA, it is based on a dynamic programming scheme which pre-determines potential workloads of the stations and provides a construction plan for possible station loads. This scheme is extended by the new concept of supporters and preventers which significantly enhances branching, bounding, and logical tests. Furthermore, a tailored heuristic that searches for improved initial solutions, a bidirectional branching scheme and additional dominance rules are integrated. In extensive computational experiments, we find out that our new procedure clearly outperforms all former exact solution procedures on benchmark data sets with up to 1000 tasks.     

Finding and identifying optimal inventory levels for systems with common components

In this article, we consider the problem of finding the optimal inventory level for components in an assembly system where multiple products share common components in the presence of random demand. Previously, solution procedures that identify the optimal inventory levels for components in a component commonality problem have been considered for two product or one common component systems. We will here extend this to a three products system considering any number of common components. The inventory problem considered is modeled as a two stage stochastic recourse problem where the first stage is to set the inventory levels to maximize expected profit while the second stage is to allocate components to products after observing demand. Our main contribution, and the main focus of this paper, is the outline of a procedure that finds the gradient for the stochastic problem, such that an optimal solution can be identified and a gradient based search method can be used to find the optimal solution.     

Covering and connectivity constraints in loop-based formulation of material flow network design in facility layout

The shortest loop covering at least one edge of each workcenter in a manufacturing facility layout is an instance of the generalized traveling salesman problem. The optimal solution to this problem is a promising design for non-vehicle-based material handling, typical of most types of conveyors and power-and-free systems, where the length of the path is the main driver of the total investment costs. The loop formulation is usually embedded within a larger problem of the concurrent design of the loop and the input/output stations for vehicle-based material handling typical of automatically guided vehicles and autonomous delivery robots. In these systems, it is not the length, but the total flow of the loaded and empty vehicles that drives the objective function. It has been shown that the shortest loop provides an effective heuristic scheme to achieve prosperous and robust solutions for the concurrent design of the loop and input/output stations. We review and compare covering constraints formulations, provide new insight into connectivity constraints, improve the model formulation and its solution procedure, and report computational results.     

Shortest-route formulation of mixed-model assembly line balancing problem

A shortest-route formulation of the mixed-model assembly line balancing problem is presented. Common tasks across models are assumed to exist and these tasks are performed in the same stations. The formulation is based on an algorithm which solves the single-model version of the problem. The mixed-model system is transformed into a single-model system with a combined precedence diagram. The model is capable of considering any constraint that can be expressed as a function of task assignments.     

Pattern Based Vocabulary Building for Effectively Sequencing Mixed-Model Assembly Lines

In this paper, the problem of sequencing mixed-model assembly lines in case of fixed rate launching and closed stations is considered. The problem consists of finding an intermixed sequence of different models of a basic product, which are jointly produced on an assembly line, such that customer demands are fulfilled and total work overload is minimized. For solving this problem an informed tabu search procedure with a pattern based vocabulary building strategy is developed. Computational tests demonstrate that considerable improvements are obtained by comparison to methods which do not incorporate such an approach.     

A scatter search based hyper-heuristic for sequencing a mixed-model assembly line

We address a mixed-model assembly-line sequencing problem with work overload minimization criteria. We consider time windows in work stations of the assembly line (closed stations) and different versions of a product to be assembled in the line, which require different processing time according to the work required in each work station. In a paced assembly line, products are feeded in the line at a predetermined constant rate (cycle time). Then, if many products with processing time greater than cycle time are feeded consecutively, work overload can be produced when the worker has insufficient time to finish his/her job. We propose a scatter search based hyper-heuristic for this NP-hard problem. In the low-level, the procedure makes use of priority rules through a constructive procedure. Computational experiments over a wide range of instances from the literature show the effectiveness of the proposed hyper-heuristics when compared to existing heuristics. The relevance of the priority rules was evaluated as well.     

Work allocation to stations with varying learning slopes and without buffers

In this paper, we address the problem of allocating the work elements, belonging to the products of a lot, to the stations of an assembly line so as to minimize the makespan. The lots that are processed on the assembly line are characterized by a low overall demand for each product. There is no buffer permitted in between the stations, and the line operates under learning. In particular, the stations’ learning slopes are assumed to be different. We present a procedure to determine the optimal assignments of the workload to the stations under learning variability and show that it considerably affects these assignments.     

OR at Work in Modern Manufacturing

By describing the industrial assembly of a real product, methodologies and considerations are discussed for the re-alignment of discrete assembly systems in line with modern standards. Poor manufacturing procedures are highlighted, and a number of alternative strategies for system replacement are presented. A decision tree is used to categorize assembly into one of three types, and an integrated solution is proposed. The possible financial benefits, essential to maintain market position, are identified for each stage of an evolutionary cycle of continuous product design and changing manufacturing methods.