A new algorithm for optimally balancing assembly lines is formulated and tested. Named “FABLE,” it obtains proven optimal solutions for ten 1000 task lines, which each possess the computationally favorable conditions of an average of at least 6 tasks per work station and a small number of between-task precedence requirements, in less than 20 seconds of IBM 3033U CPU time for each problem. FABLE also performs very favorably on a benchmark group of 64 test problems drawn from the literature, which are of up to 111 tasks each. FABLE finds and proves an optimal solution to the 64 problems in a total of 3.16 seconds of IBM 3090 CPU time. FABLE is a ‘laser’ type, depth-first, branch-and-bound algorithm, with logic designed for very fast achievement of feasibility, ensuring a feasible solution to any line of 1000 or even more tasks. It utilizes new and existing dominance rules and bound arguments. A total of 549 problems of various characteristics are solved to determine conditions under which FABLE performs most and least favorably. Performance is sensitive to average number of tasks per work station, number of between-task precedence requirements (measured by ‘order strength’), and the total number of tasks per problem. A heuristic variant of FABLE is also described.
This paper describes a branch and bound algorithm which can solve assembly line balancing probems with nine modifications to the originally formulated problem of minimizing the required number of assembly stations, given a cycle time, a set of tasks with given deterministic performance times, and between-task precedence relationships. The first two formulation modifications are those of permitting planned imbalance in the total of task performance times at each assembly station, and allowing specific tasks to be assigned to specific types of assembly stations. Seven further problem modifications can be solved by the proposed algorithm, or by any algorithm or heuristic that can solve problems containing these first two modifications. They are: treatment of stochastic task performance times on unpaced lines; requirement of particular tasks to be assigned to particular stations; requirement of task groupings according to task skill levels; requirement of particular tasks to be assigned to only a left-of-line or right-of line station; required task separations; some mixed model situations; and where paralleling of a specified task into two (or more stations) is permitted. The algorithm is presented in both conceptual and detailed form. Computer computation times to solve a selected cross-sectional sample of problems are provided.production/scheduling: line balancing, facilities/equipment planning: design, networks/graphs: applications
A descriptive problem definition and a tested computerized heuristic solution procedure are offered for the problem of relative location of facilities in (or layout of) a multi-floor building. The problem definition and solution procedure overcome the problem of severe nonlinearity of inter-department movement times relative to distance, which enter the multi-floor problem because of the indirectness of routing, and because of different movement speeds compared with the single floor case. Both the definition and solution procedure are application-oriented, concentrating on practical aspects of multi-floor space allocation. Substantial savings in an implementation are reported. The procedure is particularly relevant to planning for an organization moving into a new multi-floor building. Additionally, the procedure can be used, without modification, for an organization spread over more than one building, and for single floor facilities. The possibility of alternative inter-floor routings is incorporated.production/scheduling: materials handling, facilities/equipment planning: layout, networks/graphs: applications
We present a rough-cut analysis tool that quickly determines a few potential cost-effective designs at the initial design stage of flexible assembly systems (FASs) prior to a detailed analysis such as simulation. It uses quantitative methods for selecting and configuring the components of an FAS suitable for medium to high volumes of several similar products. The system is organized as a series of assembly stations linked with an automated material-handling system moving parts in a unidirectional flow. Each station consists of a single machine or of identical parallel machines. The methods exploit the ability of flexible hardware to switch almost instantaneously from product to product. Our approach is particularly suitable where the product mix is expected to be stable, since we combine the hardware-configuration phase with the task-allocation phase.For the required volume of products, we use integer programming to select the number of stations and the number of machines at each station and to allocate tasks to stations. We use queueing network analysis, which takes into account the mean and variance of processing times among different products to determine the necessary capacity of the material-handling system. We iterate between the two analyses to find the combined solution with the lowest costs. Work-in-process costs are also included in the analysis. Computational results are presented.
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