In this survey paper we discuss the development of the simple assembly line balancing problem SALBP; modifications and generalizations over time; present alternate 0-1 programming formulations and a general integer programming formulation of the problem; discuss other well-known problems related to SALBP; describe and comment on a number of exact i.e., optimum-seeking methods; and present a summary of the reported computational experiences. All models discussed here are deterministic i.e., all input parameters are assumed to be known with certainty and all the algorithms discussed are exact. The problem is termed "simple" in the sense that no "mixed-models," "subassembly lines," "zoning restrictions," etc. are considered.

Due to the richness of the literature, we exclude from discussion here a the inexact i.e., heuristic/approximate algorithms for SALPB and b the algorithms for the general assembly line balancing problem including the stochastic models.

A survey of exact algorithms for the simple assembly line balancing problem

SUMMARY This paper reports the results of a comprehensive review and analysis of the assembly line balancing literature. Quantitative developments and qualitative issues are addressed at both the strategic and tactical levels. The numerous quantitative and qualitative factors which the literature mentions could impact the design, balancing and scheduling of assembly systems are organized into an eight-level hierarchical, factor/decision taxomony. This comprehensive taxonomy is used to assess our progress in assembly system design and operation. Finally, from the results of the literature review and progress assessment, suggestions for future research on socio-technical assembly systems are offered.

A comprehensive literature review and analysis of the design, balancing and scheduling of assembly systems

Mass production system design is a key for the productivity of an organization. Mass production system can be classified into production line machining a component and production line assembling a product. In this paper, the production line assembling a product, which is alternatively called as assembly line system, is considered. In this system, balancing the assembly line as per a desired volume of production per shift is a challenging task. The main objectives of the assembly line design are to minimize the number of workstations for a given cycle time (type 1), to minimize the maximum of the times of workstations for a given number of workstations (type 2), and so forth. Because this problem comes under combinatorial category, the use of heuristics is inevitable. Development of a mathematical model may also be attempted, which will help researchers to compare the solutions of the heuristics with that of the model. In this paper, an attempt is made to present a comprehensive review of literature on the assembly line balancing. The assembly line balancing problems are classified into eight types based on three parameters, viz. the number of models (single-model and multi-model), the nature of task times (deterministic and probabilistic), and the type of assembly line (straight-type and U-type). The review of literature is organized as per the above classification. Further, directions for future research are also presented.

Literature review of assembly line balancing problems

In this paper, we describe an integer programming algorithm for assigning tasks on an assembly line to work stations in such a way that the number of work stations is minimal for the rate of production desired. The procedure insures that no task is assigned to a work station before all tasks which technologically must be performed before it have been assigned precedence restrictions are not violated, and that the total time required at each work station performing the tasks assigned to it does not exceed the time available cycle time restrictions are not violated. The procedure is based on a systematic evaluation enumeration of all possible task assignments to work stations. Significant portions of the enumeration process are performed implicitly, however, by utilizing tests described in the paper which are based on the specific structure of the line balancing problem. An artifice termed a network cut is also developed which eliminates from explicit consideration the assignment of tasks to work stations where such assignments would not lead to improved line balances. Results reported demonstrate that the procedure can obtain optimal balances for assembly lines with between 50 and 100 tasks in a reasonable amount of computation time and with modest computer storage requirements.

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An Integer Programming Algorithm with Network Cuts for Solving the Assembly Line Balancing Problem

This paper presents a zero-one integer-programming formulation of the assembly line balancing (ALB) problem. Results indicate that this formulation requires as few as 50 to 60 percent of the number of variables required by other zero-one formulations of the ALB problem now in existence. Once formulated, problems are solved by examining a sequence of 0-1 programming problems for feasible solutions. Full advantage is taken of the structure of the 0-1 programs in determining feasibility. Computational results demonstrate the efficacy of the approach.

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Technical Note—Assembly-Line Balancing: Zero-One Programming with Fibonacci Search

In this study we will present an improved version of the Bowman-White zero-one integer programming formulation of an assembly line balancing problem. We will demonstrate that in solving the above problem, certain steps in Geoffrion's 0–1 integer programming algorithm can be simplified or eliminated. Computational results are given which indicate that the proposed algorithm is faster than the present exact methods.

S. R. Thangavelu

Papers

Assembly Line Balancing by Zero-One Integer Programming