Assembly line voting

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The assembly line balancing is a planning problem of production economy , which is in the design of production lines as part of the Production Line sets and methods of operations research can be modeled. The questions often concern the cycle time , the number of processing stations (machines) or the line efficiency.

Basics

In this context, assembly line production is understood to mean production in which all products pass through a number of machines in the same order on which they are processed. All products are moved synchronously. This can be done by a continuously running conveyor belt that runs at a constant speed. The other possibility is to stop the belt for the cycle time and then to convey all products to be processed on to one station. The case of series production , in which buffer stores are set up between the stations and each station can work as long as desired, is dealt with in the context of flow shop problems.

For all models it is assumed that all product types to be manufactured must be processed in n work steps that cannot be further divided. There are predecessor and successor relationships between the individual work steps. For technical or economic reasons, a single work step can in principle also have several direct predecessors and successors. With the help of graph theory , they can be represented as a cycle-free digraph G. The operations form the node set V, and the arrow set E depicts the predecessor and successor relationships.

classification

In the literature there is a large number of different models which can differ in the following points.

  1. Number of Products
    1. Single product models
    2. Multi-product models: When producing variants or types, different products are manufactured that are very similar. Differences result from the processing times of the individual work steps. An optimal sequence must be planned in these models. If the differences between the products are so great that the assembly line has to be retooled, there is still a lot size problem at the same time .
  2. Processing times
    1. static-deterministic models have fixed processing times
    2. With dynamic-deterministic models, the processing times can be changed. Either because of changes in the production process or because of learning effects
    3. Stochastic models have random processing times.
  3. Structure of the assembly line: parallel or serial machines, or mixtures thereof.
  4. Allocation restrictions with regard to equipment, position of the workpieces , work processes, qualification of employees.
  5. Equipped with workers and machines: single-manned, multiple-manned or fully automatic workstations.
  6. Station limitation
  7. Trigger rate: (How often is a new workpiece placed on the belt?) Fixed or variable
  8. Transport system: Can workpieces be taken from the belt?
  9. Process alternatives: a fixed, or several freely selectable manufacturing processes
  10. Objective: Minimizing the total costs, the throughput time , the number of stations, the cycle time, etc.

Basic model

A basic model often considered in the literature (simple assembly line balancing problem, SALBP) is based on the following assumptions:

  • Single product case
  • The production process is specified.
  • fixed processing times t j for j = 1, 2, ..., n
  • All stations have the same cycle time.
  • fixed trigger rate
  • All stations are equipped with equivalent personnel and machines.
  • serial arrangement of the machines
  • immovable workpieces (cannot be removed from the belt)
  • no assignment restrictions
  • With regard to the objective function, four different models are distinguished:
    • SALBP-G: (G for General (general)) Determination of a cycle time c and the number of stations m, as well as assignment of the n work steps to the stations, so that the line efficiency BG is maximized . BG = t sum / (mc)
    • SALBP-1: For a given cycle time c, minimize the number of stations m
    • SALBP-2: With a given number of stations m, minimize the cycle time c
    • SALBP-f: (feasibility (feasibility)) For given m and c, examine whether there is an assignment of the n operations to a maximum of m machines, in which the cycle time is less than or equal to c.

Maximizing the line efficiency

If the upper limit for the cycle time is greater than the sum of the individual processing times, the line efficiency can be maximized by having all operations carried out at a single station. The cycle time is then t sum .

As a rule, however, a maximum permissible cycle time is specified. It results from a planned sales quantity q in a period with the duration T. The takt time can then be a maximum of c max : = T / q.

literature

Individual evidence

  1. ↑ Domschke, Scholl, Voß: Production planning - process organizational aspects . 2nd edition, Berlin, Springer, 1997, p. 182f.
  2. ↑ Domschke, Scholl, Voß: Production planning - process organizational aspects . 2nd edition, Berlin, Springer, 1997, p. 181.
  3. ↑ Domschke, Scholl, Voß: Production planning - process organizational aspects . 2nd edition, Berlin, Springer, 1997, pp. 184-189.
  4. ↑ Domschke, Scholl, Voß: Production planning - process organizational aspects . 2nd edition, Berlin, Springer, 1997, pp. 189f.