The Design of Production Lines
3.1 Introduction
This chapter is essentially a prelude to the rest of the text and its objective is to assist the reader to understand the main initial design problems that arise with produc- tion lines. It is important for the reader to clarify the context of any design problem related to any production line, e.g., is it a green fields situation, a modification of an existing production line to enhance performance or the adaptation of an existing line to produce products not produced already?
Once the strategic decision to use a production line to manufacture the products has been made, the design of the line must be undertaken. To remind the reader of the complexities involved, in Figure 3.1, an example of a relatively complex production line, adapted from Li (2003), is shown.
In Figure 3.1, the rectangles represent machines and the circles represent buffers.
Although it is traditional in analysis to indicate machines by rectangles, it must be remembered that associated with many such machines are human operators and that human operators may in fact form a separate work-station without any machines.
Indeed, it is these human operators that add variability to the production line in that many machine processes are essentially deterministic in practice. Here, it is assumed that the ergonomic design of the systems is undertaken by relevant specialists while the physical requirements of the system are being fully specified by others. All these specialists are of course in a position to contribute to an understanding of the vari- ability involved in production lines on an ongoing basis during the design process of the production line.
Quality is a major performance characteristic of modern manufacturing and in particular there are inspection and test stations embedded in production lines. The precise arrangement for handling rework of defective material is generally dependent on the materials handling arrangements. Sometimes feedback is possible resulting in the reuse of the inspection and testing facilities whereas in other situations rework and further inspection are effectively performed off the main line. Either of these cases may be handled in most models.
C. T. Papadopoulos et al., Analysis and Design of Discrete Part Production Lines, Springer Optimization and Its Applications,
DOI: 10.1007/978-0-387-89494-2_3, © Springer Science+Business Media, LLC 2009 101
Bf1Mf1Bf2BfFMfFBfF+1 Main Line: M1,..,Mp,Mq,..,MK, B1,..,Bp,Bq,..,BK Feeder Line: Ma1,..,MaA, Ba2,..,BaA+1 Feed-Forward Line: Mf1,..,MfF, Bf1,..,BfF+1 Rework Loop: Mr1,..,MrR, Br1,..,BrR+1 Parallel Lines: Mij,i=1,..,k, j=1,..,Mi, Bij, i=1,..,k, j=2,..,Mi Merge machines: Ma (assembly merge), Mjr (rework merge), Mjf (feed-forward merge) Split machines: Mr (rework split), Mf (feed-forward split), Mrs (scrap) Split/merge buffers: Bp (parallel split), Bq (parallel merge)
Br 1 Mr 1 Brs
M11B12 M1M 1 FeedbackBqMqBfMfBr MrBj fMj f BKMK Line 5Line 6 MrR Mrs+1Brs+1Mrs
BrR+1
Line 9 Line 7Line 8
Line 12 Scrap
Line 10
M1B2MαBα+1BjrMjrBjr+1MpBp+1 Line 1Line 3Line 4
Line 2 Assembly
Ma1Ba 2Ma ABa A+1 Mk1Bk2MkMk Line 11 Fig.3.1.Atypicalstructureofacomplexproductionline
As shown in Figure 3.1, there is one main production line (Line 1, Line 3, Line 4, Line 12, Line 5, Line 6, Line 7 and Line 8), with Line 12 being a parallel-machine line consisting ofκ sub-lines, a feeder line (Line 2), a feed-forward line (Line 9) as well as a rework line/loop (Line 10 and Line 11). Machine Ma is an assembly merge machine, machine Mjris a rework merge machine and machine Mj f is a feed- forward merge machine, while machine Mr is a rework split machine, machine Mf
is a feed-forward split machine and machine Mrsis a scrap split machine. There are split/merge buffers associated with the parallel line (Line 12).
By design is meant the specification of some of the parameters (structure of the production system) to achieve a specific objective. The approach is quite different to the use of methods to evaluate the performance of a specified system which has been already discussed in Chapter 2.
In this chapter, it is assumed that the production processes at each machine are specified. To arrive at this situation may have involved considerable engineering work. In addition, the sequencing of the machines/layout of the production line has been determined. For the purposes of this chapter, the details of the transportation system between the machine stations are assumed to be given and the information and control systems are not of specific interest. Essentially, what is being said is that a flow diagram of type Figure 3.1 has been developed in outline form where the production rate of each individual machine, the details of the buffer sizes and the number of parallel machines have yet to be determined. Further details of the considerations involved may be found in Buzacott and Shanthikumar (1993), Altiok (1997) and Groover (2001), among others.
In general, there are three methods of increasing the throughput of an individual work-station: (a) increasing the production rate of an individual machine, (b) using machines in parallel, or (c) a combination of both. These involve technological and managerial choices. The design of production lines as understood here is confined to the following issues:
1. Work-load at each station: There are well-known design guidelines, discussed below in Chapter 4, which result in increased throughput of the line (units pro- duced per unit time over the entire line). The application of these guidelines will specify the mean production rates of each of the work-stations. These design problems are referred to as work-load allocation problems, WAP. In such prob- lems it is normal to assume fixed specified buffer sizes and single-machine work-stations.
Readers will be aware that research results of interest to manufacturing systems designers may arise in work not specifically oriented towards manufacturing sys- tems. This is particularly true in relation to the work allocation problem where a series of papers have developed quite strong results mainly using mathematical analysis. Interested readers are referred to the papers listed in Chapter 4.
2. Determination of the number of machines at each work-station: The use of parallel systems will affect the throughput of the line. The associated design prob- lem is referred to as the server allocation problem, SAP, and is treated also in
Chapter 4. Normally, in such design problems it is assumed that there are fixed station specific buffer sizes between the parallel machine stations.
3. Specification of the sizes of the buffers: It is more usual to have machine or station specific buffers but occasionally common buffers for more than one machine or station are sometimes used. Such designs are referred to as the buffer allocation problem, BAP, which is the subject of Chapter 5.
The design problem from the point of view of the systems engineer is as follows Given:
• Fixed number of work-stations (K). This number is determined by tech- nological, precedence and economic considerations. Servers at these K work-stations may consist of machines only, of human operatives only or of a feasible and necessary combination of these two types of resources.
• Number of servers S(S≥K).
• Total work-load of the line, normalized to K (time units).
• Total number of buffer spaces (N).
The design problem in general is to do the following meet a specified objective, usally expressed in throughput, work-in-process or cost terms:
(i) Allocate the number of servers S over the given K stations; clearly there must be at least one server at each station;
(ii) Allocate the normalized work-load to each of the given fixed K stations;
(iii) Allocate the total number of buffer spaces N over the K−1 buffer stor- age areas. Usually, the buffer in front of the first station is assumed to be of adequate size (theoretically infinite) to accommodate the flow of work and these buffer spaces are not included in the N buffer spaces which are considered as a parameter of the design problem. Likewise, the storage spaces after the last (Kth) station are excluded from consideration leaving just K−1 storage areas among the K stations.
Needless to say, it is possible to consider the design problem of maximizing the throughput of production lines in which none of the following are specified a priori:
the production rate at each station, the inter-station buffer sizes and the number of parallel servers at each station. This leads to a very general design problem with con- siderable computational complexities. In practice however, it is more usual, initially, to consider simpler design problems with two of the three decisions listed above already made, and these simpler design problems may be considered to be “pure”
allocation problems.
It should be noted that usually the word ‘allocation’ has a very specific meaning.
In the pure work-load allocation problem, the objective is to allocate a total capacity of K time units over K work-stations so as to maximize throughput given the machine specific buffers in the system. In the pure buffer allocation problem, the objective is to maximize throughput by allocating an overall buffer space of size N among the K−1 buffer locations, where each station has a fixed production rate. Finally, in the pure server allocation problem the total number of servers in the system is fixed
and the objective is to maximize throughput of the system by allocating an integer number of servers to each station given fixed station specific buffers.
The words ‘work-stations’ and ‘machines’ are used interchangeably in produc- tion line design problems. However, it should be noted that here ‘machines’ is a generic term which includes the following meanings: physical machines alone, operators alone or a combination of these two resources or more generally, servers.
Usually, designers are concerned with maximizing throughput. There are a few other possible objective functions which may be of interest. These include the minimization of average work-in-process, W IP, having in mind current operations philosophies of lean production. In such models, a threshold throughput, X0, must be achieved and W IP is minimized in the context of this achievement while satisfying other constraints in relation to buffer allocation, server allocation and work-load allo- cation. Finally, a more specific cost/financial objective function may be developed to include machining cost and buffer space and inventory holding costs.
The two performance measures mentioned above, viz., throughput, X , and aver- age work-in-process, W IP, may be characterized as efficiency and effectiveness performance measures, respectively. Increasing the throughput of the line is normally associated with increasing average WIP and vice versa. Usually, other measures of performance such as mean flow or production time, utilization of individual stations, often a favorite of earlier generations of production engineers and managers, etc., may be easily obtained from the computer results.
In production lines, machines may be considered to be reliable or unreliable.
Unreliable machines have an associated reliability or survival curve from which the mean time to failure (MTTF) may be determined. Failed machines may be repaired in accordance with a repair time distribution from which the mean time to repair (MTTR) may be determined.
The processing time at a machine may be assumed to be deterministic or stochas- tic. If stochastic, the mean service time and its coefficient of variation may be determined from the associated processing time distribution. Often the exponential distribution is used, resulting in a coefficient of variation of 1. In practice, it has been observed that the coefficient of variation is less than 1 and thus a strict exponential distribution of processing times is inappropriate. However, phase type distributions (e.g., Coxian distribution with two phases) can be used to accommodate situations where the coefficient of variation of service time is less than 1 while retaining the analytical benefits of the exponential distribution.
The reader might note that the justification of any particular design of a man- ufacturing system raises complex issues, particularly in the case of systems which have some inherent flexibility. In the past, finished designs tended to be costed and evaluated on the basis of either meeting or not meeting a specified interest (hur- dle) rate in a discounted cash flow analysis (dcf). Many criticisms have been leveled at this approach (see for example Noble and Tanchoco, 1993). As research in this area has progressed, the methodology for the concurrent evaluation of design perfor- mance and economic evaluation has been developed. In production line design, the full realization of this approach to design evaluation can only be achieved through the holistic integration of the work of the detailed engineering designers specifying
the outline of the initial system and the work of the system specialists involved in performance analysis. Chapter 7 is concerned with the costing of various designs.