The Design of Production Lines
3.3 Improvability
A different design problem arises when modifications to an existing system are con- templated. A production line may for example not be achieving desired production levels due to a deterioration in service levels or to a changed product or product mix.
Clearly, in such cases a total re-design and physical re-construction of the production line may not be justified. Using evaluative models it may be possible to determine the throughput with the parameters derived from measurements on the existing system and hopefully confirming its current performance. Such models might point to the existence of a bottleneck station through for instance the starving of a downstream station and/or the blocking of an upstream station and so the design effort could be concentrated on alleviating the bottleneck station. In other cases it may be possible to design for optimal throughput and to determine how far the existing system is from optimal in terms of such measures as work-load allocation, machine specific buffers and number of parallel machines at each work-station. Clearly, in all such cases there would be a concern to achieve maximum impact on the performance measure desired at minimum cost in re-designing the current system.
It should be noted that in practice, the concept of buffers has several meanings.
For example, a buffer between two single-machine stations might be considered to
be in series or in shunt (parallel). The discipline for the series buffer would normally be First-In, First-Out (FIFO), whereas the discipline for the shunt buffer would be Last-In, First-Out (LIFO). Where a station with parallel machines is concerned, the buffer discipline can be quite complex, in that an idle machine may not be in a posi- tion to service a waiting unit due to the materials handling protocol. So, the usual assumption of queueing theory that an idle server would immediately serve a wait- ing job may be violated. Clearly, care should be taken by the analyst to ensure that the buffer protocols used in any modeling work are in accordance with the actual situation.
The reader might note that the design problems specified above are not the same as those problems faced by operations management in their quest for continuous improvement (KAIZAN). When issues of improving the performance of an exist- ing system arise, the work of Meerkov and his colleagues is particularly relevant.
Meerkov defines a production system to be improvable if the limited resources involved in its operation can be redistributed so that a performance measure is improved. It must be understood that in practice there may be constraints on the redistribution process and improvability as such may not reach the optimality achiev- able in a mathematical sense. Performance measures involved here could relate to throughput, work-in-process (WIP), workforce (WF) allocation and due-time per- formance. Details of improvement strategies may be found in Jacobs and Meerkov (1995a). The role of bottlenecks in production systems is well known and in the paper cited above, Jacobs and Meerkov, gave a very precise definition of a bottleneck machine or buffer, as follows.
Let PI(μ1,...,μK,N1,...,NK) be the performance index of interest, e.g., the throughput, the due-time performance, the workforce allocation, product quality, and so forth.
A production system is called improvable with respect to WIP if there exists a sequence N1∗,...,NK∗such that∑Ki=1Ni∗=N and
PI(μ1,...,μK,N1∗,...,NK∗)>PI(μ1,...,μK,N1,...,NK), where,∑Ki=1Ni=N.
A production system is called improvable with respect to workforce (WF) if there exists a sequenceμ1∗,...,μK∗such that∏Ki=1μi∗=μ∗and
PI(μ1∗,...,μK∗,N1,...,NK)>PI(μ1,...,μK,N1,...,NK), where,∏Ki=1μi=μ∗.
The reader will note that the second equation above is in product form and is a bound on the workforce (WF). The assignment of the workforce defines the pro- duction rate (machine operators) and the average up-time (repair personnel) of each machine. The available workforce can be assigned to the work-stations in accordance with the constraint given by the second equation. This constraint may be referred to as the machine efficiency constraint and changes in the allocation of resources within the production line are required to maintain this overall constraint. In con- trast, the design problem in the earlier paragraphs of this chapter was formulated
using the work-load allocation, where the usual summation constraint was used, i.e.,∑Ki=1wi=1.
A production system is called improvable with respect to WIP and WF simulta- neously if there exist sequences N1∗,...,NK∗ andμ1∗,...,μK∗ such that∑Ki=1Ni∗=N,
∏Ki=1μi∗=μ∗and
PI(μ1∗,...,μK∗,N1∗,...,NK∗)>PI(μ1,...,μK,N1,...,NK), where,∑Ki=1Ni=N.
Machine i is the bottleneck machine if
∂PI(μ1,...,μK,N1,...,NK)
∂ μi >∂PI(μ1,...,μK,N1,...,NK)
∂ μj , ∀j=i. Buffer i is the bottleneck buffer if
PI(μ1,...,μK,N1,...,Ni+1,...,NK)>PI(μ1,...,μK,N1,...,Nj+1,...,NK), ∀j=i.
Other definitions of bottlenecks exist, for example, the bottleneck machine is the machine with the lowest isolated production rate. A buffer is considered to be a bottleneck buffer if the expected size of the work-in-process (WIP) at that buffer is larger than the expected size of the work-in-process, W IP, at the other buffers on the assumption that all buffer capacities are equal. More detailed examination of issues related to bottlenecks are covered in Goldratt and Cox (1986) in the context of the theory of constraints. As is clear from the precise definition given by Jacobs and Meerkov (1995), the bottleneck machine is not necessarily the machine with the lowest isolated mean production rate nor is the bottleneck buffer that buffer with the smallest capacity. The reader is referred to an interesting example given in the work by Jacobs and Meerkov (1995a). Further extensions in the general area on the topic of improvability are contained in the following papers: Jacobs and Meerkov (1995b) Kuo, Lim and Meerkov (1996), Chiang, Kuo and Meerkov (1998), Chiang, Kuo and Meerkov (2000), Li and Meerkov (2000), Li and Meerkov (2001), Chiang, Kuo, Lim and Meerkov (2000a) and Chiang, Kuo, Lim and Meerkov (2000b). Other references of interest include Enginarlar, Li and Meerkov (2003a) and Enginarlar, Li and Meerkov (2003b). Collectively, these papers contain a rich source of infor- mation to determine bottleneck stations and buffers and insightful design guidelines which would enhance the performance of existing systems and could also be used to check the appropriateness of systems design using the methods that are more germaine to the main stream of the methods proposed in this text.
In Chapters 4, 5, and 6, design problems of particular importance to production line designers are presented. The objectives of these chapters are to assist designers in the solution of practical problems using software available at the website associated with this text. Where possible, design guide rules are given with respect to specific situations. It must be understood that these guidelines were developed by researchers following, in most cases, extensive experimentation over a wide range of parameters.
However, although useful, these guidelines must be treated with respect, particularly if applied to situations not covered by the original experimentation. In this regard, the
reader is advised to consult the original papers which are usually given in the rele- vant bibliography. Finally, the authors would urge the designer to carry out, using the software provided, a series of experiments, if at all possible, over the range of param- eters of interest, so that the appropriateness of the set of the design guidelines may be tested. It should also be remembered that it is important to develop some expe- rience of the relative accuracy of some of the algorithms being used by researchers generally in this area and that perhaps it is true to say that algorithms developed more recently tend to be more accurate and more efficient. Nevertheless, it is vital to be fully familiar with the assumptions of any particular model being used because although most models will give a result, the really important issue is how realistic is the result obtained when applied to the problem in hand.
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