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Automatic production control applying control theory
Int. J. Production Economics 63 (2000) 33} 46
Automatic production control applying control theory Hans-Peter Wiendahl, Jan-Wilhelm Breithaupt* Institute of Production Systems, University of Hannover, Callinstrasse 36, 30167 Hannover, Germany Received 1 April 1998; accepted 22 October 1998
Abstract A new dynamic production model for the planning level will be presented in this paper. The model is based on methods of control theory, which provide a large variety of appropriate tools for analysing and controlling dynamic systems. With the help of the funnel model and the theory of the logistic operating curve, a continuous #ow model of a single work centre has been designed. For the control task a backlog controller and a WIP controller have been developed. The controllers interact to adjust the capacity and the input rate of the work centre so as to eliminate the backlog as soon as possible and to set the WIP to a de"ned level. By means of envelope curves of capacity #exibility, which are easily applicable to industry, the individual range of capacity adjustments at a single work centre can be modelled. Simulation experiments con"rm that this concept ensures the synchronisation of capacity and work. The objective is to develop a closed-loop control for PPC with de"ned control and reference variables based on the logistical objectives. ( 2000 Elsevier Science B.V. All rights reserved. Keywords: PPC; Control theory; Dynamic systems; Production logistics; Production model
1. Challenges of global markets The frequently discussed challenges facing today's companies can be summarised as **meeting customer demands in the short-term within an agile network of competent partners in order to succeed in global competition++. Superiority in global markets is not dependent simply on continuous improvements in respect of the classical objectives costs, quality and time. These are expected by the customer as a matter of course and are not su$cient to * Corresponding author. Tel.: ##49-511-762-3813; fax: # #49-511-762-3814. E-mail address: [email protected] (J.-W. Breithaupt).
distinguish a company from potential competitors. Rather, new features of performance are becoming increasingly important. They can be described by the catchwords innovation capability, learning capability, and agility (Fig. 1) [1]. Agile companies distinguish themselves through speed in the planning and realisation process. Furthermore, they are strong in their adaptability to changing conditions in the production environment. Industry and researchers therefore need to develop their own innovative ideas and to expand them to create new tools and procedures. This paper o!ers a new perspective for the PPC of tomorrow. Going under the catchword automatic production control (APC), it could be very helpful in improving companies' competitiveness in the future.
0925-5273/00/$-see front matter ( 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 5 - 5 2 7 3 ( 9 8 ) 0 0 2 5 3 - 9
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Fig. 1. Features of global competition.
2. A continuous 6ow model of a job shop 2.1. The logistical objectives The quality of the logistical performance is determined by lead-time and due-date performance in the job shop as outlined in Fig. 2. On the other hand, the loading of the production facilities and the work-in-process (WIP) a!ect the pro"tability of the manufacturing process. From these partly
con#icting requirements within PPC the four main objectives of the production process can be derived. Short lead time and low schedule deviation represent the market-related objectives, whereas low inventory and high and steady loading of the work systems are the factory-related objectives. In order to be able to adjust the logistical objectives given their mutual dependency and the pressure for competitive production, it is necessary to design controllable production and order processing. While conventional PPC systems predominantly operate open-loop control and therefore lack automatic feedback, a self-controlling process can be achieved by a closed-loop control by de"ning appropriate reference and correction variables [3,4]. 2.2. Shortcomings of today's PPC systems
Fig. 2. Logistical objectives in manufacturing [2].
Today's PPC systems di!erentiate between the planning level and the operational level. The di!erentiation can also be applied to automatic production control. Because of the di!erent nature of the levels, di!erent models are required. Single orders are of interest on the operational level. A more global view on the planning level allows the application of #ow models in continuous time (e.g. [5,6]), for which control theory o!ers many more
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methods than for discrete models. Furthermore, the planning level de"nes the boundary conditions for achieving the targets on the operational level. It is therefore essentially the planning level which will be looked at in the following pages [3,4]. Countless approaches to modelling and controlling the dynamics of production systems have already been developed. The "rst works in this "eld were published by Forrester in the book Industrial Dynamics [5]. Most of these approaches are based on a simple control loop. The feedback in today's MRP II systems, which is restricted to the closing of information circuits, can be mentioned here as an example. The response has to be made by the system user according to the results. Such concepts lack a clear de"nition of the control variables and reference variables as well as a description of the relationship between e!ects. Thus, the correcting variables cannot be derived e!ectively. The deterministic models underlying this system merely describe reality statically (i.e. assumptions of in"nite capacities and "xed lead times) and are not appropriate for representing the dynamics of reality. Most of the systems are designed to enforce the plans that are thereby generated and are therefore characterised by a strong static nature [3,7]. 2.3. A yow network in continuous time with time inhomogeneous dynamics As mentioned above, continuous models are particularly suited for the application of methods and techniques based on control theory. It is therefore necessary to develop a continuous (i.e. #oworiented) stochastic job shop model for which control mechanisms have been designed and tested in a current research project at the Institute of Production Systems. A large amount of related literature can be found which deals with continuous #ow models (e.g. [6,8,9]). Within the scope of an investigation of #uid models Chen, and Mandelbaum [6] present a formula to describe the work-in-process of a work centre within a #ow network in continuous time with time inhomogeneous dynamics (Eq. (1)). The network outlined in the article consists of k work centres, each with an in"nite storage capacity. The work centres are interconnected by frictionless
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pipes through which #uid #ows in and out of the work centres. mwip (t)"mwip (0)#extin (t) 03$%3,k 03$%3,k 03$%3,k k # + [out (t) 03$%3,.!9,j j/1 !out (t)]Hp 03$%3,-044,j j,k ![out (t)!out (t)] 03$%3,.!9,k 03$%3,-044,k (1) where mwip (t) 03$%3,k mwip (0) 03$%3,k extin (t) 03$%3,k out (t) 03$%3,.!9,j out (t) 03$%3,-044,j
out (t) 03$%3,.!9,k out (t) 03$%3,-044,k p jk
: mean work-in-process of centre k at time t (number of orders), : initial mean work-in-process of centre k (number of orders), : cumulative external input of centre k until time t (number of orders), : cumulative potential out#ow of upstream centre j until time t (number of orders), : cumulative potential lost of out#ow due to empty upstream centre j until time t (number of orders), : cumulative potential out#ow of centre k until time t (number of orders), : cumulative potential loss of out#ow due to empty centre k until time t (number of orders), : fraction of total output from centre j #owing directly to centre k (!).
The momentary work-in-process of work centre k depends on its initial inventory, its cumulated external input, the actual cumulative output of its upstream work centres #owing directly to k and its own actual cumulative output until time t. By means of Eq. (1), the dynamic behaviour of a work centre can only be described if the required parameters can be determined. Usually this can be done easily for the initial work-in-process, the external input, and the potential cumulative output of each work centre. More complicated is the determination of the relation between losses in
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utilisation (OUT ) and the momentary WIP-044,k level. In the literature, the only boundaries are those among which losses in utilisation are possible. A clear de"nition of the interdependencies between WIP and utilisation is missing. The funnel model and the derived theory of logistic operating curves are appropriate for "lling this gap. In contrast to the #ow network mentioned above and the models of queueing theory (e.g. Little's Law [10] (Eq. (2))), these models are based on a work-content description and not an orderrelated one. Also with the funnel model the order processing of a work system can be described as the #ow of a liquid through the funnel. The incoming orders, here measured in hours of work content, form a stock of pending lots, which have to #ow through the funnel outlet. The diameter of the outlet can be described as the capacity of the work system (also measured in hours of work content), which is adjustable within limits (actual performance). It is obvious that the lead time for incoming orders changes with the stock of pending orders and the system's performance [2]. These interdependencies between mean lead time (here: mean range, mr), mean work-in-process, mwip, and mean performance, mper, are stated through the funnel formula (Eq. (3)). Detailed derivations of the funnel model and formula are speci"ed in [2,11,12]. A comparison between the funnel formula and Little's Law is made in the following. For a better understanding variable names have been modi"ed. ¸ittle1s ¸aw: mwip "inrHmlt, 03$%3
(2)
Funnel formula: mwip "mperHmr, 803,
(3)
where mwip : mean order-related work-in-process 03$%3 [number of orders], minr : mean input (arrival) rate [number of orders/shop calendar day (scd)], mlt : mean lead time [scd], mwip : mean work-content-related work-in803, process [h], mper : mean performance [h/scd], mr : mean range [scd].
Another di!erence exists in the point of view: Little's Law focuses on the incoming orders (mean input rate), whereas the funnel model focuses on the outgoing orders (mean performance). Over a certain period of time a work centre can function in a stable state only if the mean input and output of the work centre match each other, because otherwise wip will increase constantly (minr'mper), or it will decrease (mper'minr) until the centre runs out of work. In a stable state minr can be principally equated with mper. Another di!erence exists in the description of the length of stay of orders at the work centre. Little uses the mean lead time, whereas the funnel formula includes the mean range (mean runout time of the work centre). Under speci"c circumstances the mean lead time can be derived directly from the mean range. This brief comparison shows that both models, whilst similar, have their individual range of applications. A more detailed comparison between the two formulas can be found in [13]. Nevertheless, the mutual dependencies between work-in-process and performance cannot be described directly by means of the funnel formula or Little's Law. To "ll this gap, the theory of logistic operating curves, which is based on the funnel model, has been developed by Nyhuis [14]. The logistic operating curve forms the connection between the mean wip, the mean range and the mean performance, with the aid of the capacity and the ideal minimal wip (order structure) as input parameters (Fig. 3) [2,14]. The curve states that the output of a work centre is independent of the mean work-in-process as long as every work system has a stock of pending orders at all times. If so, the performance of the system is equal to its capacity. Only if the inventory is further reduced will losses in production occur due to interruptions in the material #ow. On the other hand, the range decreases in proportion to the WIP until the physical minimum is reached. Beyond this point the range cannot be further reduced because it is limited by the sum of the operation time and transport time (ideal minimum of range). With regard to an ideal process, the ideal mean wip minimum (mwip ) represents the WIP level .*/ necessary to run the system, assuming that no arriving order has to wait and no interruption occurs
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Fig. 3. Interdependency between output, range and work-in-process (WIP) [14].
in the material #ow. This cannot be found in practice, so the realistic curves di!er from the idealised ones shown in (Fig. 3). Nyhuis [14] found that it is possible to calculate these realistic curves for most of the job shop productions with the following equations: mwip(x)"mwip (1!(1!Jx)4)#mwip 4 a x, .*/ .*/ 1 (4) mper(x)"mper (1!(1!Jx)4), 4 .!9
(5)
where mwip(x) : mean work-in-process [h], mper(x) : mean performance per shop calendar day [h/scd], mwip : idealised mean work-in-process min.*/ imum [h], mper : maximally available performance .!9 [h/scd], a : streching parameter } (default-value: 1 10), x : running parameter (0(x(1). The mean wip minimum necessary to determine mwip(t) can be calculated easily by means of
Eq. (6): mwip "mot #mtt .*/ 8%*')5%$ 8%*')5%$ +n (ot ot )2 +n (tt ot )2 " i/1 i i # i/1 i i , (6) +n ot +n ot i/1 i i/1 i where ot : order time of order i [h], i mot : mean weighted order time [h], 8%*')5%$ tt : transportation time of order i [h], i mtt : mean weighted transportation time 8%*')5%$ [h]. A detailed derivation of these formulas is speci"ed in [13,14]. With the aid of Eqs. (4) and (5), a pair of values for wip and performance can be calculated depending on the running parameter x. With these pairs, the course of the performance is de"ned. Using the funnel formula, the course of the mean range can also be determined. To come back to the #ow network described in Eq. (1), the work content of the orders #owing through the pipes can now be considered. It is thus possible to determine the actual output of the work centres by means of the operation curve. Eqs. (7)}(9) describe the continuous model of the job shop, which is presented in the following by means of
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control-theory elements:
where per (mwip (t)) : mean performance of centre j dej j pendent to the mean work-in-process of j at time t (h/scd), extinr (t) : external input rate of centre k at 03$%3,k time t (number of orders/scd), to
A
(t) mwip (t)"mwip (0)# extin 03$%3,k k k k # + [out (t)!out (t)] j,.!9 j,-044 j/1
B
1 ] p mot k mot j,k j ![out (t)!out (t)], k,.!9 k,-044
(7)
where mwip (t) k
: mean work-in-process of centre k at time t [h], mwip (0) : initial mean work-in-process of k centre k [h], extin (t) : cumulative external input of centre 03$%3,k k until time t [number of orders], out (t) : cumulative potential out#ow of up.!9,j stream centre j until time t [h], out (t) : cumulative potential lost of out#ow -044,j due to empty upstream centre j until time t [h], out (t) : cumulative potential out#ow of .!9,k centre k until time t [h], out (t) : cumulative potential loss of out#ow -044,k due to empty centre k until time t [h], p : fraction of total output from centre jk j #owing directly to centre k[!], mot : mean order time of upstream centre j j [h], mot : mean order time of centre k [h]. k Eq. (7) can be simpli"ed by means of
PA t
B
k 1 + per (mwip (t)) p dt j j mot j,k 0 j/1 j k 1 p " + [out (t)!out (t)] .!9,j -044,j mot j,k j j/1
(8)
and
P
t
extinr (t)dt"extin (t), 03$%3,k 03$%3,k 0
(9)
(10)
Determining the mean performance directly from the work-in-process is problematical because the resulting equations are fairly complex. By means of Newtons approximation procedure, a value for the running parameter x can be found in relation to the actual WIP-level. This value can be inserted into Eq. (5) to determine the centres actual performance. 2.4. A continuous job shop model based on control theory For the development of appropriate controllers based on control theory, the model described in Eq. (10) has to be designed on the basis of controltheory elements. A basic control-theory model for a single work centre has been developed and evaluated by Petermann [3]. In the following section, this model is extended for modelling several work systems connected via the material #ow. The input and output variables as well as a simple control loop of the continuous model are shown in Fig. 4. The incoming orders are converted into the input rate (dimension: number of orders per unit of time). Multiplied by the mean order time the dimension of the input rate is changed into work content per time unit. Similar to the input rate, the output of the work system is converted into the output rate by dividing the mean performance through the mean order time. These transformations are required because
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Fig. 4. Continuous model of a work centre.
the material #ow between two work centres is measured in number of orders per unit of time, whereas within the work centre the work content is of interest [2]. In reality the order time of several orders processed by a speci"c work system di!er. Therefore, the transformation leads to practicable result only over time periods long enough to enable the di!erent order times to balance. This can be mentioned on the planning level. The various sizes of the orders are considered through the mean weighted order time as a parameter of the order structure (Eq. (6)). As mentioned above, a simple control loop is depicted inside the continuous model. With the aid of an integrator the input rate is integrated over a time interval into the cumulated input (in) of the system. Analogous to this, the same procedure is followed for the cumulated output (out). The mean wip (mwip) is calculated as the di!erence between the input and output (summation point). With the aid of Eq. (3) the mean range can be calculated by dividing the mean wip through the output rate. The four variables, output rate, mean performance, mean range and mean wip, are the output variables of the system. The transmission function of the work centre is the logistic operating curve (Fig. 3). A major problem for the production control occurs due to the structural parameters, mwip and .*/ per , of the logistic operating curve which vary .!9
over time. This behaviour leads to a variable transmission function which is unacceptable for a control task. Therefore it is necessary to normalise the logistic operating curve. The normalised version describes the interdependence between the mean relative work in process (Eq. (11) based on Eq. (4)) and the mean utilisation (Eq. (12) based on Eq. (5)) [14]. mwip(x) mwip (x)" "1!(1!Jx)4#at, 4 (11) 3%mwip .*/ mper(x) mut(x)" "1!(1!Jx)4, 4 (12) mper .!9 where mwip : mean relative work-in-process [h], 3%mut : mean utilisation [h]. Therefore, the normalised logistic operating curve is the transmission function of the continuous model and forms the connection between the input and output variables. The control-theory model for a single work centre based on control-theory elements is appropriate for the connection of several work systems via the material #ow as described in Eq. (10). However, the connection itself between the systems is still missing. In order to implement the connections of a k : k model as described in Eq. (10) and to create a job shop model based on control theory, it
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Fig. 5. Derivation of the normalised material #ow matrix.
is essential to de"ne the transition probabilities. With the aid of a common material #ow matrix (MFM), which can be calculated using real feedback data from the job shop, it is possible to determine the probabilities. The MFM shows how many orders have been transported from each work system to another within the job shop during a speci"c period of time. The virtual starting and ending points are de"ned to describe the #ow of incoming and outgoing orders [2]. In the upper right part, Fig. 5 shows
a MFM for a job shop of consisting of six work systems. For the calculation of the transition probabilities, the absolute number of orders #owing from previous work systems to the subsequent ones is not of interest. What is far more important is the percentage relation of the distribution of the system's output as mentioned above. It is therefore necessary to normalise the material #ow in relation to the summarised output of each work system (Fig. 5, lower right part).
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Fig. 6. Example of a continuous job shop model (with 6 work systems).
Apart from this, the content of the normalised MFM is time independent as long as the structure of the production program remains the same. Only if the production program varies over a longer period of time, the model has to be adapted by using actual feedback data to calculate a new MFM. The normalised MFM can be integrated into the model based on control theory as a transition probability matrix. Fig. 6 shows a simulation model based on the job shop mentioned before. Each work system is represented through a `superblocka, which contains the elementary work system model. Analogous to the elementary work system model, each superblock has four inputs and outputs. Via the input and the output rate the superblocks are connected with the transition probability matrix block, which has the task to distribute the output of each work system to other work systems. The input as well as the output of the whole job shop is directly connected with this block.
3. The design of controller under consideration of the logistical objectives The design of a controller concept has to be divided into two di!erent steps. First of all, it is
necessary to de"ne the controllable output variables under consideration of the input variables. Afterwards, the connection and interaction of the controller has to be designed. 3.1. Dexnition of reference and control variables With the aid of the models presented two controllers for a work system have been modelled. The input and output variables of the continuous model have been discussed in Section 2.3. The variables output performance, wip, and range are linked through the funnel formula as mentioned above. Therefore only two of the variables are controllable simultaneously. The essential task of a work system is to allocate the required performance to process the system load (production schedule). For this reason the output performance, respectively, the output rate attains importance. On a closer examination of the system's output performance, the actual output rate is of less importance. The question of interest is whether the planned work is "nished by a certain date. The di!erence between the planned sum and the actual output is de"ned to be the backlog of the system. The backlog of the system thus becomes the most important control variable for monitoring
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Fig. 7. Concept of an automatic backlog controller.
the output performance of the production system. In order to utilise a clear de"nition, the developed controller is therefore named backlog controller instead of output controller. The capacity is used here as a correcting variable of the system. Fig. 7 shows the concept of a backlog controller. The planned performance is the reference variable. The di!erence between the actual and the planned performance is integrated over a time interval. The result is the above-mentioned backlog. Referring to the actual backlog the backlog controller adjusts the required capacity of the work system to reduce the backlog to zero as fast as possible. Because in reality it is impossible to adjust the capacity immediately, a reaction time between the request for capacity and the following allocation was introduced [3,4]. In an existing job shop the systems' capacity can normally be increased respectively decreased in different sized steps. For each step a speci"c reaction time is required. The fastness in that an increase or a decrease can be realised, is a measure for the system's capacity #exibility. Fig. 8 shows an example for a capacity installation/de-installation curve. These curves are integrated in the backlog controller of each single work system in the extended model. The capacity can be increased in several steps, considering the speci"c reaction time,
until the requested amount of capacity has been provided. Thereby, the controller also considers the minimum installation time of each capacity level, because in reality e.g. an additional shift cannot be employed for only one day, but for at least one week. This check is necessary, when the reaction time of the next step has been expired and a small backlog still remains. Using a higher capacity level the backlog can be decreased faster than with a lower one. But if the minimum installation time of this level will lead to an additional amount of capacity acap , that will exceed the requested .*/ amount, this capacity increase will not be realised. This check prevents from the installation of additional capacity that is not required. The de-installation of capacity is realised the same way using the de-installation curve. After de"ning the backlog as a control variable, a decision whether the range or the WIP shall be controlled is necessary. A controllable order processing based on production scheduling supports the implementation of the range as control variable. Two basic problems result from an implementation of the range: "rst of all, the measurement of the variable is di$cult; secondly, the range is limited at the bottom through the sum of the transportation and operation time. This is a major problem if the
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Fig. 8. Envelope curves of capacity #exibility.
set the system to an operating point on the operating characteristic curve that was de"ned within the scope of production planning. The planned wip is the reference variable. Referring to the di!erence between planned and actual wip the WIP controller adjusts the input rate of the production system [3,4]. 3.2. Combination of the backlog and the WIP controller
Fig. 9. Concept of an automatic WIP controller.
reference value of the range falls short of this limit. The mean wip as control variable is not limited. Moreover its measurement is easier and more precise. Therefore, it is obvious to use WIP control. The main task of the WIP controller (Fig. 9) is to
The calculation of the required capacity for the next period depends on the operating point on the operating characteristic curve for the work system. The developed concept for the backlog controller only functions, when the planned utilisation of the system is reached since otherwise backlog does not arise. The WIP controller is suitable for this task. The basic functionality of both controllers can be compared with the conventional production control methods. In the case of increasing backlog in a production system, it is useful to increase the capacity. If the range keeps growing, the line-up
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Fig. 10. Concept of a combined WIP and backlog controller.
(queue) in front of the work system can be diminished through reducing the input rate of the system. The logistic operating curve is a quali"ed tool for combining both concepts with each other. Simulation experiments have con"rmed that this approach guarantees the synchronisation of capacity and work. Fig. 10 shows the integration of both controllers in a controller concept [3,4]. The "rst step is to decide in which operating state on the characteristic curve the system should be driven. This can be done by deciding which utilisation the system ought to reach. For important or expensive systems this value must be higher than for the other systems. So the backlog control loop is enhanced by calculating the planned output "rst and then using the planned utilisation for determining the necessary capacity. The relative wip is multiplied by the mean wip minimum (mwip ). .*/ This results in the planned mean wip. Deviations between the planned and realised performance of
the system are integrated over a time interval and de"ned to be the backlog of the system. The backlog controller calculates the planned performance for the next period which is divided by the planned utilisation. The result represents the corrected capacity of the system. The planned relative mean wip is multiplied by the actual minimum mean wip. This delivers the planned mean wip as the reference value of the WIP controller for the next period. This value is compared with the actual mean wip in the system. If deviations occur the WIP controller corrects the input rate. The whole concept and the control design were created by using control theory methods and simulations. Furthermore simulations were used to evaluate the control design. Those simulation experiments testify that the described strategy ful"ls the requirements that were postulated in the beginning. The market often requires short-term changes for orders to be carried out without being planned in the production program. This leads to orders which must be executed unplanned but with high priority. In the upper part, Fig. 11 illustrates the e!ect of such an urgent order on a balanced system without control; in the lower part, with the described control system installed. The unplanned order with a work content of 10 hours arrives on shop calendar day scd 26. As it is called an urgent order it is processed immediately after its arrival. Due to this, WIP increases by 10 hours to 17 hours and backlog comes up because planned work cannot be carried out. Because of its low time constant the system is able to reduce both backlog and WIP to the initial level relatively fast (34 scd). If the balanced system was driven with a higher utilisation this would take much more time. For example, running with 98% utilisation the same system needs approximately 200 scd to balance the disturbance caused by one single unplanned order of 10 hours work content. The controlled system reacts completely di!erent (Fig. 11, lower part). As the "rst measure the WIP controller reduces the input rate to decrease WIP to the planned level. The backlog controller works periodically every 5 days and corrects the capacity after 2 days reaction time at scd 32 exactly to that
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4. Integration of the developed controllers in a PPC environment The PPC system of tomorrow will certainly not be based on an integrated circuit. From today's view, three areas can be identi"ed in which changes in PPC could arise from the previously mentioned approach. To begin with, it is to be expected that new elements enlarge the understanding of the process and its rules of behaviour as it was shown in the example above. Beyond this, it is quite imaginable that improved techniques and algorithms for the planning and enforcing of order processing can be developed on the basis of these models. It can be determined quite de"nitely, that it is necessary to think over the functional architecture in PPC if a controlled process is to be attained. The following are new characteristics of a process governed by controlling: Fig. 11. Impact of an unplanned urgent order on the control parameters.
value that is necessary to decrease the backlog to zero during the following period. Considering the reaction and the minimum installation time of Fig. 8, additional amounts of capacity greater than 2 additional hours daily are not suitable. Theoretically, the controller is able to correct the capacity to 12 hours/scd after 5 days of reaction time, but the minimum additional capacity area resulting from that, exceeds the target by 16 hours. At the same time the WIP controller increases the input rate. So there is enough work in the system. This demonstrates that work that cannot be performed is not released until there is su$cient capacity available to carry the work out. Capacity and work come together at the same time keeping ranges at the planned level and compensating disturbances between load and capacity. The quality of this process in a system with this control strategy installed is independent from the initial operating state of the production system. The behaviour of the uncontrolled system becomes worse in proportion with a higher utilisation as previously mentioned [3,4].
f short-term realisation of changing goals with respect to time and place (guidance behaviour), f compensation of occurring disturbances (disturbance sensitivity), f quickest possible attainment of a state of balance (stability). A proposal for such a functional concept is shown in Fig. 12. The levels, planning and operation, are kept in the usual form [15]. Main tasks are named within the levels with respect to production control. Three cross reference functions are mentioned alongside. The entire architecture must demonstrate a time independent transparency between the control variables and the parameters used in the functions. This can be realised most consistently when all implemented procedures are based as much as possible on the same models. The WIP controller a!ects the input side through the order release; the backlog controller has to guarantee the capacity. The higher the capacity #exibility of a production is, the more the output performance control attains importance. Capacity #exibility can be described by the length of time, in which a change of capacity can be realised and by the limits within which this change can range. The scheduling and generating of orders
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has to guarantee a continual and highest possible automatical adjustment of the models used, because even controlling cannot function correctly when the underlying control path model does not comply with reality anymore. All three cross-section functions work closely together and can mutually support each other [3,4].
References
Fig. 12. Functional architecture of an APC system.
are to be understood as correcting variables. The order generation results in the corresponding order structure which most likely arises in the work system. The scheduling sets up a dynamic loading plan for the work system and determines, beyond this, the planned start dates. The con"guration represents a function, which is largely unknown in the classical "eld of PPC. Its task is to secure the commitment of consistent and also reachable goals. On top of this, it represents the connecting link between goals and process parameters which brings about the transparency demanded above. The total system does not work automatically, but rather with a strong linkage to the human being. Other important cross-section functions are the model adaptation and the parameter evaluation. The task of the latter is the monitoring of the parameter adjustments during operation and, if necessary, to point out inconsistencies that arise. These inconsistencies can occur from disturbances or from the process itself. The model adaptation
[1] J. Milberg, Produktion } Eine treibende Kraft fuK r unsere Wirtschaft, Conference Proceedings `MuK nchener Koloquium &97 } Mit Schwung zum Aufschwunga (in German), Munich, February 1997. Moderne Industrie, Landsberg/Lech, 1997, pp. 17}39. [2] H.-P. Wiendahl, Load-Orientated Manufacturing Control, Springer, New York, 1995. [3] D. Petermann, Modellbasierte Produktionsregelung (in German), Fortschritt-Berichte VDI, Reihe 20, Nr. 193, VDI, DuK sseldorf, 1996. [4] H.-P. Wiendahl, J.-W. Breithaupt, Production planning and control on the basis of control theory, in: N. Okino, H. Tamura, S. Fujii (Eds.), Advances in Production Management Systems } Perspectives and Future Challenges, Chapman & Hall, London, 1997, pp. 351}362. [5] J.W. Forrester, Industrial Dynamics, Wiley, New York, 1961. [6] H. Chen, A. Mandelbaum, Hierarchical Modeling of Stochastic Networks, Part I: Fluid Models, in: D.D. Yao (Ed.), Stochastic Modeling and Analysis of Manufacturing Systems, Springer, New York, 1994, pp. 47}105. [7] W.J. Hopp, M.L. Spearman, Factory Physics}Foundations of Manufacturing Management, Irwin, Chicago, 1996. [8] G.F. Newell, Applications of Queueing Theory, 2nd Ed, Chapman&Hall, London, 1982. [9] D. Gross, C.M. Harris, Fundamentals of Queueing Theory, Wiley and Sons, New York, 1974. [10] J.D.C. Little, A proof for the queuing formula ¸"j=, Operations Research (9) (1961) 383}387. [11] H. Kettner, W. Bechte, Neue Wege der Fertigungssteuerung durch belastungsorientierte Auftragsfreigabe (in German), VDI-Z 123 (11) (1981) 127}138. [12] H.-P. Wiendahl, The throughput diagram, Annals of the CIRP 37 (1) (1988) 465}468. [13] P. Nyhuis, Logistische Kennlinien (in German), Habilitation at the University of Hannover, 1998. [14] P. Nyhuis, Durchlauforientierte LosgroK {enbestimmung (in German), Fortschritt-Berichte VDI, Reihe 2, Nr. 225, VDI, DuK sseldorf, 1991. [15] R. Hackstein, Produktionsplanung und-steuerung (PPS) } Ein Handbuch fuK r die Betriebspraxis (in German), VDI, DuK sseldorf, 1989.
Automatic production control applying control theory Hans-Peter Wiendahl, Jan-Wilhelm Breithaupt* Institute of Production Systems, University of Hannover, Callinstrasse 36, 30167 Hannover, Germany Received 1 April 1998; accepted 22 October 1998
Abstract A new dynamic production model for the planning level will be presented in this paper. The model is based on methods of control theory, which provide a large variety of appropriate tools for analysing and controlling dynamic systems. With the help of the funnel model and the theory of the logistic operating curve, a continuous #ow model of a single work centre has been designed. For the control task a backlog controller and a WIP controller have been developed. The controllers interact to adjust the capacity and the input rate of the work centre so as to eliminate the backlog as soon as possible and to set the WIP to a de"ned level. By means of envelope curves of capacity #exibility, which are easily applicable to industry, the individual range of capacity adjustments at a single work centre can be modelled. Simulation experiments con"rm that this concept ensures the synchronisation of capacity and work. The objective is to develop a closed-loop control for PPC with de"ned control and reference variables based on the logistical objectives. ( 2000 Elsevier Science B.V. All rights reserved. Keywords: PPC; Control theory; Dynamic systems; Production logistics; Production model
1. Challenges of global markets The frequently discussed challenges facing today's companies can be summarised as **meeting customer demands in the short-term within an agile network of competent partners in order to succeed in global competition++. Superiority in global markets is not dependent simply on continuous improvements in respect of the classical objectives costs, quality and time. These are expected by the customer as a matter of course and are not su$cient to * Corresponding author. Tel.: ##49-511-762-3813; fax: # #49-511-762-3814. E-mail address: [email protected] (J.-W. Breithaupt).
distinguish a company from potential competitors. Rather, new features of performance are becoming increasingly important. They can be described by the catchwords innovation capability, learning capability, and agility (Fig. 1) [1]. Agile companies distinguish themselves through speed in the planning and realisation process. Furthermore, they are strong in their adaptability to changing conditions in the production environment. Industry and researchers therefore need to develop their own innovative ideas and to expand them to create new tools and procedures. This paper o!ers a new perspective for the PPC of tomorrow. Going under the catchword automatic production control (APC), it could be very helpful in improving companies' competitiveness in the future.
0925-5273/00/$-see front matter ( 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 5 - 5 2 7 3 ( 9 8 ) 0 0 2 5 3 - 9
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Fig. 1. Features of global competition.
2. A continuous 6ow model of a job shop 2.1. The logistical objectives The quality of the logistical performance is determined by lead-time and due-date performance in the job shop as outlined in Fig. 2. On the other hand, the loading of the production facilities and the work-in-process (WIP) a!ect the pro"tability of the manufacturing process. From these partly
con#icting requirements within PPC the four main objectives of the production process can be derived. Short lead time and low schedule deviation represent the market-related objectives, whereas low inventory and high and steady loading of the work systems are the factory-related objectives. In order to be able to adjust the logistical objectives given their mutual dependency and the pressure for competitive production, it is necessary to design controllable production and order processing. While conventional PPC systems predominantly operate open-loop control and therefore lack automatic feedback, a self-controlling process can be achieved by a closed-loop control by de"ning appropriate reference and correction variables [3,4]. 2.2. Shortcomings of today's PPC systems
Fig. 2. Logistical objectives in manufacturing [2].
Today's PPC systems di!erentiate between the planning level and the operational level. The di!erentiation can also be applied to automatic production control. Because of the di!erent nature of the levels, di!erent models are required. Single orders are of interest on the operational level. A more global view on the planning level allows the application of #ow models in continuous time (e.g. [5,6]), for which control theory o!ers many more
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methods than for discrete models. Furthermore, the planning level de"nes the boundary conditions for achieving the targets on the operational level. It is therefore essentially the planning level which will be looked at in the following pages [3,4]. Countless approaches to modelling and controlling the dynamics of production systems have already been developed. The "rst works in this "eld were published by Forrester in the book Industrial Dynamics [5]. Most of these approaches are based on a simple control loop. The feedback in today's MRP II systems, which is restricted to the closing of information circuits, can be mentioned here as an example. The response has to be made by the system user according to the results. Such concepts lack a clear de"nition of the control variables and reference variables as well as a description of the relationship between e!ects. Thus, the correcting variables cannot be derived e!ectively. The deterministic models underlying this system merely describe reality statically (i.e. assumptions of in"nite capacities and "xed lead times) and are not appropriate for representing the dynamics of reality. Most of the systems are designed to enforce the plans that are thereby generated and are therefore characterised by a strong static nature [3,7]. 2.3. A yow network in continuous time with time inhomogeneous dynamics As mentioned above, continuous models are particularly suited for the application of methods and techniques based on control theory. It is therefore necessary to develop a continuous (i.e. #oworiented) stochastic job shop model for which control mechanisms have been designed and tested in a current research project at the Institute of Production Systems. A large amount of related literature can be found which deals with continuous #ow models (e.g. [6,8,9]). Within the scope of an investigation of #uid models Chen, and Mandelbaum [6] present a formula to describe the work-in-process of a work centre within a #ow network in continuous time with time inhomogeneous dynamics (Eq. (1)). The network outlined in the article consists of k work centres, each with an in"nite storage capacity. The work centres are interconnected by frictionless
35
pipes through which #uid #ows in and out of the work centres. mwip (t)"mwip (0)#extin (t) 03$%3,k 03$%3,k 03$%3,k k # + [out (t) 03$%3,.!9,j j/1 !out (t)]Hp 03$%3,-044,j j,k ![out (t)!out (t)] 03$%3,.!9,k 03$%3,-044,k (1) where mwip (t) 03$%3,k mwip (0) 03$%3,k extin (t) 03$%3,k out (t) 03$%3,.!9,j out (t) 03$%3,-044,j
out (t) 03$%3,.!9,k out (t) 03$%3,-044,k p jk
: mean work-in-process of centre k at time t (number of orders), : initial mean work-in-process of centre k (number of orders), : cumulative external input of centre k until time t (number of orders), : cumulative potential out#ow of upstream centre j until time t (number of orders), : cumulative potential lost of out#ow due to empty upstream centre j until time t (number of orders), : cumulative potential out#ow of centre k until time t (number of orders), : cumulative potential loss of out#ow due to empty centre k until time t (number of orders), : fraction of total output from centre j #owing directly to centre k (!).
The momentary work-in-process of work centre k depends on its initial inventory, its cumulated external input, the actual cumulative output of its upstream work centres #owing directly to k and its own actual cumulative output until time t. By means of Eq. (1), the dynamic behaviour of a work centre can only be described if the required parameters can be determined. Usually this can be done easily for the initial work-in-process, the external input, and the potential cumulative output of each work centre. More complicated is the determination of the relation between losses in
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utilisation (OUT ) and the momentary WIP-044,k level. In the literature, the only boundaries are those among which losses in utilisation are possible. A clear de"nition of the interdependencies between WIP and utilisation is missing. The funnel model and the derived theory of logistic operating curves are appropriate for "lling this gap. In contrast to the #ow network mentioned above and the models of queueing theory (e.g. Little's Law [10] (Eq. (2))), these models are based on a work-content description and not an orderrelated one. Also with the funnel model the order processing of a work system can be described as the #ow of a liquid through the funnel. The incoming orders, here measured in hours of work content, form a stock of pending lots, which have to #ow through the funnel outlet. The diameter of the outlet can be described as the capacity of the work system (also measured in hours of work content), which is adjustable within limits (actual performance). It is obvious that the lead time for incoming orders changes with the stock of pending orders and the system's performance [2]. These interdependencies between mean lead time (here: mean range, mr), mean work-in-process, mwip, and mean performance, mper, are stated through the funnel formula (Eq. (3)). Detailed derivations of the funnel model and formula are speci"ed in [2,11,12]. A comparison between the funnel formula and Little's Law is made in the following. For a better understanding variable names have been modi"ed. ¸ittle1s ¸aw: mwip "inrHmlt, 03$%3
(2)
Funnel formula: mwip "mperHmr, 803,
(3)
where mwip : mean order-related work-in-process 03$%3 [number of orders], minr : mean input (arrival) rate [number of orders/shop calendar day (scd)], mlt : mean lead time [scd], mwip : mean work-content-related work-in803, process [h], mper : mean performance [h/scd], mr : mean range [scd].
Another di!erence exists in the point of view: Little's Law focuses on the incoming orders (mean input rate), whereas the funnel model focuses on the outgoing orders (mean performance). Over a certain period of time a work centre can function in a stable state only if the mean input and output of the work centre match each other, because otherwise wip will increase constantly (minr'mper), or it will decrease (mper'minr) until the centre runs out of work. In a stable state minr can be principally equated with mper. Another di!erence exists in the description of the length of stay of orders at the work centre. Little uses the mean lead time, whereas the funnel formula includes the mean range (mean runout time of the work centre). Under speci"c circumstances the mean lead time can be derived directly from the mean range. This brief comparison shows that both models, whilst similar, have their individual range of applications. A more detailed comparison between the two formulas can be found in [13]. Nevertheless, the mutual dependencies between work-in-process and performance cannot be described directly by means of the funnel formula or Little's Law. To "ll this gap, the theory of logistic operating curves, which is based on the funnel model, has been developed by Nyhuis [14]. The logistic operating curve forms the connection between the mean wip, the mean range and the mean performance, with the aid of the capacity and the ideal minimal wip (order structure) as input parameters (Fig. 3) [2,14]. The curve states that the output of a work centre is independent of the mean work-in-process as long as every work system has a stock of pending orders at all times. If so, the performance of the system is equal to its capacity. Only if the inventory is further reduced will losses in production occur due to interruptions in the material #ow. On the other hand, the range decreases in proportion to the WIP until the physical minimum is reached. Beyond this point the range cannot be further reduced because it is limited by the sum of the operation time and transport time (ideal minimum of range). With regard to an ideal process, the ideal mean wip minimum (mwip ) represents the WIP level .*/ necessary to run the system, assuming that no arriving order has to wait and no interruption occurs
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37
Fig. 3. Interdependency between output, range and work-in-process (WIP) [14].
in the material #ow. This cannot be found in practice, so the realistic curves di!er from the idealised ones shown in (Fig. 3). Nyhuis [14] found that it is possible to calculate these realistic curves for most of the job shop productions with the following equations: mwip(x)"mwip (1!(1!Jx)4)#mwip 4 a x, .*/ .*/ 1 (4) mper(x)"mper (1!(1!Jx)4), 4 .!9
(5)
where mwip(x) : mean work-in-process [h], mper(x) : mean performance per shop calendar day [h/scd], mwip : idealised mean work-in-process min.*/ imum [h], mper : maximally available performance .!9 [h/scd], a : streching parameter } (default-value: 1 10), x : running parameter (0(x(1). The mean wip minimum necessary to determine mwip(t) can be calculated easily by means of
Eq. (6): mwip "mot #mtt .*/ 8%*')5%$ 8%*')5%$ +n (ot ot )2 +n (tt ot )2 " i/1 i i # i/1 i i , (6) +n ot +n ot i/1 i i/1 i where ot : order time of order i [h], i mot : mean weighted order time [h], 8%*')5%$ tt : transportation time of order i [h], i mtt : mean weighted transportation time 8%*')5%$ [h]. A detailed derivation of these formulas is speci"ed in [13,14]. With the aid of Eqs. (4) and (5), a pair of values for wip and performance can be calculated depending on the running parameter x. With these pairs, the course of the performance is de"ned. Using the funnel formula, the course of the mean range can also be determined. To come back to the #ow network described in Eq. (1), the work content of the orders #owing through the pipes can now be considered. It is thus possible to determine the actual output of the work centres by means of the operation curve. Eqs. (7)}(9) describe the continuous model of the job shop, which is presented in the following by means of
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control-theory elements:
where per (mwip (t)) : mean performance of centre j dej j pendent to the mean work-in-process of j at time t (h/scd), extinr (t) : external input rate of centre k at 03$%3,k time t (number of orders/scd), to
A
(t) mwip (t)"mwip (0)# extin 03$%3,k k k k # + [out (t)!out (t)] j,.!9 j,-044 j/1
B
1 ] p mot k mot j,k j ![out (t)!out (t)], k,.!9 k,-044
(7)
where mwip (t) k
: mean work-in-process of centre k at time t [h], mwip (0) : initial mean work-in-process of k centre k [h], extin (t) : cumulative external input of centre 03$%3,k k until time t [number of orders], out (t) : cumulative potential out#ow of up.!9,j stream centre j until time t [h], out (t) : cumulative potential lost of out#ow -044,j due to empty upstream centre j until time t [h], out (t) : cumulative potential out#ow of .!9,k centre k until time t [h], out (t) : cumulative potential loss of out#ow -044,k due to empty centre k until time t [h], p : fraction of total output from centre jk j #owing directly to centre k[!], mot : mean order time of upstream centre j j [h], mot : mean order time of centre k [h]. k Eq. (7) can be simpli"ed by means of
PA t
B
k 1 + per (mwip (t)) p dt j j mot j,k 0 j/1 j k 1 p " + [out (t)!out (t)] .!9,j -044,j mot j,k j j/1
(8)
and
P
t
extinr (t)dt"extin (t), 03$%3,k 03$%3,k 0
(9)
(10)
Determining the mean performance directly from the work-in-process is problematical because the resulting equations are fairly complex. By means of Newtons approximation procedure, a value for the running parameter x can be found in relation to the actual WIP-level. This value can be inserted into Eq. (5) to determine the centres actual performance. 2.4. A continuous job shop model based on control theory For the development of appropriate controllers based on control theory, the model described in Eq. (10) has to be designed on the basis of controltheory elements. A basic control-theory model for a single work centre has been developed and evaluated by Petermann [3]. In the following section, this model is extended for modelling several work systems connected via the material #ow. The input and output variables as well as a simple control loop of the continuous model are shown in Fig. 4. The incoming orders are converted into the input rate (dimension: number of orders per unit of time). Multiplied by the mean order time the dimension of the input rate is changed into work content per time unit. Similar to the input rate, the output of the work system is converted into the output rate by dividing the mean performance through the mean order time. These transformations are required because
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39
Fig. 4. Continuous model of a work centre.
the material #ow between two work centres is measured in number of orders per unit of time, whereas within the work centre the work content is of interest [2]. In reality the order time of several orders processed by a speci"c work system di!er. Therefore, the transformation leads to practicable result only over time periods long enough to enable the di!erent order times to balance. This can be mentioned on the planning level. The various sizes of the orders are considered through the mean weighted order time as a parameter of the order structure (Eq. (6)). As mentioned above, a simple control loop is depicted inside the continuous model. With the aid of an integrator the input rate is integrated over a time interval into the cumulated input (in) of the system. Analogous to this, the same procedure is followed for the cumulated output (out). The mean wip (mwip) is calculated as the di!erence between the input and output (summation point). With the aid of Eq. (3) the mean range can be calculated by dividing the mean wip through the output rate. The four variables, output rate, mean performance, mean range and mean wip, are the output variables of the system. The transmission function of the work centre is the logistic operating curve (Fig. 3). A major problem for the production control occurs due to the structural parameters, mwip and .*/ per , of the logistic operating curve which vary .!9
over time. This behaviour leads to a variable transmission function which is unacceptable for a control task. Therefore it is necessary to normalise the logistic operating curve. The normalised version describes the interdependence between the mean relative work in process (Eq. (11) based on Eq. (4)) and the mean utilisation (Eq. (12) based on Eq. (5)) [14]. mwip(x) mwip (x)" "1!(1!Jx)4#at, 4 (11) 3%mwip .*/ mper(x) mut(x)" "1!(1!Jx)4, 4 (12) mper .!9 where mwip : mean relative work-in-process [h], 3%mut : mean utilisation [h]. Therefore, the normalised logistic operating curve is the transmission function of the continuous model and forms the connection between the input and output variables. The control-theory model for a single work centre based on control-theory elements is appropriate for the connection of several work systems via the material #ow as described in Eq. (10). However, the connection itself between the systems is still missing. In order to implement the connections of a k : k model as described in Eq. (10) and to create a job shop model based on control theory, it
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Fig. 5. Derivation of the normalised material #ow matrix.
is essential to de"ne the transition probabilities. With the aid of a common material #ow matrix (MFM), which can be calculated using real feedback data from the job shop, it is possible to determine the probabilities. The MFM shows how many orders have been transported from each work system to another within the job shop during a speci"c period of time. The virtual starting and ending points are de"ned to describe the #ow of incoming and outgoing orders [2]. In the upper right part, Fig. 5 shows
a MFM for a job shop of consisting of six work systems. For the calculation of the transition probabilities, the absolute number of orders #owing from previous work systems to the subsequent ones is not of interest. What is far more important is the percentage relation of the distribution of the system's output as mentioned above. It is therefore necessary to normalise the material #ow in relation to the summarised output of each work system (Fig. 5, lower right part).
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41
Fig. 6. Example of a continuous job shop model (with 6 work systems).
Apart from this, the content of the normalised MFM is time independent as long as the structure of the production program remains the same. Only if the production program varies over a longer period of time, the model has to be adapted by using actual feedback data to calculate a new MFM. The normalised MFM can be integrated into the model based on control theory as a transition probability matrix. Fig. 6 shows a simulation model based on the job shop mentioned before. Each work system is represented through a `superblocka, which contains the elementary work system model. Analogous to the elementary work system model, each superblock has four inputs and outputs. Via the input and the output rate the superblocks are connected with the transition probability matrix block, which has the task to distribute the output of each work system to other work systems. The input as well as the output of the whole job shop is directly connected with this block.
3. The design of controller under consideration of the logistical objectives The design of a controller concept has to be divided into two di!erent steps. First of all, it is
necessary to de"ne the controllable output variables under consideration of the input variables. Afterwards, the connection and interaction of the controller has to be designed. 3.1. Dexnition of reference and control variables With the aid of the models presented two controllers for a work system have been modelled. The input and output variables of the continuous model have been discussed in Section 2.3. The variables output performance, wip, and range are linked through the funnel formula as mentioned above. Therefore only two of the variables are controllable simultaneously. The essential task of a work system is to allocate the required performance to process the system load (production schedule). For this reason the output performance, respectively, the output rate attains importance. On a closer examination of the system's output performance, the actual output rate is of less importance. The question of interest is whether the planned work is "nished by a certain date. The di!erence between the planned sum and the actual output is de"ned to be the backlog of the system. The backlog of the system thus becomes the most important control variable for monitoring
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Fig. 7. Concept of an automatic backlog controller.
the output performance of the production system. In order to utilise a clear de"nition, the developed controller is therefore named backlog controller instead of output controller. The capacity is used here as a correcting variable of the system. Fig. 7 shows the concept of a backlog controller. The planned performance is the reference variable. The di!erence between the actual and the planned performance is integrated over a time interval. The result is the above-mentioned backlog. Referring to the actual backlog the backlog controller adjusts the required capacity of the work system to reduce the backlog to zero as fast as possible. Because in reality it is impossible to adjust the capacity immediately, a reaction time between the request for capacity and the following allocation was introduced [3,4]. In an existing job shop the systems' capacity can normally be increased respectively decreased in different sized steps. For each step a speci"c reaction time is required. The fastness in that an increase or a decrease can be realised, is a measure for the system's capacity #exibility. Fig. 8 shows an example for a capacity installation/de-installation curve. These curves are integrated in the backlog controller of each single work system in the extended model. The capacity can be increased in several steps, considering the speci"c reaction time,
until the requested amount of capacity has been provided. Thereby, the controller also considers the minimum installation time of each capacity level, because in reality e.g. an additional shift cannot be employed for only one day, but for at least one week. This check is necessary, when the reaction time of the next step has been expired and a small backlog still remains. Using a higher capacity level the backlog can be decreased faster than with a lower one. But if the minimum installation time of this level will lead to an additional amount of capacity acap , that will exceed the requested .*/ amount, this capacity increase will not be realised. This check prevents from the installation of additional capacity that is not required. The de-installation of capacity is realised the same way using the de-installation curve. After de"ning the backlog as a control variable, a decision whether the range or the WIP shall be controlled is necessary. A controllable order processing based on production scheduling supports the implementation of the range as control variable. Two basic problems result from an implementation of the range: "rst of all, the measurement of the variable is di$cult; secondly, the range is limited at the bottom through the sum of the transportation and operation time. This is a major problem if the
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43
Fig. 8. Envelope curves of capacity #exibility.
set the system to an operating point on the operating characteristic curve that was de"ned within the scope of production planning. The planned wip is the reference variable. Referring to the di!erence between planned and actual wip the WIP controller adjusts the input rate of the production system [3,4]. 3.2. Combination of the backlog and the WIP controller
Fig. 9. Concept of an automatic WIP controller.
reference value of the range falls short of this limit. The mean wip as control variable is not limited. Moreover its measurement is easier and more precise. Therefore, it is obvious to use WIP control. The main task of the WIP controller (Fig. 9) is to
The calculation of the required capacity for the next period depends on the operating point on the operating characteristic curve for the work system. The developed concept for the backlog controller only functions, when the planned utilisation of the system is reached since otherwise backlog does not arise. The WIP controller is suitable for this task. The basic functionality of both controllers can be compared with the conventional production control methods. In the case of increasing backlog in a production system, it is useful to increase the capacity. If the range keeps growing, the line-up
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Fig. 10. Concept of a combined WIP and backlog controller.
(queue) in front of the work system can be diminished through reducing the input rate of the system. The logistic operating curve is a quali"ed tool for combining both concepts with each other. Simulation experiments have con"rmed that this approach guarantees the synchronisation of capacity and work. Fig. 10 shows the integration of both controllers in a controller concept [3,4]. The "rst step is to decide in which operating state on the characteristic curve the system should be driven. This can be done by deciding which utilisation the system ought to reach. For important or expensive systems this value must be higher than for the other systems. So the backlog control loop is enhanced by calculating the planned output "rst and then using the planned utilisation for determining the necessary capacity. The relative wip is multiplied by the mean wip minimum (mwip ). .*/ This results in the planned mean wip. Deviations between the planned and realised performance of
the system are integrated over a time interval and de"ned to be the backlog of the system. The backlog controller calculates the planned performance for the next period which is divided by the planned utilisation. The result represents the corrected capacity of the system. The planned relative mean wip is multiplied by the actual minimum mean wip. This delivers the planned mean wip as the reference value of the WIP controller for the next period. This value is compared with the actual mean wip in the system. If deviations occur the WIP controller corrects the input rate. The whole concept and the control design were created by using control theory methods and simulations. Furthermore simulations were used to evaluate the control design. Those simulation experiments testify that the described strategy ful"ls the requirements that were postulated in the beginning. The market often requires short-term changes for orders to be carried out without being planned in the production program. This leads to orders which must be executed unplanned but with high priority. In the upper part, Fig. 11 illustrates the e!ect of such an urgent order on a balanced system without control; in the lower part, with the described control system installed. The unplanned order with a work content of 10 hours arrives on shop calendar day scd 26. As it is called an urgent order it is processed immediately after its arrival. Due to this, WIP increases by 10 hours to 17 hours and backlog comes up because planned work cannot be carried out. Because of its low time constant the system is able to reduce both backlog and WIP to the initial level relatively fast (34 scd). If the balanced system was driven with a higher utilisation this would take much more time. For example, running with 98% utilisation the same system needs approximately 200 scd to balance the disturbance caused by one single unplanned order of 10 hours work content. The controlled system reacts completely di!erent (Fig. 11, lower part). As the "rst measure the WIP controller reduces the input rate to decrease WIP to the planned level. The backlog controller works periodically every 5 days and corrects the capacity after 2 days reaction time at scd 32 exactly to that
H.-P. Wiendahl, J.-W. Breithaupt / Int. J. Production Economics 63 (2000) 33}46
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4. Integration of the developed controllers in a PPC environment The PPC system of tomorrow will certainly not be based on an integrated circuit. From today's view, three areas can be identi"ed in which changes in PPC could arise from the previously mentioned approach. To begin with, it is to be expected that new elements enlarge the understanding of the process and its rules of behaviour as it was shown in the example above. Beyond this, it is quite imaginable that improved techniques and algorithms for the planning and enforcing of order processing can be developed on the basis of these models. It can be determined quite de"nitely, that it is necessary to think over the functional architecture in PPC if a controlled process is to be attained. The following are new characteristics of a process governed by controlling: Fig. 11. Impact of an unplanned urgent order on the control parameters.
value that is necessary to decrease the backlog to zero during the following period. Considering the reaction and the minimum installation time of Fig. 8, additional amounts of capacity greater than 2 additional hours daily are not suitable. Theoretically, the controller is able to correct the capacity to 12 hours/scd after 5 days of reaction time, but the minimum additional capacity area resulting from that, exceeds the target by 16 hours. At the same time the WIP controller increases the input rate. So there is enough work in the system. This demonstrates that work that cannot be performed is not released until there is su$cient capacity available to carry the work out. Capacity and work come together at the same time keeping ranges at the planned level and compensating disturbances between load and capacity. The quality of this process in a system with this control strategy installed is independent from the initial operating state of the production system. The behaviour of the uncontrolled system becomes worse in proportion with a higher utilisation as previously mentioned [3,4].
f short-term realisation of changing goals with respect to time and place (guidance behaviour), f compensation of occurring disturbances (disturbance sensitivity), f quickest possible attainment of a state of balance (stability). A proposal for such a functional concept is shown in Fig. 12. The levels, planning and operation, are kept in the usual form [15]. Main tasks are named within the levels with respect to production control. Three cross reference functions are mentioned alongside. The entire architecture must demonstrate a time independent transparency between the control variables and the parameters used in the functions. This can be realised most consistently when all implemented procedures are based as much as possible on the same models. The WIP controller a!ects the input side through the order release; the backlog controller has to guarantee the capacity. The higher the capacity #exibility of a production is, the more the output performance control attains importance. Capacity #exibility can be described by the length of time, in which a change of capacity can be realised and by the limits within which this change can range. The scheduling and generating of orders
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H.-P. Wiendahl, J.-W. Breithaupt / Int. J. Production Economics 63 (2000) 33}46
has to guarantee a continual and highest possible automatical adjustment of the models used, because even controlling cannot function correctly when the underlying control path model does not comply with reality anymore. All three cross-section functions work closely together and can mutually support each other [3,4].
References
Fig. 12. Functional architecture of an APC system.
are to be understood as correcting variables. The order generation results in the corresponding order structure which most likely arises in the work system. The scheduling sets up a dynamic loading plan for the work system and determines, beyond this, the planned start dates. The con"guration represents a function, which is largely unknown in the classical "eld of PPC. Its task is to secure the commitment of consistent and also reachable goals. On top of this, it represents the connecting link between goals and process parameters which brings about the transparency demanded above. The total system does not work automatically, but rather with a strong linkage to the human being. Other important cross-section functions are the model adaptation and the parameter evaluation. The task of the latter is the monitoring of the parameter adjustments during operation and, if necessary, to point out inconsistencies that arise. These inconsistencies can occur from disturbances or from the process itself. The model adaptation
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