DBR_CONWIP

Comparison of DBR with CONWIPin an unbalanced production line with three stations

Shie-Gheun Koh

Department of Industrial Engineering, Pukyong National University

Robert L. Bulfin

Department of Industrial and Systems Engineering, Auburn University

[Corresponding author]

S. G. Koh, Ph.D.

Department of Industrial Engineering

Pukyong National University

San 100, Yongdang, Namgu

Busan 608-739, South Korea

Phone : 82-51-620-1554 Fax : 82-51-620-1546

E-mail : [email protected]

Number of words : 5,565

Keywords : DBR(Drum-Buffer-Rope), CONWIP, Markov process, optimization

Comparison of DBR with CONWIP

in an unbalanced production line with three stations

Abstract

The recently developed alternatives to traditional production planning and control systems such as MRP

and Kanban are the drum-buffer-rope (DBR) and CONWIP (CONstant Work In Process) systems. Each

system is best described as a combination push (like an MRP) / pull (like a Kanban) logistical procedure.

Materials are pulled into the shop via the appropriate logic, and once released, materials are then pushed

to subsequent workcentres. We analyse and compare the performance of the DBR and CONWIP control

policies in a three-stage unbalanced tandem production line. Using a continuous Markov process model,

steady state probability distributions for the systems are derived, and then we can evaluate the

performance measures of the systems. To compare the two systems, we propose an optimization model

for each system. From sensitivity analyses for the optimization models, we validate the proposed models,

investigate differences of the two systems, and can find that DBR is better than CONWIP under the

proposed performance measures.

1. Introduction

Effective production control systems are those that produce the right parts, at the right time, at a

competitive cost. Traditional industries use a push type of production control such as material

requirement planning (MRP) to indicate the timing and quantity of production. In a push system, the

information flows from the beginning of the production line to the end of the line. Demand originates at

the initial stage and the production at this stage starts when the required raw material for this demand

arrives. Once the job is finished at that stage, it is moved to the next stage for further processing.

Production activation at the next stage is thus triggered by those items released from the preceding stage.

The problem with the push system including MRP is the high dependence on forecasted lead time that

leads to high inventory levels and poor lead time performance if a large forecasted error is included

(Chang and Yih 1994).

The success of Toyota’s kanban system has drawn a great deal of attention from researchers and

practitioners. This pull type of production control seeks to reduce the inventory to a minimal level and

shorten the lead time. In a pull system, production activation of a stage is triggered by a demand of the

subsequent stage. As opposed to a push system, demand originates at the end of the production line.

When demand arrives at the final stage, components for producing the demanded product are checked to

determine if they are available. If so, the production of this stage starts; otherwise, a request is issued to

1

the previous stage for the required parts. A similar procedure is followed backward through each

production process until the beginning stage. However, because of the restrictions in repetitive

environments, a kanban operation is generally not applicable to dynamic environments with variable

demands and variable processing times.

A recently developed alternative to traditional planning and control systems such as MRP and kanban

is the drum-buffer-rope (DBR), which is the key component of the theory of constraints (TOC) in

manufacturing organisations. The DBR methodology was developed by Goldratt and is now being

implemented by a growing number of manufacturing organisations. Schragenheim and Ronen (1990)

emphasized that this approach to shop floor control can reduce work-in-process (WIP) and improve the

general productivity of job shop operations.

The DBR consists of three major components, the drum, the buffer, and the rope. The drum is the

bottleneck resource, in other words, the constraint of the system; the constraint dictates the overall pace of

the system. In many cases, the drum has to include a detailed schedule of the constraint in order to ensure

the exploitation of the constraint. The buffer is protection time. Buffers are used to protect the bottleneck

from disruptions in the processing steps preceding the constraint. The rope is a mechanism to force all the

parts of the system to work up to the pace dictated by the drum and no more. The DBR is best described

as a combination push/pull logistical procedure. Materials are pulled into the shop via the rope based

upon the rate of usage of these materials at the bottleneck. Once released, materials are then pushed to

subsequent workcentres.

Another push/pull hybrid control system is CONWIP (CONstant Work In Process) proposed by

Spearman et al. (1990), which sets a limit on the total WIP in the entire system. In this system, materials

are pulled into the shop based upon the demand rate, and then materials are pushed to subsequent

workcentres. Spearman et al. (1990) say that CONWIP shares the benefits of kanban (e.g. shorter lead

times and reduced inventory levels) while being applicable to a wider variety of production environments

than kanban.

Although developed along very different reasoning, there are many similarities between DBR and

CONWIP. DBR is more general than CONWIP in that it can be applied to a pure job shop environment

whereas CONWIP cannot. However, when applied to flow lines, DBR and CONWIP result in similar

systems (Spearman et al. 1990). Despite the similarities between DBR and CONWIP, there are little

research results to compare these two control systems. Very recently (Gilland 2002), a simulation study

was done to investigate the performances of the two control systems in a specific production line.

In this paper we investigate a simple production line to compare the two control policies, DBR and

CONWIP. Using a continuous time Markov process model, the long run behaviour of the system is

investigated. To do this, the steady state probability distributions for the systems are derived, and then we

evaluate the performance measures of the systems.

The paper is organised as follows. Section 2 reviews the relevant literature. Section 3 introduces the

2

procedures to model the systems and proposes some performance measures to compare the two control

systems. Some numerical examples and sensitivity analysis are proposed in Section 4. Finally, Section 5

contains a summary and discussion of the results.

2. Literature review

2.1 DBR system

TOC/DBR emerged in the mid-1980s. In 1984, Goldratt and Cox (1984) presented the basic

performance measurement principles and logic of TOC in the form of a novel. Later, Goldratt and Fox

(1986) developed the production planning and control techniques further, and identified that component

of TOC as DBR. These planning and control techniques were further developed into buffer management

as described by Schragenheim and Ronen (1990).

In the 1990s, increased attention has been given to the implementation of DBR. Using simulation,

Cook (1994) compared three approaches to production and inventory control, a traditional manufacturing

system, the JIT system, and the TOC system and concluded that the TOC outperformed the other two

systems. Chakravorty (1996) documented an implementation of cellular manufacturing and DBR

concepts for a millwork shop. Miltenburg (1997) presented a five-step technical procedure for embedding

TOC into MRP along with an illustrative example from a micro-electronics plant. Russel and Fry (1997)

investigated two issues relating to the operation of the DBR, which include the order review/release

methodologies and the impact of splitting process batches into several transfer batches. Radovilsky

(1998) described an approach to calculate the optimal size of the time buffer, in which the problem was

formulated in terms of a single server finite queue. Sivasubramanian et al. (2000) presented a case study

to analyse the effect of the DBR approach on the performance of the system.

2.2 CONWIP system

Since Spearman et al. (1990) introduced the CONWIP system, much research dealing with the system

has been published. Hopp and Spearman (1991) studied CONWIP production lines in which processing

times are deterministic but machines are subject to exponential failures and repairs. Duenyas and Hopp

(1992) developed structural results and an approximation for the throughput of an assembly system fed by

multi-station fabrication lines where releases are governed by the CONWIP protocol and all machines

have deterministic processing times but are subject to random outages.

Spearman and Zazanis (1992) compared the CONWIP system with the pure kanban system and

offered theoretical motivations for the apparent superior performance of pull systems. Using a simulation

study, Roderick et al. (1994) compared the CONWIP and a typical MRP with respect to due dates and

cycle times to check the validity of the CONWIP model in an actual plant environment – Westinghouse

3

Electric. Chang and Yih (1994) proposed a modified kanban system to control a dynamic production

system and compared it with the original kanban system and the CONWIP system using simulation.

Duenyas and Keblis (1995) provided a simple, robust heuristic for the throughput of kanban controlled

and CONWIP controlled assembly systems.

In their two papers, Muckstadt and Tayur (1995 a, b) considered, simultaneously, four sources of

variability in production lines – processing time variability, machine breakdowns, rework and yield loss –

and showed some similarities and differences in their effects on the performance of the line. Gstettner and

Kuhn (1996) classified different pull production systems and analysed kanban and CONWIP with respect

to production rate and average WIP. Hopp and Roof (1998) developed an adaptive production control

method, termed Statistical Throughput Control, for setting WIP levels to meet target production rates in

the CONWIP system. Huang et al. (1998) introduced a simulation study that compared the CONWIP

system and the original control system for four situations in a cold rolling plant. Bonvik et al. (2000)

presented a decomposition method for approximation performance analysis of tandem production systems

that are controlled by the CONWIP/finite buffer hybrid policy. Duri et al. (2000) developed an

approximation method to obtain some performance measures in three stage production lines with random

processing time and random inspection. Framinan et al. (2000) studied the input control and dispatching

rules that might be used in a flow shop controlled by the CONWIP system within a make-to-stock

environment.

2.3 Buffer allocation problem

Numerous research has dealt with the optimal placement of a predetermined amount of buffer

capacity in production systems. Relatively small numbers of articles, however, are found in the area of the

unbalanced (or bottlenecked) production systems. Powell (1994) studied an unbalanced three-station

serial line and established a rule for buffer allocation in the line, in which imbalances in both means and

variances are considered. Baker et al. (1994) developed methods for predicting the throughput of

unbalanced three-station serial lines. They modeled the variability of processing times using a variety of

probability distributions that span the range of variability encountered in practise. Powell and Pyke (1996)

studied the optimal placement of buffers in serial lines with bottlenecks by undertaking detailed analyses

of the allocation of small numbers of buffers to lines with four, six, and eight stations. Later (1998), they

investigated unbalanced assembly systems and developed some heuristic rules that can be used to

improve existing operations and to design new assembly systems.

The studies in this category considered that the amount of WIP in each station is limited by the size of

the station’s buffer. In DBR and CONWIP systems, however, the WIP level is not limited for a single

station, but for a group of stations.

3. Model development

4

The system consists of three stations as depicted in figure 1. In front of each station, a storage buffer

exists to wait for processing in the station. To represent the system with a queueing network model, we

assumed the followings:

1) The processing time at each station is a random variable following the negative exponential

distribution with a mean , i=1, 2, 3.

2) The stations do not fail.

3) The second station ( ) is the constraint of the system. In other words, and .

<Insert figure 1 about here>

3.1 CONWIP system

In CONWIP system, the total amount of work is held constant by authorizing production of a new

part only when a finished part leaves the system. So, we can think that there are N kanbans in the system.

Let be the number of parts in the i-th storage buffer (i.e. ) and i-th station (i.e. ). Then we can

define the system state as follows:

, where and (1)

Notice that is not included in the system state variables. Since there are N kanbans in the system,

we know that , and then the system state does not need . From the system state, the

state space E and the total number of states NS are

(2)

(3)

Now we want to find the transition matrix for this Markov process. Let be exponentially

distributed and mutually independent random variables with a mean of for each , =1, 2, …, .

Then it can be easily shown that

(4)

and

(5)

5

Using equation (4), the elements of the transition matrix are easily found and the results are listed in table

1. For example, when , the possible states the system can reach from state (2, 3) are state (1, 3),

state (2, 2), and state (3, 3) with the associated parameters being , , and respectively. Thus, from

(4), the transition probability from state (2, 3) to state (1, 3) becomes .

<Insert table 1 about here>

Let be the duration of time the system remains at state , once it enters the state. Then, from (5),

is another exponential random variable with a mean of where

, for , ,

for ,

for and ,

for , and (6)

Let us define an NS-component row vector and an NS-component

column vector . Then there is a unique solution to

(7)

where is the transition matrix of the Markov chain. But this system of equations is redundant since it

has NS unknowns and NS + 1 equations. And we set a transformed system of equations as follows:

(8)

where is an NS-component row vector and is an matrix which is

derived by converting the first column of to where is an identity matrix. It is well

known that is a nonsingular matrix and

. (9)

This equation says that is the first row vector of .

Now consider a time interval (i.e. cycle time) starting with an entrance to a state and ending with

the next entrance to the state. It can be shown that the expected length of the cycle, , is

. (10)

Therefore, the long-run probability of a state is derived from the ratio of the expected value of the time

spent in the state to the expected cycle time for the state as follows:

. (11)

3.2 Performance measures

6

Once the probability of each state is obtained, the following performance measures that are

emphasized in TOC can be calculated.

1) System throughput

(12)

where is unit throughput value.

2) Operating expense

(13)

where is inventory holding cost per unit item.

3) Net profit

(14)

3.3 DBR system

In a DBR system, the total amount of work in the constraint and its preceding stations is held constant

by authorizing production of new part only when a part leaves the constraint. We assume that there are K

kanbans in the constraint and its preceding stations. Also we assume that the final station and its storage

buffer can hold M items. Let be the number of parts in i-th storage buffer (i.e. ) and i-th station (i.e.

). Then we can define the system state as follows:

, where and (15)

In this case, since there are K kanbans in , , , and , we know that , and then

the system state does not need . From the system state, the state space E and the total number of states

NS are

(16)

(17)

Using the same procedure as the CONWIP system, the transition matrix can be found. Table 2 lists

each element of the transition matrix.

7

<Insert table 2 about here>

In this case, the duration of time the system remains at state is an exponential random variable with

a mean of where

, for ,

for ,

for and ,

for , ,

for , and . (18)

The remaining procedure to find the long-run probability distribution for the states of DBR system is

the same as for the CONWIP system, e.g. equation (7) through (11). In the equations to calculate the

performance measures, however, there are some differences as follows:

(19)

and

. (20)

But the net profit can be calculated by the same way.

(21)

To distinguish from the CONWIP result, in these equations, we represented the long-run probability

distribution by instead of .

3.4 Optimal control policy

Using the performance measures, one can find the optimal control policy (N or K and M) that

maximizes the net profit NP for each system. In the CONWIP system, the procedure to find an optimal

control policy is very easy since there is only one decision variable as follows:

P1.

Max (22)

8

s.t.

(23)

where is the number of all stations (In our model, the value is 3.) and means

that is a function of the integer variable and then the decision variable is .

It seems to be impossible to verify the convexity of equation since is not

represented in a closed form. From the viewpoint of number of states, however, it seems to be a convex

function of . The equation is a sum of probabilities of states while the total number of states is

from equation (3). So, the ratio of state numbers is , and this is a decreasing

convex function.

After calculating numerous example problems, we believe the first term of the equation (22), the

system throughput, is an increasing concave function, and we can see an example of this in the figure 2. If

this is true for all the cases, equation (22) is a unimodal concave function, and then one can easily find an

optimal value of the discrete, lower bounded, and single decision variable for the unimodal concave

function.

In DBR system, however, there are two decision variables as follows:

P2.

Max (24)

s.t.

(25)

(26)

where is the number of stations including constraint itself and its preceding stations (In

our model, the value is 2.) and is the number of succeeding stations of the constraint (In

our model, the value is 1.). The objective function means that is a function

of the two integer variables and .

Observing many example problems, we found the equation (24) also seems to be a unimodal concave

function of the variable (or ) when the other variable, (or ), was fixed. So, there is no

difficulty to design a search procedure to find an optimal solution.

4. Comparison between DBR and CONWIP

As stated earlier, much research has compared the performances of production control systems like

MRP, JIT (kanban), CONWIP, and some modified versions of them. For example, Spearman and Zazanis

9

(1992) showed that a CONWIP system has better performance than a kanban system with the same

number of pallets. Later, Gstettner and Kuhn (1996) compared a modified kanban system with the

CONWIP system. But little has been done comparing DBR and CONWIP. Now, we compare the

performances of the DBR system with those of the CONWIP system.

4.1 Output versus average WIP

First of all, we compared the two systems on the output per unit time with the same WIP level. The

results are depicted in figure 2. In this figure, the horizontal axis represents the average WIP level of each

system while the vertical one represents its throughput. The throughput is represented by a percentage

value of the system’s output to the capacity of the system constraint. This figure shows that the system’s

output cannot exceed the capacity of the constraint. This is a basic principle of TOC. The TOC says that

the system’s throughput depends only on the system constraints and we have to control a system from the

viewpoint of constraints.

In figure 2 the value of WIP in the CONWIP system equals since there always exist WIPs in

the CONWIP system. On the other hand, the WIP level in the DBR system can be varied, and so, one has

to use an average value in this figure. Comparing two lines in this figure, we see that the DBR system is

slightly better than the CONWIP system. When the average WIP level of DBR system equals the value of

CONstant WIP level of the CONWIP system, the DBR system can produce more (0.05% to 2.81% in the

figure) products during the same time period.

<Insert figure 2 about here>

4.2 Comparison by optimum values

In this section we compare the results of the optimization models, P1 and P2, given in section 3.4.

The results are shown in table 3, 4, 5, and 6. In each table, one parameter varies over a range, while all

other parameters are held constant. We set = 15 units per unit time, = 10 units per unit time, =

15 units per unit time, = 50 dollars per unit, and = 2 dollars per unit per unit time as standard

parameter values. For example, the results of table 3 are calculated for when the

others are fixed as = 10, = 15, = 50, and = 2.

The values in each table are optimal values of P1 and P2. For example, the last row of table 3 shows

the results of the case = 26. First, in problem P1 (e.g. CONWIP system), the optimal value of N is 10

and thus the average WIP is 10. System throughput in this case is $455.7 per unit time. And the value

475.7 means the optimal objective function value of the problem, e.g. the net profit of the system. The

other values in the row are related to problem P2 (e.g. DBR system). The optimal values of K and M are 5

and 31, respectively. Moreover, the throughput, average WIP, and net profit of the system are $469.6 per

unit time, 6.9 units, and $483.5 per unit time, respectively.

10

Now we observe the effects of the system parameters to optimal values of the system performance

measures (throughput, average WIP, and net profit). In tables 3 through 6, we see that the two systems

(CONWIP and DBR) respond very similarly to changes of the system parameters. But, from the

viewpoint of net profit, DBR is better than CONWIP.

Tables 3 and 4 show that the optimal values of system throughput become large as or increases

in both the systems. Also the pattern of the increase is concave as in the curve in figure 2. This is a

reasonable result since the system’s output increases with a limit (equal to the capacity of the system

constraint) as the capacity of the non-constraint becomes large. On the other hand, the optimal values of

average WIP become small as or increases in both systems. The reason is that the system with

small WIP level can produce more products (or throughput) to maximize net profit if the machine

capacity becomes large.

In tables 3 and 4, we see that the optimal net profit value of DBR is larger than CONWIP with

differences varying from 0.16% to 1.64% and from 0.13% to 1.24%, respectively. As increases or

decreases, the difference becomes large, in other words, DBR becomes better and better than CONWIP.

This result means that the difference of control policies for a production line becomes small if the

capacities of rear stations in the line are relatively larger than fore stations of the line. If the capacities of

succeeding stations are greater than preceding stations, there will be less blocking problems in the flows

of materials, and then the control policy becomes less important.

<Insert table 3 and 4 about here>

Table 5 shows that the optimal system throughput values increase almost linearly as increases in

both the systems (DBR and CONWIP). From the viewpoint of equation (12) and (19), this result agrees

with intuition. Moreover, we can see the optimal values of average WIP levels become large as

increases in the two systems. The reason is that the bigger buffer capacity will result in a more productive

system. If the systems have larger , in other words, the benefit of increasing productivity resulting

from higher WIP is relatively lager than the increase of the WIP cost. Table 6 shows the effects of .

The results are the reverse of table 5. We agree with these results since we know that the two cost

parameters, and , have opposite characteristics.

Like the earlier tables, tables 5 and 6 also show that the optimal net profit value of DBR is larger than

CONWIP with differences varying from 0.47% to 2.51% and from 0.42% to 3.77%, respectively. One can

find the difference becomes large as decreases or increases. This can be explained as follows: If

increases or decreases, the WIP level of the system tends to increase to produce more products.

And if the system has much WIP, the importance of a control policy becomes small. So, the difference of

optimal net profit values of the two systems becomes small.

11

<Insert table 5 and 6 about here>

5. Conclusions

In this paper we investigated the behaviours of DBR and CONWIP systems and compared the

performance of the two systems. For the investigation and comparison, we use a simple linear production

line that consists of three unbalanced (e.g. different in their capacities) stations. Production times in each

station are assumed to be negative exponential random variables. Using the continuous Markov process

model, steady state probability distributions for the systems are derived, allowing evaluation of the

performance measures of the systems. To compare the two systems, we proposed an optimization model

for each system. From sensitivity analyses for the optimization models, we verified the proposed models

and investigated differences of the two systems.

From the viewpoint of the proposed performance measures, we find that DBR was better than

CONWIP. Although the difference varies, optimal net profit values of DBR are bigger than CONWIP for

all the cases tested. The only downside of DBR is that the system has large buffer areas at the succeeding

stations of the constraint (values of M in tables 3 through 6). This may be one of the reasons for the

consistently higher throughput of DBR relative to CONWIP. As one can see from the average WIP values

in these tables, however, the probabilities to get much WIP in those buffers are very small, and there is

little problem using a DBR system.

Even though this paper showed the benefits of a DBR system, it was only for a simplified production

system. So, this paper should be extended to more generalized systems that have multi stations, non-linear

material flow, non-exponential processing times, and a possibility of failure. But it may be difficult to

study these complicated systems by analytic procedures, then one has to use simulation approach to study

more generalized systems.

Acknowledgement

This work was supported by Pukyong National University Research Abroad Fund in 2002.

12

References

Baker, K.R., Powell, S.G. and Pyke, D.F., 1994, A predictive model for the throughput of unbalanced,

unbuffered three-station serial line. IIE Transactions, 26(4), 62-71.

Bonvik, A.M., Dallery, Y. and Gershwin, S.B., 2000, Approximate analysis of production systems

operated by a CONWIP/finite buffer hybrid control policy. International Journal of Production

Research, 38(13), 2845-2869.

Chakravorty, S.S., 1996, Robert Bowden Inc.: a case study of cellular manufacturing and drum-buffer-

rope implementation. Production and Inventory Management Journal, 37(3), 15-19.

Chang, T.M. and Yih, Y., 1994, Generic kanban systems for dynamic environments. International Journal

of Production Research, 32(4), 889-902.

Cook, D.P., 1994, Simulation comparison of traditional, JIT, and TOC manufacturing systems in a flow

shop with bottlenecks. Production and Inventory Management Journal, 35(1), 73-78.

Duenyas, I. and Hopp, W.J., 1992, CONWIP assembly with deterministic processing and random outages.

IIE Transactions, 24(4), 97-109.

Duenyas, I. and Keblis, M.F., 1995, Release policies for assembly systems. IIE Transactions, 27(4), 507-

518.

Duri, C., Frein, Y. and Lee, H.S., 2000, Performance evaluation and design of a CONWIP system with

inspections. International Journal of Production Economics, 64(1-3), 219-229.

Framinan, J.M., Ruiz-Usano, R. and Leisten, R., 2000, Input control and dispatching rules in a dynamic

CONWIP flow-shop. International Journal of Production Research, 38(18), 4589-4598.

Gilland, W.G., 2002, A simulation study comparing performance of CONWIP and bottleneck-based

release rules. Production Planning and Control, 13(2), 211-219.

Goldratt, E.M. and Cox, J., 1984, The Goal (North River Press).

Goldratt, E.M. and Fox, R.E., 1986, The Race (North River Press).

Gstettner, S. and Kuhn, H., 1996, Analysis of production control systems kanban and CONWIP.

International Journal of Production Research, 34(11), 3253-3273.

Hopp, W.J. and Roof, M.L., 1998, Setting WIP levels with statistical throughput control (STC) in

CONWIP production lines. International Journal of Production Research, 36(4), 867-882.

Hopp, W.J. and Spearman, M.L., 1991, Throughput of a constant work in process manufacturing line

subject to failures. International Journal of Production Research, 29(3), 635-655.

Huang, M., Wang, D. and Ip, W.H., 1998, Simulation study of CONWIP for a cold rolling plant.

International Journal of Production Economics, 54(3), 257-266.

Miltenburg, J., 1997, Comparing JIT, MRP and TOC, and embedding TOC into MRP. International

Journal of Production Research, 35(4), 1147-1169.

Muckstadt, J.A. and Tayur, S.R., 1995(a), A comparison of alternative kanban control mechanisms. I.

13

Background and structural results. IIE Transactions, 27(2), 140-150.

Muckstadt, J.A. and Tayur, S.R., 1995(b), A comparison of alternative kanban control mechanisms. II.

Experimental results. IIE Transactions, 27(2), 151-161.

Powell, S.G., 1994, Buffer allocation in unbalanced three-station serial lines. International Journal of

Production Research, 32(9), 2201-2217.

Powell, S.G. and Pyke, D.F., 1996, Allocation of buffers to serial production lines with bottlenecks. IIE

Transactions, 28(1), 18-29.

Powell, S.G. and Pyke, D.F., 1998, Buffering unbalanced assembly systems. IIE Transactions, 30(1), 55-

65.

Radovilsky, Z.D., 1998, A quantitative approach to estimate the size of the time buffer in the theory of

constraints. International Journal of Production Economics, 55(2), 113-119.

Roderick, L.M., Toland, J. and Rodriguez, F.P., 1994, A simulation study of CONWIP versus MRP at

Westinghouse. Computers & Industrial Engineering, 26(2), 237-242.

Russel, G.R. and Fry, T.D., 1997, Order review/release and lot splitting in drum-buffer-rope. International

Journal of Production Research, 35(3), 827-845.

Schragenheim, E. and Ronen, B., 1990, Drum-buffer-rope shop floor control. Production and Inventory

Management Journal, 31(3), 18-22.

Sivasubramanian, R., Selladurai, V. and Rajamramasamy, N., 2000, The effect of the drum-buffer-rope

(DBR) approach on the performance of a synchronous manufacturing system (SMS). Production

Planning and Control, 11(8), 820-824.

Spearman, M.L., Woodruff, D.L. and Hopp, W.J., 1990, CONWIP: a pull alternative to kanban.

International Journal of Production Research, 28(5), 879-894.

Spearman, M.L. and Zazanis, M.A., 1992, Push and pull production systems: issues and comparisons.

Operations Research, 40(3), 521-532.

14

B1 S1B2 S2

B3 S3

Figure 1. A serial production line

Table 1. Transition matrix for CONWIP system

State before transition State after transition Probability Subscript

(0,0) (1,0) 1

1

and

1

Table 2. Transition matrix for DBR system

State before transition State after transition Probability Subscript

(0,0) (1,0) 1

and

1

1

Figure 2. Performance comparison of the CONWIP and the DBR systems

Table 3. Effects of to the system performances

CONWIP DBR

N T NP K M T NP

10 17 400.8 17 434.8 15 22 402.2 16.6 435.5

12 15 430.4 15 460.4 12 27 434.4 13.8 462.0

14 13 442.2 13 468.2 10 29 447.3 11.9 471.1

16 11 449.6 11 471.6 8 29 455.9 9.9 475.8

18 11 451.3 11 473.3 7 29 460.7 8.9 478.5

20 10 454.3 10 474.3 6 30 464.4 7.9 480.2

22 10 455.0 10 475.0 6 31 465.8 7.9 481.7

24 10 455.4 10 475.4 6 30 466.6 8.0 482.5

26 10 455.7 10 475.7 5 31 469.6 6.9 483.5

Table 4. Effects of to the system performances

CONWIP DBR

N T NP K M T NP

10 17 400.8 17 434.8 7 22 405.8 17.2 440.2

12 15 430.4 15 460.4 8 46 443.6 12.4 468.5

14 13 442.2 13 468.2 9 33 450.1 11.4 472.9

16 11 449.6 11 471.6 9 26 453.2 10.6 474.4

18 11 451.3 11 473.3 9 22 454.8 10.2 475.2

20 10 454.3 10 474.3 9 16 455.7 10.0 475.6

22 10 455.0 10 475.0 9 17 456.3 9.8 476.0

24 10 455.4 10 475.4 9 15 456.8 9.7 476.2

26 10 455.7 10 475.7 9 15 457.1 9.6 476.4

Table 5. Effects of to the system performances

CONWIP DBR

N T NP K M T NP

10 7 65.9 7 79.9 5 20 68.7 6.6 81.9

12 9 157.8 9 175.8 7 25 160.7 8.8 178.3

14 10 253.3 10 273.3 7 25 258.7 8.8 276.3

16 11 349.6 11 371.6 8 27 355.2 9.9 374.9

18 12 446.3 12 470.3 9 29 452.0 10.9 473.8

20 12 545.1 12 569.1 9 29 551.1 10.9 572.9

22 13 642.3 13 668.3 10 30 648.2 11.9 672.0

24 13 741.5 13 767.5 10 30 747.6 11.9 771.5

26 14 838.8 14 866.8 10 31 847.0 11.9 870.9

Table 6. Effects of to the system performances

CONWIP DBR

N T NP K M T NP

1 14 469.1 14 483.1 10 30 473.2 11.9 485.1

3 11 426.0 11 459.0 8 28 434.1 9.9 463.7

5 9 394.4 9 439.4 7 25 401.7 8.8 445.8

7 8 366.2 8 422.2 6 24 376.2 7.7 430.3

9 7 343.6 7 406.6 5 23 356.6 6.6 416.3

11 7 315.6 7 392.6 5 21 330.1 6.6 403.0

13 6 301.6 6 379.6 4 20 319.7 5.5 390.9

15 6 277.6 6 367.6 4 19 297.8 5.5 379.9

17 6 253.6 6 355.6 4 17 275.9 5.5 369.0