Equipment utilization based maintenance task scheduling in a job shop

European Journal of Operational Research 45 (1990) 191-202 North-Holland

191

Equipment utilization based maintenance task scheduling in a job shop Avijit B A N E R J E E and Jonathan S. B U R T O N

Department of Management and Organizational Sciences, Drexel Unioersity, Philadelphia, PA 19104, USA

Abstract: This study examines, through a series of simulation experiments, the performance of a dynamic job shop, where the equipment is subject to failure. A number of decision rules are developed and tested based on individual machine utilization, for the purpose of scheduling the maintenance activities, in terms of a number of selected performance criteria, under different operating conditions. In addition to maintenance sequencing, the issues of, first the level of preventive maintenance activity and, secondly, the size of the maintenance workforce are examined concurrently. The results of the simulation experiments are analyzed and an attempt is made in arriving at some general conclusions concerning the relative effectiveness of the various types of decision rules under consideration.

Keywords: Maintenance, job shop, scheduling, simulation

1. Introduction The failure of equipment and machinery can often be a hindrance to the efficient operation of any production system [8]. Although the literature concerning various aspects of system maintenance is substantial (see [12,14,16] for surveys), most of the work in this area is confined to systems of relatively simple configuration. Studies dealing with the application of various maintenance strategies in realistic situations, involving multiple machines, inputs and outputs, are relatively rare, due to the sheer complexity of the problem (A1calay and Buffa [1] contend that mathematical analysis of such systems may be infeasible) and most of the limited amount of work in this area employ simulation techniques. One recent simulation study has examined the effectiveness of several maintenance strategies in a group technology environment [2], while others have tended to focus largely on various aspects of maintenance manpower [4,10,15]. Nevertheless, the integration of maintenance policies with the operational tactics of complex systems, taking their Received June 1989

interactions into consideration, has received scant research attention. Our aim in this paper is to formulate and evaluate the performance of a number of maintenance policies (involving preventive maintenance frequency, repair crew size and maintenance task scheduling procedure) under various operating conditions in a dynamic job shop (which is perhaps the commonest example of a complex, multiproduct system) through a series of simulation experiments. Generally speaking, maintenance policies may be classified into the following two categories [11]: 1. Policies that attempt to reduce the frequency of failures, such as preventive maintenance, early replacement of machines, equipment overbuilding, etc. 2. Policies that attempt to reduce the severity of failures, such as speeding of maintenance service through increased resource allocation, easing the task of repair by modular design, provision of alternate means of output during repair, etc. It is conceivable that several of the maintenance decisions mentioned above may have significant interactions with scheduling decisions in a job shop environment. However, the mainstream of job shop research does not incorporate such

0377-2217/90/$3.50 © 1990 - Elsevier Science Publishers B.V. (North-Holland)

192

A. Banerjee, J.S. Burton / Maintenance scheduling in a job shop

considerations, although some recent efforts have been made towards the integration of maintenance with flight scheduling in the airlines industry [9]. By and large, job shop related simulation studies tend to be concerned with the development and evaluation of priority rules for sequencing competing jobs on one or more machines, ignoring the possibility of equipment failure and bypassing the issue of preventive maintenance by assuming that such functions are performed off-shift [7,13]. In real world job shops, nevertheless, machine failures do occur and alternate job routing, preventive maintenance, standby equipment and other policies are used to ameliorate the ill effects of breakdowns. Furthermore, some job shops operate around the clock, 24 hours a day, dictating the on-shift scheduling of preventive maintenance. In addition to the above considerations, the provision of appropriate maintenance capacity may also be a significant problem. In some instances, repair and preventive maintenance tasks are performed by the machine operators, which allow us to bypass this question. But in many other cases, the intricate nature of the equipment in use requires that such tasks be performed by specialized repair mechanics or maintenance crews. Under such a circumstance, the question of an adequate maintenance workforce size, determining the level of overall maintenance capacity, needs to be addressed. Clearly, provision of excess maintenance manpower results in excess costs and underutilization of maintenance resources, while too small a maintenance workforce is likely to impair maintenance activities and increase system downtime. Therefore, the tradeoffs involved in varying maintenance capacity need to be examined for the better design of systems, where such considerations are relevant. The notion of a job shop (which is subject to machine breakdowns) with a limited capacity for preventive and corrective (i.e. repair) maintenance gives rise to some interesting questions regarding the scheduling of these maintenance activities. Establishment of priorities among various maintenance tasks, if the number of machines requiring such service exceeds the number of maintenance workers available at a given time, appears to be of primary concern in this respect. Also, the scheduling of maintenance activities in conjunction with job sequencing may be of some importance. Unfortunately, these questions are not addressed in

the current literature. It has been suggested that equipment service priority should be established based on downtime cost or degree of utilization as a surrogate measure, in the absense of such cost estimates [6,15]. There is, however, no research evidence to either prove or disprove the efficacy of such an approach. One important thrust of this paper lies in the development and testing of utilization based maintenance scheduling procedures under various operating conditions and decision rules, in terms of some selected performance criteria. In addition, we also focus on the concurrent issues of maintenance capacity (i.e. maintenance workforce size) and preventive maintenance frequency, suggesting some broad guidelines towards the development of an effective integrated maintenance approach. It is hoped that this study will establish the groundwork and point the way towards more effective approaches for system maintenance in conjunction with scheduling of jobs on machines.

2. Simulation model

In order to pursue our objectives, we employ a simulation model of a hypothetical job shop, consisting of four distinct machine groups. Each group (i.e. department) contains three similar, but not identical, machines. The shop operates around the clock, 24 hours a day. Incoming jobs are assumed to arrive at a Poisson rate from outside the system. These jobs are routed within the shop by means of a fixed transition matrix, so that the workloads on the various machines are considerably different. This imbalance is created deliberately for the purpose of testing the ability of utilization based decision rules to alleviate production bottlenecks. The number of operations per job is selected randomly from a uniform distribution ranging from two to six. The processing time of each operation is randomly chosen from an exponential distribution with a mean of 5 hours. We introduce the possibility of machine failures, as a departure from the classical job shop model. Machine breakdowns are modeled by the Erlang-4 distribution, which is not uncommon in the maintenance literature [12]. The mean time between failures (MTBF) varies from 70 to 130 hours of operation, for the 12 machines in the shop. In the event of a failure, the breakdown repair time is

A. Banerjee, J.S. Burton / Maintenance scheduling in a job shop

assumed to be exponentially distributed, with a mean of 2 to 8 hours, depending on the machine. A machine can fail only while performing an operation, and, when a breakdown occurs, the incomplete job is set aside until the repair work is completed. Once repaired, the machine completes the processing of this job before the next job is selected from queue, if any. It is assumed that no scrap or rework results from an equipment failure. For the purpose of reducing the frequency of breakdowns, a number of preventive maintenance (PM) policies are used. The PM service time for each machine is modeled by a uniform distribution defined in the range 0.9 (Tp) to 1.1 (Tp), where Tp is the mean. This is a reasonable assumption, since PM tasks are relatively routine in nature. The average PM service time varies from 1 to 4 hours for the various machines in the shop. For simplicity, the ratio of expected PM service time to expected repair service time for each machine is fixed at 0.5. Breakdown repair and PM service tasks are performed by maintenance personnel, who are employed in addition to the machine operators. An individual maintenance worker is capable of performing corrective (repair), as well as preventive maintenance tasks. We also assume that any required repair or PM service task is performed by a single maintenance worker. Thus, varying maintenance workforce sizes represent varying levels of maintenance capacity and the severity of breakdowns and the resulting disruptive effects may be reduced by increasing the number of such workers.

3. Experimental design As Baker [3] has pointed out, the multiple objectives of the job shop scheduling problem fall in two major categories: shop time measures and due date performance. Previous research has established that the shortest processing time (SPT) job sequencing rule, or modified versions of it, tend to dominate other priority rules with respect to the shop time related criteria [7]. Unfortunately, there is no single job sequencing rule that is similarly dominant in terms of the due date related performance measures. Thus, we incorporate the following two job priority rules in this study: 1. The first come first served (FCFS) rule. 2. The shortest processing time (SPT) rule, which focuses on the shop time criteria.

193

The overall workload on the shop is varied by using different job arrival rates. By trial and error, we select three mean interarrival times of 2.0, 2.2 and 2.4 hours, that, with the SPT rule in effect and without allowing machine failures to occur, result in individual machine utilizations of approximately 80% to near 100%, 70% to 95% and 60% to 80%, respectively. These various degrees of overall shop load are arbitrarily termed, respectively, "heavy", "medium" and "low". Furthermore, we vary the maintenance capability of the system with different maintenance workforce sizes, i.e. 1, 2 and 3 such workers. By changing this factor we intend to examine the effects of changing the tightness of the maintenance capacity constraint. In attempting to reduce the frequency of equipment breakdowns, a total of five PM policies are used: 1. NOPM: No PM is performed, only corrective maintenance (CM) is used in the event of failure. 2. PM(0.3): for each machine, a PM service is scheduled after every 0.3 (MTBF) periods of operation since the last PM or CM service. 3. PM(0.5): for each machine, a PM service is scheduled every 0.5 (MTBF) periods of operation. 4. PM(1): a PM service is scheduled after exactly MTBF periods of operation for each machine. 5. PM(1.5): for each machine, a PM service is scheduled after every 1.5 (MTBF) periods of operation. With any of the last four policies in effect, at the time of a scheduled PM task, the current job being processed, if any, is allowed to be completed before beginning the maintenance task. For allocating the limited maintenance personnel to CM and PM tasks, when they become necessary, the following maintenance task scheduling techniques are defined: 1. FCFS~": when two or more machines require CM a n d / o r PM service and a maintenance worker becomes available, the first come first served rule is used to assign this worker to a particular machine. 2. SSTm: an available worker is assigned to the machine which has the shortest expected CM or PM, as the case may be, service time (SST). 3. LNGQm: an available worker is assigned to the machine which has the longest queue of jobs among those that require service.

194

A. Banerjee, J.S. Burton / Maintenance scheduling in a job shop

4. LTQm: an available worker is assigned to the machine requiring service, for which the total time of all the jobs in queue is the largest. 5. MAXUm: an available worker is assigned to the machine which has the maximum utilization to date, among those that require service. 6. WLTQm: for each of the machines that require service, a weighted priority index is calculated by multiplying the total time for all jobs in queue by its utilization to date and an available worker is assigned to the machine which has the highest value of this index. In the case of each of these maintenance task scheduling rules, breakdown repair (CM) tasks are given priority over scheduled PM activities. Ties are broken by means of the FCFS rn rule. The FCFS m rule, which is often used in practice by default, is selected to serve as a benchmark, while the SST m procedure, being analogous to the SPT job sequencing technique, is of some interest. The rationale for the L N G Q m method is that, at a given instant, the machine with the longest queue of jobs reflects high current utilization, and, possibly, a bottleneck in the system. The L T Q r" rule is similar, but uses the total time of all jobs in queue, rather than their number, as a measure. The M A X U m procedure is based on historical, rather than current, utilization, which is computed on the basis of uptime. The last of the above rules, i.e. W L T Q m, attempts to schedule maintenance tasks according to both historical utilization and a surrogate of current utilization. In summary, the simulation experiments are conducted within the framework of a full factorial design, as follows: Factor 1: Shop load - 3 levels. Factor 2: Job sequencing rule - 2 levels. Factor 3: Maintenance scheduling rule - 6 levels. Factor 4: PM policy - 5 levels. Factor 5: Maintenance workforce size - 3 levels. From the above, we have 3 × 2 x 6 x 5 x 3 = 540 experimental conditions, i.e. cells, in our design. With five replications per cell, a total of 2700 simulation runs are made. For each of these factor level combinations, we start with an empty system. After 1000 hours of operation, which have been found to be adequate for the system to achieve steady state under any experimantal condition, the performance criteria counters are reset to zero and from this point data are collected for

another 3000 hours of system operation for each replication. For evaluating the performance of the system under the various decision rules used and operating conditions adopted, we select the following eight performance measures, likely to be of importance: 1. The average flow time of all jobs completed in hours. 2. The standard deviation of flow times in hours. 3. The utilization of maintenance workforce expressed as a percentage. 4. The total number of machine failures. 5. The total number of PM tasks performed. 6. The average number of hours a machine has to wait, due to the lack of a maintenance worker, before its repair work can begin. 7. The average hours of delay incurred in starting scheduled PM tasks on a machine, due to either an in-process job on the machine or the unavailability of maintenance personnel at the scheduled time. 8. Overall system downtime as a percentage of total time. Although a bulk of the existing work in system maintenance attempt to maximize profits or minimize costs [16] we deliberately do not assign any costs or monetary measures to the above criteria. In the first place, such monetary coefficients get assigned in an arbitrary fashion in most simulation studies. Secondly, every real world system has its own cost characteristics, and arbitrary assignments of monetary coefficients to the performance measures, may obscure some of the general conclusions that may be drawn otherwise. In the case of each performance measure cited above, the results are analyzed using five-way analysis of variance. The differences resulting from the various levels of the factors are tested pairwise using the N e w m a n - K e u l s procedure. For these tests the experimentwise probability of type I error is limited to 10%.

4. Results and analysis The results of the simulation experiments are summarized in Table 1. Under each performance criterion, the marginal means resulting from the levels of each factor are arranged in groups indi-

A. Banerjee, J.S. Burton /Maintenance scheduling in a job shop

195

Table 1 M a r g i n a l m e a n s of the factor levels Factor

Ave. flow

Flow time

M a i n t . w.f.

A v e . no.

A v e . no.

Ave. CM

Ave. PM

levels

time

std. dev.

util.

of

of PM

wait

delay

Ave. downtime

(hrs.)

(hrs.)

(%)

failures

tasks

(hrs,)

(hrs.)

(%)

Shop load High

151.5 a

136.4 a

29.7 a

197.3 a

282.2 a

0.80 a

5.58 a

4.59 a

Medium

99.1 b

79.7 b

27.5 b

181.9 b

263.0 b

0.74 b

5.33 b

4.21 b

Low

72.9 c

54.2 c

25.2 ¢

166.2 c

242.1 c

0.65 c

5.18 ~

3.79 c

145.3 a

87.2 b

27.4

181.8 a

263.0 b

0.74 a

5.35 a

4.19 a

70.3 b

95.0 a

27.5 a

181.8 a

264.4 a

0.73 a

5.37 a

4.20

27.3 ~

181.4 a

262.5 a

0.71 b

5.29 a

4.18 a

27.4 ~

181.9 a

262.4 ~

0.71 b

5.35 a

4.18 ~

Job seq. rule FCFS SPT

a

a

Maint. seq. rule FCFS m

107.9 a

90.7

SST m

107.5 a

90.0 ~

LNGQ m

108.1 ~

90.2 a

27.5 ~

181.5

a

262.7 a

0.77 a

5.35 ~

4.22 a

LTQ m

108,0 a

90.2 a

27.5 ~

182.1 a

262.2 ~

0.75 ~b

5,39 ~

4.21 a

MAXU m

107.5 a

89.6 a

27.4 ~

181.7 ~

262.6 ~

0.71 b

5,37 ~

4,18 ~

WLTQ m

107.8 a

89.9

27.5 ~

182.1 a

262.1 a

0.73 ab

5A2 a

4.20 ~

a

a

PM policy PM(0.3)

110.7 ~

92.8 a

36.3 ~

56.3 e

a

0.51 d

7.38 a

5.17 ~

PM(0.5)

105.7 ~

88.5 b

27.9 b

104.6 a

426,2 b

721,6

0.56 c

6.54 c

4.01 c

PM(I)

106.0 c

88.2 b

24.1 e

210.3 c

128.1 c

0.77 b

6.27 d

3.74 e

PM(1.5)

107.8 b~

90.4 ab

24.3 d

257.6 b

36.2 d

0.89 ~

6.62 b

3.96 d

NOPM

108.8 at,

90.6 ~b

24.7 ~

280.2 ~

0 ~

0.93 ~

--

4.10 b

Maint. workforce 1 2

114.0 a 104.9 b

96.2 ~ 87.3 b

44.3 ~ 22.7 b

189.3 ~ 178.7 b

231.6 c 275.4 b

2.07 a 0.12 b

8.00 ~ 4.19 b

4.91 a 3.86 b

3

104.6 b

86.9 b

15.3 c

177.4 ~

280.2 ~

0.01 ~

3.90 ~

3.82 c

cated by superscripts "a", " b " , etc. These arrangements are in descending order of magnitude, i.e. the highest means are grouped under "a", the next highest under " b " and so on. Means belonging to a particular group indicated by a specific superscript letter are not significantly different from one another on the basis of the pairwise Newm a n - K e u l s tests at the 0.1 level. Not unexpectedly, the main effects due to the shop load factor are statistically significant. As Table 1 indicates, the simulated shop exhibits its worst performance in terms of every selected measure under heavy load conditions. Under low load, shop performance improves quite dramatically, while under medium load, its performance lies between the two extremes. The results clearly show that with increasing load, machines in the shop are busier, as a consequence of which the need for CM, as well as PM activities increase. Thus, the busier the shop, the higher is the system downtime, especially when maintenance tasks are performed on-shift.

The main effects due to job sequencing rule turn out to be significant at the 10% level in terms of the average flow time, the standard deviation of flow times and the number of PM tasks. Compared to FCFS, the SPT rule dramatically reduces the average flow time, albeit at the expense of somewhat increased standard deviation of flow times. These results reinforce those obtained from a number of previous studies [7,13]. From Table 1, it appears that with respect to maintenance workforce utilization, number of breakdowns, average delay in performing PM, average waiting time for CM and downtime, there is virtually no difference between the two sequencing rules examined. Nevertheless, slightly, but statistically significant, fewer PM tasks are performed under the FCFS rule. This can be explained by the fact that the SPT job sequencing rule tends to result in higher equipment utilization, to the extent that a few more PM tasks become necessary, but not to the extent where more CM service is required. Somewhat surprisingly, the main effects due to

196

A. Banerjee, J.S. Burton / Maintenance scheduling in a job shop

the maintenance scheduling rule are statistically significant only in terms of the average waiting time for machines requiring CM service. In this respect, the FCFS m, SST m and MAXU m rules tend to outperform the L N G Q ~ procedure, but are not statistically superior to the LTQ ~ and WLTQ m rules. In addition, the latter two techniques are not significantly different from the L N G Q m rule. Nevertheless, in strictly numerical terms, the first three maintenance task sequencing rules result slightly lower values of repair waiting time when compared with the others. With respect to the other performance measures, the differences between the various maintenance scheduling rules, including FCFS m, appear to be marginal at best. These findings do not seem to support conjectures and assertations made in earlier work that it may be worthwhile to allocate repair resources on the basis of priority indices derived from machine utilization [6,15]. This, however, is not to say that there will never be any differences between various maintenance scheduling rules in more tightly

constrained systems. But, given the shop characteristics adopted in this study, we do not find any strong evidence for recommending any such rule over others in terms of most of the selected criteria. In contrast to maintenance sequencing, the main effects due to the PM policy are statistically significant at the 0.1 level. (Incidentally, it should be mentioned here that for each of the machines in our shop, a PM interval of 1.1 (MTBF) periods will minimize the individual downtime, which has been derived in [2].) As expected, Table 1 shows that with increasing PM frequency, i.e. decreasing PM interval, the number of machine breakdowns are reduced substantially, which is achieved at the expense of significantly larger number of PM tasks performed. Similarly, decreasing the PM interval also results in reduced average repair waiting time, since fewer machines are allowed to fail. In general,increasing the PM interval results in a reduction of the average delay in performing PM service, as a direct consequence of a decreasing PM

(B) Job S e q u e n c i n g and Shop Load 30O

(A) Job S e q u e n c i n g and W o r k f o r c e 160 140 120

SPT

w

8,

FCFS SPT

~0O

>=

lOO

,<

6O

!

!

I

1

2

3

0 4

!

I

I

High

Medium Shop Load

Low

Workforc.e (C) S h o p Load and W o r k f o r c e

(D) PM Policy and W o r k f o r c e

180

130

• 160E i: 140 - 4- H i g t ~ ' ' ' ' ~ ~ .-e- Medium 120 4 - Low

.B- 0.3 4- 0.5 4=. 1.0 1.5

O

E I::: 120 '

0

_

~

.

e

-

0

loo

110 '

80 60

i

i

2

3

100 4

0

I

I

I

1

2

3

Workforce Figure 1. Significantinteractions affectingaverage flow time

Workforce

A. Banerjee, J.S. Burton / Maintenance scheduling in a job shop

(A) Job Sequencing and Shop Load

197

(B) Shop Load and Workforce

31

50

29

~

FCFS

l

I

I

High

Medium

Low

40

I1~,~

-o- MediUmow

I

0

Shop Load

1

2

3

(C) PM Policy and Shop Load

(D) PM Policy and Workforce

40

60

0.3 -e- 0.5 1.0 1.5 None

50 .o

N

20

4

Workforce

I

|

I

High

Medium

Low

~

40

None ~

30

~

2o 0

Shop LOad Figure 2. Significant interactions affecting workforce utilization

workload. However, comparing the PM(1) and PM(1.5) policies, we find that both repair wait time and PM delay time are higher in the case of the latter, which stems from the fact the advantage of a reduced PM workload is more than offset by the increase in the CM workload. The system down-time appears to be a convex function of the PM interval, as do the measures of flow time and its standard deviation. In terms of the first and the last of these criteria, the PM(1) policy outperforms all the others. With respect to the average flow time, however, there is no statistical difference between the PM(0.5) and PM(1) policies, although the former performs marginally better. This perhaps lends some credence to the conjecture made by Belgen and Nylehn [5] that increased system complexity is likely to require increased PM effort for insuring efficient operation. With regard to average flow time, there seems to be some evidence to support this.

2

3

4

Workl'oroe

The main effects due to the maintenance workforce size are also significant in terms of all the criteria. Increasing this crew size from 1 to 2 results in dramatic improvement in every respect. It appears that doubling of the maintenance capacity enables the system to perform more PM tasks in a timely fashion, thus significantly reducing the number of machine failures, downtime, repair wait time and the flow time criteria. The improvements resulting from increasing the workforce from 2 to 3 are less dramatic (exhibiting a leveling off effect) although significant in terms all but the flow time measures. It should be pointed out that with the addition of each maintenance worker, the average worker utilization goes down rather dramatically. The second order interaction effects that are significant at the 0.1 level, in terms of each performance measure, are presented in Figures 1 through 7. Figure 1 shows that in terms of average flow

A. Banerjee, J.S. Burton / Maintenance scheduling in a job shop

198

(A) Shop Load and Job Sequencing

(B) Workforce and Shop Load

4.8 •

4.6

~

4.4

a

4.2

~

4.0

E

-a- FCFS

•Q- High ..e- Medium Low

=e

a

Q

a.

3.8

a.

(a)

3.6

m

m

(b) , High

, Medium

, Low

3

0

I

I

I

1

2

3

4

(D) Workforca and PM Policy

(C) Shop Load and PM Policy

6 0.3 0.5

O

E 5'

e¢

1.0 1.5

O

-B-

O a.

"~" 0.3

~

1.0 1.5 None

5

None It

(c)

(d) !

High

I

Medium

!

Low

0

!

!

!

1

2

3

4

Workforce

Shop Load

Figure 3. Significant interactions affecting downtime

time, the interactions between shop load and maintenance workforce size, shop load and job sequencing technique, PM policy and workforce, and job sequencing rule and maintenance workforce size are statistically significant. Expectedly, the differences between PM policies, as well as job sequencing rules become more pronounced under the smallest maintenance crew size. Also, the improvements resulting from higher maintenance capacity or more efficient job sequencing is more marked under a relatively heavy shop load. Furthermore, when PM tasks are scheduled too frequently, the average flow time goes up as the maintenance crew size is increased, as a result of the increased number of PM tasks actually performed. With less frequent scheduling of PM tasks, on the ther hand, the flow time decreases as more maintenance workers are added. Figure 2, showing the significant second order interaction effects in terms of maintenance workforce utilization, indicates that with a low shop load, the two selected job sequencing rules per-

form equally well. However, under a high workload, SPT results in higher worker utilization and the opposite occurs under a medium shop load. Also, the differences between the PM policies tend to be more marked with less maintenance capacity (i.e. workforce) or under a high shop load. In terms of downtime, we see from Figure 3 that the effects of a high workload is felt more severely when the maintenance workforce consists of fewer workers. Also, the selection of an appropriate PM policy is relatively more critical in this respect when the shop load is high. Again, it seems that with a policy of too frequently scheduled PM tasks, the downtime increases with the addition of more maintenance workers, as more PM tasks are actually performed. Otherwise, increasing the maintenance workforce size tends to reduce this measure. Figure 4, showing the interactions affecting the machine breakdowns, indicates that a heavy workload or more restrictive maintenance capacity

A. Banerjee, J.S. Burton / Maintenance scheduling in a job shop

(A) Shop Load and Job Sequencing

199

(13) Shop Load and PM Policy

2OO

40O -a-e'-0-4-

!.

190

300 -

..e.- FQ:S T

200-

170

0.3 0.5 1.0 1.5 None

100 -

160

I

I

I

l

I

l

High

Medium

Low

High

Medium

Low

Shop Load

Shop Load

(D) Workforce and PM Policy

(C) Workforce and Shop Load 210

300

-a- High

2OO

~

-

~

/

-

Medium i Low

180

=

-

-41- 0.3 J.-e- 0.5 -a- 1.0

200

~"~ ~

1.5 Non

100

170 160

i

!

2 Workforce

0

3

4

0

2 Workforce

3

Figure 4. Significant interactions affecting breakdowns

(B) Workforce and Shop Load

A) Job Sequencing and Shop Load 320

29O

300

r

28O

29o

270-

:l O

"6

200

(~ 260" Z 250-

•e- High -4- Medium 4 - Low

240

I

I

FCFS

SPT

Job

u. • 240 B.

220 200

"6 d z

0.3 ..e.- 0.5 ..B- 1.0 i~' 600 "4" 1,5

L

|

g" 40o ,,'r

1

2OO 0

(D) Workforce and PM Policy 800

6004OO

I

3

Workforoe

(C) Shop Load and PM Policy

II

I

2

Sequencing

8O0

o.

I

1

j

4 - 0.3 •. ~ 0.5 -I~ 1.(1 -e- 1.5

~

~ 200 I

High

I

Medium Shop Load

I

Low

I

!

!

1

2

3

Figure 5. Significant interactions affecting no. of PM tasks

Workforoe

200

A. Banerjee, J.S. Burton / Maintenance scheduling in a job shop

(B) Workl'orce and Shop Load

(A) Workforce and Repair Sequencing 3 -J-e4•44•o-

~' 2 I,. m

n.

I

1

FCFS (M) LNGQ (M) SST (M) LTQ (M) MAXU (M) WLTQ (M)

-m- High

-e- Medium -a- Low

m T

!

"1

2

4

3

0

1

2 Workforoe

Workforce

(D) Workforce and PM Policy

(C) Shop Load and PM Frequency 1.1

-B-

0.90.8-

0.3

-e- 0.5

1.0i

3

~

~,~None

÷

1.5

-la- 0.3 -e- 0.5 -II- 1.0 "4" 1.5

2

j,

0.7-

-a- None

0.60

0.5 High

Medium Shop Load

Low

'

1

~

"

3

Work force

Figure 6. Significant interactions affecting repair delay

extract more pronounced differences between the PM policies. Furthermore, the advantage of increasing the maintenance crew size is more readily apparent under a high shop load. By the same token, the system's ability to perform scheduled PM tasks by increased crew size is more markedly improved under heavier workloads (see Figure 5). Also, the PM service requirements differences due to the PM policy choices tend to be more pronounced under higher shop loads. As Figure 6 indicates, the choice of a specific maintenance scheduling method attains some importance in terms of CM delay, only when the maintenance workforce size is 1. Such a low level of maintenance capacity also makes the selection of a PM policy critical, particularly under high workloads if repair wait time reduction is important. Finally, these comments also apply with respect to the criterion of average PM delay (see Figure 7).

5. Conclusions In terms of the aspects that have been examined in prior job shop research (for example, the relative performance of job sequencing rules or the effects of varying the PM interval), the results obtained from our experiments, to a large extent, reinforce the conclusions arrived at in earlier studies. An important finding resulting from this work is that, at least under the adopted conditions, the selection of a maintenance sequencing rule is not of critical importance in terms of the selected criteria, unless there are severe limitations in the system's maintenance capacity. Even then, the maintenance sequencing rules exhibit only minor differences among themselves. This observation seems to run contrary to conventional wisdom. While no previous study has explicitly tested

A. Banerjee, J.S. Burton / Maintenance scheduling in a job shop

201

(B) Workforce and Shop Load

(A) Job Sequencing end PM Policy 9

7.5 ~r~

-a" -e-

~' 7.0

dF 1.0 4"

I =" 6.5

X2

0.3 0.5 1.5

u Q

¢3

=E r

6.0

a.

~

,

,

FCFS

!

SPT

1

J o b Sequencing

(C) Shop Load end PM Policy

!

2 Workforce

I

3

(D) Workforce and PM Policy 12

4-

=,

I0

7

e8

a

=E 0.

6

a

-----.4

0.3

•.e- 0.5 4 - 1.0 •.e-

1.5

8

-'m-

"41- 0.5 •-e-

6

1.0 1.5 !

High

I

"

I

Medium

Low

I

i

I

1

2

3

Shop L o a d

Workforce

Figure 7. Significant interactions affecting PM delay

different techniques for sequencing maintenance activities, Davale and Otterson [6], as well as Poulsen [15] have suggested that it may be desirable to assign service priorities to machines based on downtime costs or other criteria, such as utilization. In terms of the performance measures examined, our results do not provide sufficient evidence to support this contention. It must, however, be mentioned that under different conditions, not examined in this paper, the differences between maintenance scheduling rules may be less blurred. To say the least, the possibility of developing more effective maintenance sequencing techniques exist. These remain matters for further research in this area of endeavor. The appropriate choices concerning job sequencing rule, PM policy and the level of maintenance workforce or capacity are, nevertheless, of critical importance for the efficient operation of the system, in terms of most of the selected performance criteria. Furthermore, the selection of a suitable PM policy should be made in conjunction with the number of maintenance workers, care-

fully considering the associated tradeoffs among the criteria, which have been discussed earlier. As alluded to above, we do not assert that our results pertaining to aspects that have not been addressed adequately in prior research (maintenance task sequencing, for instance), will hold under all possible operating conditions. By the same token, it cannot be said with any degree of certainty that our findings depend Critically upon the specific assumptions underlying the simulation model used. This issue can only be resolved through more research incorporating system characteristics (such as machine failure and repair time distributions) other than the ones adopted in this paper. Finally, in future extensions of this work, due date performance measures and decision rules based on such criteria should be examined.

References [1] Alcalay, J.A., and Buffa, E.S., "A proposal for a general model of a production system", International Journal of Production Research 2 (1963) 73.

202

A. Banerjee, J.S. Burton / Maintenance scheduling in a job shop

[2] Banerjee, A., and Flynn, B.B., "A simulation study of some maintenance policies in a group technology shop", International Journal of Production Research 25 (1987) 1595-1609. [3] Baker, K.R., "Sequencing rules and due date assignments in a job shop", Management Science 30 (1984) 1093-1104. [4] Basket, B.A., and Husband, T.M., "Simulating multi-skill maintenance: A case study", Maintenance Management International 3 (1982) 173-182. [5] Belgen, H.M., and Nylehn, B., "Organising the maintenance function", International Journal of Production Research 7 (1968) 75-81. [6] Dhavale, D.G., and Otterson, G.L., "Weight the averages to lighten downtime", Production Engineering 27 (1980) 46-50. [7] Day, J.E., and Hottenstein, M.P., "Review of sequencing research", Naval Research Logistics Quarterly 17 (1970) 11-39. [8] Glazerbrook, K.D., "Evaluating the effects of machine breakdowns in stochastic scheduling problems", Naval Research Logistics Quarterly 34 (1987) 319-335. [9] Holst, O., and Sorenson, B., "Combined scheduling and maintenance planning for an aircraft fleet", Operational Research "84: Proceedings of the lOth IFORS Conference, North-Holland, Amsterdam, 1984, 735-748.

[10] Husband, T.M., and Basker, B.A., "Optimising maintenance/production systems", Maintenance Management International 3 (1982) 75-81. [11] Krajewski, L,J., and Hardy, S.T., "Interactive effects of maintenance policies", Division of Research Working Paper Series, The Ohio State University, Columbus, OH, 1974. [12] Lie, C.H., Hwang, C.L., and Tillman, F.A., "Availability of maintained systems: A state-of-the-art survey", A I I E Transactions 9 (1977) 247-259. [13] Panwalker, S.S., and Wilson, R.C., "A survey of scheduling rules", Operations Research 25 (1977) 45-61. [14] Pierskalla, W.P., and Volker, J.E., "A survey of maintenance models: The control and suveillance of deteriorating systems", Naval Research Logistics Quarterly 23 (1976) 353-388. [15] Poulsen, L., "Simulating maintenance work in a fully loaded machine shop: a model", Maintenance Management International 4 (1984) 89-101. [16] Sherif, Y.S., and Smith, M.L., "Optimal maintenance models for systems subject to failure: A review", Naval Research Logistics Quarterly 28 (1981) 47-74.