Pom Lecture (43)

Unit 3 Scheduling Operations Chapter 13: Scheduling Lesson 42 - CHARACTERISTICS OF THE SEQUENCING RULES Learning Objectives After reading this lesson you will b able to understand Sequencing through multiple work centers Simulated intermittent systems Detailed scheduling Expediting

My dear students, let us pick up the threads of the last discussion and start with a comparison. Not quite the start we usually have, but there’s a reason for it. Let’s see why. A comparison

When we compare the performance of FCFS and SPT (see Table) we see that SPT is superior. Although total completion time is 55 days for both sequences, SPT affords a lower average flow time, so inventories are tied up to a lesser extent, and quicker service can be provided to customers. With SPT, the average number of jobs in the system is reduced, so the shop is less congested and inventory levels are lower. Finally, since average lateness is reduced, deliveries to customers are more prompt. The superior performance of the SPT rule in our example was not an accident. For jobs processed in one work center, the SPT rule is consistently superior to other rules; it is optimal for minimizing average flow time, average number of jobs in the system, and average lateness.

TABLE of Comparison of SPT and FCFS rules Criterion Total Completion Time

Rule

. (in days)

Average

Average

Flow Time

Average Jobs in

(in days)

System Each Day (in days)

Lateness

FCFS

55

31.8

2.89

18.6

SPT

55

26.8

2.44

13.6

Of the five rules cited, only two- EDD and LS-are based on the due date. This criterion is especially appropriate for MRP scheduling systems because the MRP outP\lts identify scheduled receipts in weekly or even daily time periods that become the due dates for batches of component items. Now that the implication is clear, let us pay a visit to:SQUENCING THROUGH MULTIPLE WORK CENTERS Our discussion of sequencing, up to this point, has focused on processing jobs through a single work center and, for this simple problem, optimal analytical solutions are possible. For most facilities, however, jobs must be processed through many (often a hundred or more) work centers. Furthermore, the routing of jobs varies considerably: some jobs pass through a few work centers; others pass through many. As jobs arrive at facilities in a variety of patterns, so do they leave. Thus the composition of waiting jobs at a work center may change continuously, and priority sequencing becomes an ongoing process. For facilities like these, optimal analytic solutions do not exist. One approach by mathematicians and operations researchers has been to apply queuing theory to jobs as they "wait in lines" (queues) to be processed. The strength of queuing theory is that, potentially, it provides optimal solutions. Application of queuing theory is severely limited, however, because the mathematical complexity becomes overwhelming when

assumptions about arrival times and processing times differ from a few well-known distributions (exponential and Poisson, for example) to more realistic empirical distributions. Friends, all of us are familiar with simulation. Now let us see how it is applied to the INTERMITTENT (JOB-SHOP) SYSTEMS

SIMULATION OF INTERMITTENT (JOB-SHOP) SYSTEMS Simulation techniques can be used to evaluate various sequencing rules in job-shop facilities. The following is list of data the modeler must be able to specify in order to stimulate the sequencing problem. The modeler can use historical data and patterns for this purpose, and during simulation can use the Monte Carlo method to randomly select portions of the historical data that the simulation requires as it runs.

1. Work centers. The number of work centers in the shop must be specified. 2. Job arrivals. The pattern and timing of jobs "arriving" at the facility must be specified.

.

3. Job clas5ification. The processing requirements or routing of jobs must be

specified.

4. Processing times. The time it takes to process jobs must be specified. 5. Performance parameters. Any number of parameters that .gauge the performance at the facility can be incorporated into the simulation; the quantification of these parameters must be specified. Options include percent idle time, number of jobs in the queue, average waiting time, amount of inventory, average lateness of jobs, average job flow, and so on. Sequencing rule. A sequencing rule must be specified.

The simulation known as a simulation run, is conducted over time. The simulation runs through a very large number of jobs, say 10,000 or more. The simulation generates new jobs arriving at various times, determines their routings, loads them to the appropriate work centers, sequences them according to the sequence rule, and determines their processing times. When a work center completes one job, it begins processing the next job in the queue, according to the sequence rule. After all jobs have been processed, the simulation evaluates the performance of the facility according to the parameters specified. The performance statistics are saved for later comparison. The modeler may now run the simulation again, specifying a .different sequence rule. When the simulation evaluates the performance of the facility accordingly, the results of both simulation runs can be compared. Any number of sequence rules may be evaluated and compared in this way. Let me share with all of you the results of an interesting study. Simulation Results for Job Flow Time One study tested ten sequence rules in six different job-shop configurations using computer simulation. I The results are based on processing over 2 million jobs through the simulated system. Our main interest in the results has to do with the job flow performance of the rules, an important concern to shop managers. Job flow is commonly measured in two ways: as the average flow time of jobs through the system; and as the dispersion of job flow times through the system (measured by a standard deviation or variance). The simulation study found that average (mean) flow time per job was lowest (0.99) using the SPT rule; using other rules it was as high as 2.54. The standard deviation of flow time ranged from 1.55 to 5.43 using the various rules. Although the standard deviation of flow time was lower using two of the other rules, SPT did well on this parameter also. These results are not surprising when you consider how the SPT rule works. Since the highest priority job is the one whose processing time is shortest, this job does not have to wait long in the queue; its flow time (waiting plus processing time) is

low. Simulation Results for Job Lateness and Work-in-process Inventories Using a computer simulation, another researcher examined how well 39 sequencing rules performed in terms of job lateness and inventories. Z In terms of percentage of jobs late, SPT performed far better than most other rules tested. This same stUdy found that the SPT rule was not optimal for minimizing in-process inventory, although its performance was still relatively good. The optimal rules were found to be compound rules. They require somewhat more complex calculations than does the SPT rule. These compound rules are a weighted combination of the SPT and other rules, all combined into one.3 In short, the SPT, although not optimal, performed well, and it did so without requiring the extensive calculations of the more complex rules. At this point in our discussion, I must tell you something about the Additional sequencing rules. SEQUENCING PROCEDURES FOR OTHER CRITERIA Additional sequencing rules are available for more specialized situations. First we examine sequencing when setup costs are the primary consideration. Next we look at a rule that minimizes the elapsed time to completion for the last job through two successive work centers.

'

Setup Dependence Sometimes the dominant consideration is the setup, or changeover, cost for processing the different jobs. Table 11.4 shows that total setup costs for the aircraft repair facility depend on the. sequence in which the five jobs are processed. These data show the setup cost when job) is processed after job i. It assumes that job A is already being processed and jobs B, C, D, and E remain to be done. If we choose job B to follow A, a setup cost is high: ($29). If we choose job D to follow A, the setup cost is only $18. Which sequence of jobs minimizes total set up costs?

Matrix of setup costs (in dollars) Predecessor Job

Successor Job A

B

C

0

E

A

0

29

20

18

24

B

0

0

14

19

15

C

0

35

0

37

26

D

0

15

10

0

10

E

0

18

16

40

0

The Next Best (NB) Rule One heuristic approach, the next best (NB) rule states, "Given that job i is being processed, assign highest priority to the job j where setup cost is least.." For example, if job A is being processed, job 0 would be selected next, since it has the least setup cost for succeeding job A. After job 0, job C or E ($10 setup cost) would be selected next. The NB rule would yield two sequences: Sequence

Cost

NB1: A-D-C-E-B

$18 + 10 + 26 + 18 = $72

NB2: A-D-E-C-B

$18 + 10 + 16 + 35 = $79

NB1 is preferred, since its cost is lower than NB22uThis NB. sequence is not optimal. A cost analysis of all 24 possible sequences, irrespective of the NB rule, shows that the optimal sequence is A-D-E-B-C, with a total setup cost of $60. However, NB, may be considered satisfactory. especially if we are dealing with larger problems for which complete enumeration of all alternatives is not feasible. In this example, sequence NB2 happens to be identical to the sequence according to the SPT (shortest processing time) rule. In general, however, sequences of the NB and SPT rules are not expected to coincide. If they do not, you must choose between the two

rules. Your choice depends on the relative importance you place on costs of machine setup (NB) .as opposed to the value of gaining overall shop effectiveness (SPT). Friends, the question that should naturally come to our minds is, How is Sequencing achieved Through Two Work centers? Sequencing Through Two Work Centers Imagine that all the jobs waiting must be processed through two successive work centers. Furthermore, suppose a customer wants you to get the entire set of jobs completed as rapidly as possible. You want to minimize the flow time of the last job in the sequence and an optimal procedure for doing so is available. Suppose that jobs A through E in the aircraft repair facility must each pass through the sheet metal center and then through the paint center. We wish to find the sequence that minimizes completion time of the last job. The processing time for each job in each center is shown in Table below TABLE: Processing times (in days) for jobs at two work centers Job

Work Center

A

B

C

D

E

1

4

17

14

9

11

2

5

7

12

2

6

Since there are five jobs, there will be five positions in the processing sequence. These steps tell how to assign the jobs to the five positions in the sequence. We use the notation PT ij to mean the processing time of job i at work center j. Here, i can be A, B, C, D, or E, and j can be 1 or 2. 1.

Determine the minimum processing time PTij for all unassigned jobs.

If the minimum PTij is associated with work center 1, assign the corresponding job to the earliest available position in the sequence; if the minimum PTij is associated with work center 2, assign the corresponding job to the latest remaining position in the sequence. Eliminate this job and its processing times from further consideration.

2.

If all jobs are assigned a sequence, quit. This sequence is the optimal sequence.

3.

If jobs remain unassigned, return to step 1.

4.

Using the data from Table 11.5, the assignments proceed as follows: 1. PTD2 is the minimum: 2 days. 2. Since PTD2 if associated with work center 2, job D is assigned to the last (fifth) position in the sequence.

Since job D has been assigned, job D and its processing time are eliminated. 3. Jobs A, B, C, and E remain to be assigned. 4. (Return to step 1.) Of the remaining eight PT PTAI is the smallest. 5. (Repeat step 2.) Since job A's line is associated with center 1, job A is assigned to position 1 in the sequence. Job A and it's times are eliminated. 6. (Repeat step 3.) Jobs B, C, and E have yet to be assigned to remaining positions 2, 3, and 4 in the sequence. 7. (Repeat Step 1.) Of the remaining six PT' PtE2 is minimum. Since it is associated with work center 2, job E is assigned to the last available position in the sequence (position 4). Continuing in this manner, we find the finished sequence to be A-C-B-E-D. The time-phased flow of this sequence is shown graphically in Figure . Flow time of job D, the last job in the sequence, is 57 days, the minimum last-job flow time possible. It is important to remember that this rule applies when all jobs must be processed first on center t, then on center 2. Work Centre1 Sheet Metal A

0

C

4

B

9

18

30

E

35

D

42

46

52

55 57 Time in Days Work Center2 Paint E

A

C

B

D

Idle Time,

Completed Job A

FIGURE Job flow for sequencing five jobs in two centers in sequence A-C-B-E-D In concluding our coverage of sequencing, you should note two of its overriding features. First, an abundance of sequencing methods is available; such methods can affect shop performance in different ways. Second, in choosing among these methods you should carefully evaluate them in terms of the criteria that are of greatest importance for your organization's competitive posture. Now, let us deliberate on the issue of:Detailed Scheduling Having discussed the loading and sequencing steps of scheduling intermittent systems, let's examine how detailed scheduling is accomplished. Operating personnel need detailed schedules so that they know when to start which job and when it should be finished. Gantt Scheduling Chart We previously showed a Gantt load chart. Another version of the Gantt chart can be helpful for visualizing detailed scheduling. Figure shows one possible schedule for jobs A through E in the aircraft repair facility. On the time scale, each pair of brackets denotes the estimated beginning and ending of a job. The solid bars beneath the brackets show the cumulative work loads at each work center. Overall, then, 55 days of job processing, 2

days of setup, and 19 days of idle time constitute the 76-day sheet metal schedule. As work is completed, the "Time now" arrow moves to the right, and a heavier or colorcoded line may be used between the brackets to denote work actually completed. Scheduled and completed work can thus be compared.

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 Time now 58 60 62 64 66 68 70 72 74 76 78 [

][

B

J[

E

]

A [

[

D

]

heet metal

D ]

[...!..J [

] lectronics

5 [

[

C

C

E.

]

]

t! ?J

[

E

Paint

] Hydraulics

FIGURE of Gantt chart for order scheduling (job sequence: A-C-B-E-D) Another important concept is of:EXPEDITING: Let’s say we have done all the work we have discussed so far. We have finished loading, sequencing and detailed scheduling. Now we wait for things to happen, but there is a

hitch, material or manpower is not coming at the time required. So what do we do now? We have to reschedule the whole process i.e. do a control process. If the progress of the work is unsatisfactory, the job has to be expedited. More and specific attention is to given and priorities are to be shifted at work centers to “rush up the job” may be ahead of others. This process is sometimes necessary, but it should be done very cautiously. So far we have been discussing about how thongs are to be done. We have also studied at some point of time that we should also keep monitoring about the progress of work at the various work centers. Let us see how we can do this measurement.. Reporting here is the essence for carrying out any measurement. The table below illustrates how capacity is being utilized. Standard hrs per week 1

2

3

4

5

Planned output

400

350

350

300

300

Actual output

400

350

350

300

– planned)

0

0

0

0

Planned output

450

400

400

350

Actual output

440

410

405

330

– planned)

-10

0

+5

-15

Planned

250

200

150

100

Backlog

260

200

145 175

115

Cumulative deviation ( Actual

300

Cumulative deviation ( Actual

100

Actual backlog Back log at time 0 = 300 units. The table above shows labor hour requirements of new jobs for the work center for each

week are recorded in the first row as planned input”. The work center” planned output” is the weekly work rate (hours of capacity to be expected each week) chosen by the management. Here we see that planned output exceeds planned inputs, reflecting managements intentions to decrease the work centers backlog, wee by week, from the beginning level of 300 units at week 0 to 100 units (labor hrs ) by week 4. With that, we have come to the end of today’s discussions. I hope it has been an enriching and satisfying experience.