Learning Objectives. Scheduling. Learning Objectives

Transcription

1 Scheduling 16 Learning Objectives Explain what scheduling involves and the importance of good scheduling. Discuss scheduling needs in high-volume and intermediate-volume systems. Discuss scheduling needs in job shops. McGraw-Hill/Irwin Copyright 2007 by The McGraw-Hill Companies, Inc. All rights reserved Learning Objectives Use and interpret Gantt charts, and use the assignment method for loading. Discuss and give examples of commonly used priority rules. Describe some of the unique problems encountered in service systems, and describe some of the approaches used for scheduling service systems. Scheduling: Establishing the timing of the use of equipment, facilities and human activities in an organization Effective scheduling can yield Cost savings Scheduling Increases in productivity

2 High-Volume Systems Flow system: High-volume system with Standardized equipment and activities Flow-shop scheduling: Scheduling for highvolume flow system Work Center #1 Work Center #2 Output High-Volume Success Factors Process and product design Preventive maintenance Rapid repair when breakdown occurs Optimal product mixes Minimization of quality problems Reliability and timing of supplies Intermediate-Volume Systems Outputs are between standardized highvolume systems and made-to-order job shops Run size, timing, and sequence of jobs Economic run size: Q 0 2DS H p p u Scheduling Low-Volume Systems Loading - assignment of jobs to process centers Sequencing - determining the order in which jobs will be processed Job-shop scheduling Scheduling for low-volume systems with many variations in requirements

3 Figure 16.2 Gantt Load Chart Gantt chart - used as a visual aid for loading and scheduling Work Mon. Tues. Wed. Thurs. Fri. Center 1 Job 3 Job 4 2 Job 3 Job 7 3 Job 1 Job 6 Job 7 4 Job 10 Loading Infinite loading jobs are assigned to work centers without regard for the capacity of the work center. Finite loading jobs are assigned to work centers taking into account the work center capacity and job processing times Loading (cont d) Forward scheduling scheduling ahead from some point in time. Backward scheduling scheduling by working backwards in time from the due date(s). Schedule chart a form of Gantt chart that shows the orders or jobs in progress and whether they are on schedule. Assignment Method of linear programming The assignment model is a special-purpose linear programming model that is useful in situations that call for assigning tasks or other work requirements to resources. Typical examples include assigning jobs to machines or workers, territories to salespeople, and repair jobs to repair crews. The idea is to obtain an optimum matching of tasks and resources

4 Example 1 Determine the optimum assignment of jobs to machines for the following data : Example 1 a. Subtract the smallest number in each row from every number in the row, and enter the results in a new table. The result of this row reduction is b. Subtract the smallest number in each column from every number in the column, and enter the results in a new table. The result of this column reduction is c. Determine the minimum number of lines needed to cross out all zeros. (Try to cross out as many zeros as possible when drawing lines.) Example 1 Sequencing d. Since only three lines are needed to cross out all zeros and the table has four rows, this is not the optimum. Note that the smallest uncovered value is 1. e. Subtract the smallest uncovered value from every uncovered number that hasn t been crossed out, and add it to numbers that are at the intersections of covering lines. The results are as follows: f. Determine the minimum number of lines needed to cross out all zeros (four). Since this equals the number of rows, you can make the optimum assignment. g. Make assignments: Start with rows and columns with only one zero. Match jobs with machines that have a zero cost. Sequencing: Determine the order in which jobs at a work center will be processed. Workstation: An area where one person works, usually with special equipment, on a specialized job

5 Sequencing Table 16.2 Priority Rules Priority rules: Simple heuristics used to select the order in which jobs will be processed. Job time: Time needed for setup and processing of a job. Everything is #1 Priority FCFS - first come, first served SPT - shortest processing time EDD - earliest due date CR - critical ratio S/O - slack per operation Top Priority Rush - emergency Job flow time. Performance Measures This is the length of time a job is at a particular workstation or work center. It includes not only actual processing time but also any time waiting to be processed, transportation time between operations, and any waiting time related to equipment breakdowns, unavailable parts, quality problems, and so on. Job lateness. (tardiness) This is the length of time the job completion date is expected to exceed the date the job was due or promised to a customer. Makespan. Makespan is the total time needed to complete a group of jobs. Average number of jobs. Jobs that are in a shop are considered to be work-in-process inventory. Average number of jobs = Total flow time Makespan Assumptions of Priority Rules The setup of jobs is known Setup time is independent of processing sequence Setup time is deterministic There will be no interruptions in processing such as: Machine breakdowns Accidents Worker illness

6 Example 2 Example 2-a) FCFS times (including setup times) and due dates for six jobs waiting to be processed at a work center are given in the following table. Determine the sequence of jobs, the average flow time, average tardiness, and average number of jobs at the work center, for each of these rules: a. FCFS b. SPT c. EDD d. CR Assume jobs arrived in the order shown. Job Time (days) (days) A 2 7 B 8 16 C 4 4 D E 5 15 F The FCFS sequence is simply A-B-C-D-E-F. The measures of effectiveness are as follows (see table): Job (1) Time (2) Flow Time (3) Average flow time: = 20 days. Average tardiness: 54 6 = 9 days. The makespan is 41 days. Average number of jobs at the work center: = (2) - (3) Days Tardy [0 if negative] A B C D E F Example 2-b) SPT Example 2-c) EDD The FCFS sequence is simply A-B-C-D-E-F. The measures of effectiveness are as follows (see table): Job (1) Time (2) Flow Time (3) (2) - (3) Days Tardy [0 if negative] A C E B D F The FCFS sequence is simply A-B-C-D-E-F. The measures of effectiveness are as follows (see table): Job (1) Time (2) Flow Time (3) (2) - (3) Days Tardy [0 if negative] C A E B D F Average flow time: = 18 days. Average tardiness: 40 6 = 6.67 days. The makespan is 41 days. Average number of jobs at the work center: = Average flow time: = days. Average tardiness: 38 6 = 6.33 days. The makespan is 41 days. Average number of jobs at the work center: =

7 Example 2-d) Critical Ratio Example 2-d) Critical Ratio Using the critical ratio we find Job Due Critical Ratio Time Dates Calculation A 2 7 (7-0)/2 = 3.5 B 8 16 (16-0)/8 = 2.0 C 4 4 (4-0)/4 = 1.0 D (17-0)/10 = 1.7 E 5 15 (15-0)/5 = 3.0 C At day 16 [C and F completed], the critical ratios are Job Due Critical Ratio Time Dates Calculation A 2 7 (7-16)/2 = -4.5 B 8 16 (16-16)/8 = 0 C F A D (17-16)/10 = 0.1 E 5 15 (15-16)/5 = -0.2 At day 18 [C,F and A completed], the critical ratios are F (18-0)/12 =1.5 At day 4 [C completed], the critical ratio are Job Due Critical Ratio Time Dates Calculation A 2 7 (7-4)/2 = 1.5 B 8 16 (16-4)/8 = 1.5 Job Due Critical Ratio Time Dates Calculation B 8 16 (16-18)/8 = D (17-18)/10 = -0.1 E 5 15 (15-18)/5 = -0.6 C F A E At day 23 [C,F,A, and E completed], the critical ratios are D (17-4)/10 = 1.3 E 5 15 (15-4)/5 = 2.2 F (18-4)/12 =1.17 C F Job Due Critical Ratio Time Dates Calculation B 8 16 (16-23)/8 = D (17-23)/10 = -0.6 C F A E B D Example 2-d) Critical ratio The FCFS sequence is simply A-B-C-D-E-F. The measures of effectiveness are as follows (see table): Job (1) Time (2) Flow Time (3) Average flow time: = days. Average tardiness: 58 6 = 9.67 days. Average number of jobs at the work center: = (2) - (3) Days Tardy [0 if negative] C F A E B D Table 16.4 Rule FCFS SPT EDD CR Average Flow Time (days) Example 2 Average Tardiness (days) Average Number of Jobs at the Work Center

8 Example 3 Example 3- Solution Use the S/O rule to schedule the following jobs. Note that processing time includes the time remaining for the current and subsequent operations. In addition, you will need to know the number of operations remaining, including the current one. Job Time (days) (days) Remaining number of operations A B C D E F Determine the difference between the due date and the processing time for each operation. Divide the difference by the number of remaining operations, and rank them from low to high. This yields the sequence of jobs: Job (1) Remaining Time (2) Due Date (3) (2)-(1) Slack (4) Remaining Number of Operations (5) (3)/(4) Ratio (6) Rank A B C D E F Two Work Center Sequencing Johnson s Rule Conditions Johnson s Rule: technique for minimizing completion time for a group of jobs to be processed on two machines or at two work centers. Minimizes total idle time Several conditions must be satisfied Job time must be known and constant Job times must be independent of sequence Jobs must follow same two-step sequence Job priorities cannot be used All units must be completed at the first work center before moving to second

9 Johnson s Rule Optimum Sequence 1.List the jobs and their times at each work center 2.Select the job with the shortest time 3.Eliminate the job from further consideration 4.Repeat steps 2 and 3 until all jobs have been scheduled Scheduling Difficulties Variability in Setup times times Interruptions Changes in the set of jobs No method for identifying optimal schedule Scheduling is not an exact science Ongoing task for a manager Example 4 Example 4- Solution A group of six jobs is to be processed through a two-machine flow shop. The first operation involves cleaning and the second involves painting. Determine a sequence that will minimize the total completion time for this group of jobs. times are as follows: Time (Hours) Job Work Center 1 Work Center 2 A 5 5 B 4 3 D 2 7 E 6 8 a. Select the job with the shortest processing time. It is job D, with a time of two hours. b. Since the time is at the first center, schedule job D first. Eliminate job D from further consideration. 1 st 2 nd 3 rd 4 th 5 th 6 th D c. Job B has the next shortest time. Since it is at the second work center, schedule it last and eliminate job B from further consideration. We now have 1 st 2 nd 3 rd 4 th 5 th 6 th D B t Job C1 C2 A 5 5 D 2 7 E 6 8 t Job C1 C2 A 5 5 B 4 3 E

10 Example 4- Solution Example 4- Solution d. The remaining jobs and their times are Note that there is a tie for the shortest remaining time: job A has the same time at each work center. It makes no difference, then, whether we place it toward the beginning or the end of the sequence. Suppose it is placed arbitrarily toward the end. We now have 1 st 2 nd 3 rd 4 th 5 th 6 th D A B e. The shortest remaining time is six hours for job E at work center 1. Thus, schedule that job toward the beginning of the sequence (after job D). Thus, 1 st 2 nd 3 rd 4 th 5 th 6 th D E A B t Job C1 C2 A 5 5 E 6 8 t Job C1 C2 E 6 8 f. Job C has the shortest time of the remaining two jobs. Since it is for the first work center, place it third in the sequence. Finally, assign the remaining job (F) to the fourth position and the result is t 1 st 2 nd 3 rd 4 th 5 th 6 th Job C1 C2 D E C F A B g. One way to determine the throughput time and idle times at the work centers is to construct a chart: Minimizing Scheduling Difficulties Set realistic due dates Focus on bottleneck operations Consider lot splitting of large jobs Theory of Constraints The Theory of Constraints Goal is to maximize flow through the entire system Emphasizes balancing flow Improve performance of bottleneck: Determine what is constraining the operation Exploit the constraint Subordinate everything to the constraint Determine how to overcome the constraint Repeat the process for the next constraint

11 Scheduling Services Considerations Scheduling services different from manufacturing Inability to store or inventory services Random nature of customer requests for service Point of customer contact Back-office operations Front-office operations Scheduling Services Appointment systems Controls customer arrivals for service Reservation systems Estimates demand for service Scheduling the workforce Manages capacity for service Scheduling multiple resources Coordinates use of more than one resource Yield Management Yield Management the application of pricing strategies to allocate capacity among various categories of demand. The goal is to maximize the revenue generated by the fixed capacity Fixed capacity Hotel, motel rooms Airline seats Unsold rooms or seats cannot be carried over Cyclical Scheduling Hospitals, police/fire departments, restaurants, supermarkets Rotating schedules Set a scheduling horizon Identify the work pattern Develop a basic employee schedule Assign employees to the schedule