1. Scheduling 2012.10.16 Process and Production Management

2. Scheduling Establishing the timing of the use of equipment, facilities and human activities in an organization. –High volume systems (characterized by standardized equipment and activities that provide identical or highly similar operations on products – autos, personal computers, radios, TVs) –Intermediate – volume systems (output fall between the standardized type of output of the high volume systems and made-to-order output of job shops. Work centers periodically shift from one product to another, but lot size relatively high. –Low-volume systems (products are made to order, and orders differ in terms of processing requirements, materials needed, processing time.)

3. High volume systems Standardized equipments and parts Standardized process Smooth flow of work  flow-shop scheduling Main problem: line balancing Success of the system: –Process and product design –Preventive maintenance –Rapid repair –Optimal product mix –Minimization of quality problems –Reliability and timing of suppliers

4. Intermediate – volume systems Standardized output, volume is not so large,  produce intermittently Main problem: run size of jobs (economic run size), timing of jobs, sequence D-demand S-setup cost H-production cost P- production rate U-usage rate

5. Low-volume systems Products are made to order Different jobs, Main problem: job-shop scheduling –Loading (assigning jobs to processing centers) –Sequencing (determine the order of jobs at work centers) Gantt chart: visualize the problem

6. Loading: –Infinite loading (no regards to the capacity of workstations) –Finite loading (capability is taken into account) Scheduling: –Forward scheduling: scheduling ahead from a point of time –Backward Scheduling: scheduling backward from a due date

7. Loading Hungarian rule: –Subtract the smallest number in each row from, every number in the row –Subtract the smallest number in each column from, every number in the column. –Test weather an optimum assignment can be made (determining the minimum number of lines needed to cross out all zeros, if it is equals the number of rows  optimum assignment) Go to step 6 –Modify the table Subtract the smallest uncovered number from every uncovered number Add the smallest uncovered number to the numbers at intersections of cross-out lines. –Repeat step 3 and 4 until obtain optimal solution –Make assignments

8. Exercise Worker ABCD Job18624 2671110 33576 45 129

9. Priority rules Select the order in which job will be processed First come first served (FCFS) – jobs are processed in the order which they arrive at a machine or work center Shortest processing time (SPD) – according to processing time, shortest job first Earliest due date (EDD) – according to due date, earliest due date first. Critical ratio (CR) – smallest ratio of time remaining until due date to processing time remaining.

10. Assumptions The set of jobs is known Setup time is independent of processing sequence Setup time is deterministic Process time are deterministic There will be no interruptions in processing such as machine breakdowns, accidents, or workes illness.

11. Example 1 Job/ product Processing time (days) Due date (days) A27 B816 C44 D1017 E515 F1218 Determine the sequence of jobs/products Determine average flow time Determine average tardiness Determine average number of jobs at the workcenter

12. Job flow time – the length of time a job is at a particular workstation or work center. (it includes not only processing time, but waiting time, transportation time) –Average flow time = total flow time /number of jobs Job lateness – length of time the job completion date is exceed the date the job was due to promised to the customer –Average tardiness=total lateness/number of products Makespan – is the total time needed to complete a group of jobs (time between start the first and completion of the last one) –Average number of jobs=total flow time/makespan (it reflects the average work-in-process inventory if the jobs represent equal amount of inventory)

13. FCFS Job/ product Processin time (days) Due date (days) (2) Flow time (3) Days tardy (0 if negative) (3)-(2) A2722-7=-5  0 B8162+8=1010-16=-6  0 C4410+4=1414-4=10 D101714+10=2425-17=7 E51524+5=2929-15=14 F121829+12=4141-18=23 4112054 Aft=120/6=20 days At=54/6=9 days M=41  Aj=120/41=2,93 pieces  ABCDEF

14. SPT Job/ product Processin time (days) Due date (days) (2) Flow time (3) Days tardy (0 if negative) (3)-(2) A2722-7=-5  0 C442+4=66-4=2 E5155+6=1111-15=-4  0 B81611+8=1919-16=3 D101719+10=2929-17=12 F121829+12=4141-18=23 4110840 Aft=108/6=18 days At=40/6=6,67 days Aj=108/41=2,63 pieces  ACEBDF

15. EDD Job/ product Processin time (days) Due date (days) (2) Flow time (3) Days tardy (0 if negative) (3)-(2) C4444-4=0 A274+2=66-7=-1  0 E5155+6=1111-15=-4  0 B81611+8=1919-16=3 D101719+10=2929-17=12 F121829+12=4141-18=23 4111038 Aft=110/6=18,33 days At=38/6=6,33 days Aj=110/41=2,68 pieces  CAEBDF

16. CR Job/ product Process in time (days) Due date (days) (2) CR0 A27(7-0)/2=3,5 B816(16-0)/8=2 C44(4-0)/4=1 D1017(17-0)10=1,7 E515(15-0)/5=3 F1218(18-0)/12=1,5 41 Remaining time untill due to dat (on the 0th day) 1. CR4 (7-4)/2=1,5 (16-4)/8=1,5 ------- (17-4)/10=1,3 (15-4)/5=2,2 (18-4)/12=1,17 2.  ???

17. Job/ productCR16 A(7-16)/2=-4,5 B(16-16)/8=0 C------- D(17-16)/10=0,1 E(15-16)/5=-0,2 F----- CR18 -------- (16-18)/8=-0,25 ------- (17-18)/10=-0,1 (15-18)/5=-0,6 --------- 1. 2. 3. 4. CR23 -------- (16-23)/8=-0,875 ------- (17-23)/10=-0,6 ------- --------- 4. 5.

18. CR  CFAEBD Job/ product Processin time (days) Due date (days) (2) C44 F1218 A27 E515 B816 D1017 41 Flow time (3) 4 4+12=16 16+2=18 18+5=23 23+8=31 31+10=41 133 Aft=133/6=22,16 days At=58/6=9,66 days Aj=133/41=3,24 pieces Days tardy (0 if negative) (3)-(2) 4-4=0 16-18=-2  0 18-7=11 23-15=8 31-16=15 41-17=24 58

19. Sequencing Jobs through two Work Center Job time is known and constant Job time is independent of job sequence All job must follow the same two-step job sequence Job priorities cannot be used All units must be completed at the first work center before moving on to the second work center

20. Example 2 Job/ product #1#2 A55 B43 C89 D27 E68 F1215 Select the job with the shortest time. –If the shortest time at first wc, schedule that job first. –If the time at the 2nd wc, schedule the work last. Eliminate the job and its time from further consideration Repeat steps D BAECF

21. Chart DECFAB #1 DECFAB #2 2816 283337 291726 Idle time 28434851 Flow time: 51 hours

22. Thank you for your attention!