1. MODELING AND ANALYSIS OF MANUFACTURING SYSTEMS Session 6 SCHEDULING E
MODELING AND ANALYSIS OF MANUFACTURING SYSTEMS Session 6 SCHEDULING E. Gutierrez-Miravete Spring 2001

2. TYPES OF FLOW SYSTEMS PRODUCT LAYOUT PROCESS LAYOUT CELLULAR LAYOUT
ASSEMBLY LINES
TRANSFER LINES
PROCESS LAYOUT
FLOW SHOP (jobs go through same sequence)
JOB SHOP (each job has its own route)
CELLULAR LAYOUT

3. PROCESS LAYOUT FLOW SYSTEMS
PRODUCTS ARE RELEASED TO THE PRODUCTION SYSTEM IN BATCHES
IF BATCHES VISIT SAME SEQUENCE OF STATIONS --> FLOW SHOP
IF DIFFERENT BATCHES HAVE THEIR OWN ROUTE --> JOB SHOP

4. FEATURES OF JOB SHOPS WIDE VARIETY OF PRODUCT REQUIREMENTS
MUST BE DESIGNED FOR MAXIMUM FLEXIBILITY
INDIVIDUAL STATIONS MUST BE CAPABLE OF WIDE VARIETY OF TASKS

5. FEATURES OF JOB SHOPS EXPERTISE IS PROCESS RELATED
ORGANIZED BY PROCESSING FUNCTION
UP TO 95% OF JOB TIME SPENT IN NON-PRODUCTIVE ACTIVITY
REMAINING 5% SPLIT BETWEEN LOT SETUP AND PROCESSING

6. THROUGHPUT TIME
THE TIME BETWEEN WHEN THE JOB IS RELEASED TO THE SHOP AND WHEN IT IS COMPLETED AND READY FOR DELIVERY

7. COMPONENTS OF THROUGHPUT TIME
PROCESSING TIME
SETUP TIME
MATERIAL HANDLING TIME
WAITING TIME

8. SHOP FLOW AND QUEUEING THEORY
Fig. 4.1 (Group vs Serial)
JOB ARRIVAL RATE: RANDOM; EXPONENTIAL INTERARRIVAL TIMES
PROCESSING TIMES: EXPONENTIALLY DISTRIBUTED
NUMBER OF SERVERS

9. PARALLEL VS SERIAL JOB SHOPS AS QUEUES
STEADY STATE SYSTEM
GIVEN ARRIVAL RATE (), SERVICING RATE () AND NUMBER OF SERVERS (c)
SINGLE GROUP/SINGLE QUEUE
M/M/c/INF (Table 11.1)
WORK DIVISIBILITY/SERIAL SYSTEM
GI/G/1 (Sec. 11.3)

10. KEY QUESTIONS WHEN TO RELEASE ORDERS TO THE PRODUCTION FACILITY?
HOW TO SEQUENCE JOBS AT A SINGLE WORKSTATION?
HOW TO SCHEDULE JOBS THROUGH THE ENTIRE FACILITY?

11. ORDER RELEASE
BASIC PROBLEM: FROM A LIST OF PENDING ORDERS SELECT THE TIME TO BEGIN PROCESSING
SHOP MANAGER’S GOAL: KEEP ALL MACHINES BUSY
SALES DEPARTMENT GOAL: TO MEET ALL CUSTOMER DUE DATES
USE AVERAGE STATION DELAY TIME

12. AVERAGE STATION DELAY TIMES
pij = PROCESSING TIME FOR JOB i IN MACHINE j
wj = AVERAGE WAITING TIME IN QUEUE AT j
mj = TIME REQUIRED TO COLLECT AND MOVE PART i AFTER DONE AT j

13. T = S{i} ( pij + wj + mj) THROUGHPUT TIME WHERE
S{i} = SET OF STATIONS VISITED BY PART i
JOB MUST BE RELEASED AT TIME T BEFORE ITS DUE DATE
Example 4.1 and Figure 4.2

14. PROBLEMS WITH AWDT APPROACH
VALID ONLY UNDER STABLE CONDITIONS.
HOWEVER
QUEUES VARY THROUGH TIME
MACHINE FAILURE IS RANDOM
PRUDENT MANAGER WOULD RELEASE THE JOB EARLIER! (What is the likely consequence of this?)

15. HOW TO STABILIZE TIME VARYING LOADS?
BY DAMPING DEMAND VARIABILITY
USING DYNAMIC QUEUE AVERAGES
USING PREVENTIVE MAINTENANCE
USING PROCESS DESIGN IMPROVEMENTS
USING STANDARIZED PROCEDURES
COMMON TOOL FOR CONTROLLING WORK LOADS --> LOAD REPORTS (See Fig. 4.3 and Example 4.2)

16. LOAD REPORTS (contd) FOR FINITE-LOADING PRODUCTION PLANNING SYSTEMS
FCFS VS OTHER SERVICING RULES
EACH PART BETTER HAVE ITS OWN LOAD PROFILE (TIME-PHASED LISTING OF RESOURCE REQUIREMENTS ON EACH WORKCENTER TO PRODUCE A SINGLE PART UNIT)

17. LOAD REPORTS (contd) TWO BASIC RULES
IF YOU CAN’T SELL IT, DON’T RELEASE IT
IF YOU CAN’T MAKE IT NOW, DON’T RELEASE IT
MATERIALS REQUIREMENTS PLANNING (MRP) vs RELIABILITY LAW

18. BOTTLENECKS WORKCENTER WITH THE HIGHEST UTILIZATION
UTILIZATION = PROCESSING TIME/AVAILABLE TIME
BOTTLENECK SCHEDULING GOAL: TO MAXIMIZE THE PRODUCTIVE UTILIZATION OF BOTTLENECKS

19. UTILIZATION um =  pimDi/ Pm FOR PART i AND WORKCENTER m
DEMAND OF i Di
SCHEDULABLE TIME Pm
LOAD PROFILE pim
UTILIZATION um
um =  pimDi/ Pm

20. UTILIZATION (contd) Where are the largest utilizations?
What is the consequence of having a workcenter with utilization greater than 1?
Who is the bottleneck if all utilizations are less than 1?
Why it may be desirable to accumulate significant WIP in front of the bottleneck?

21. BATCH SIZE (few parts, repetitive)
SET UP COST A
AVERAGE DEMAND RATE D
INVENTORY HOLDING COST PER TIME h
BATCH SIZE Q
Q2 = 2 A D /h

22. FLOW SHOP SEQUENCING
SEQUENCING: PROCESS OF DEFINING THE ORDER IN WHICH JOBS ARE TO BE RUN ON A MACHINE
SCHEDULING: PROCESS OF ADDING START AND FINISH TIME TO THE PROCESS DICTATED BY THE SEQUENCE

23. FLOW SHOP SEQUENCING
SEMIACTIVE SCHEDULE: EACH JOB STARTS ON A MACHINE AS SOON AS THE JOB AS FINISHED ALL PRIOR OPERATIONS AND THE MACHINE HAS COMPLETED ALL EARLIER JOBS IN ITS SEQUENCE

24. FLOW SHOP SEQUENCING
REGULAR MEASURES OF PERFORMANCE (nondecreasing in job completion times)
AVERAGE COMPLETION TIME
MAXIMUM COMPLETION TIME
FLOW TIME
LATENESS
TARDINESS

25. DEFINITIONS PROBLEM VARIABLES NUMBER OF JOBS SCHEDULED (N)
NUMBER OF MACHINES (M)
DUE DATE OF JOB i (di)
SETUP AND PROCESSING TIME OF JOB i IN MACHINE j (pij)

26. DEFINITIONS SOLUTION DEPENDENT MEASURES TIME FOR COMPLETING JOB i (Ci)
LENGTH OF TIME IN SHOP (FLOW TIME) (Fi)
LATENESS (Li = Ci - di)
TARDINESS ( Ti = max{0,Li} )
MAKESPAN (TIME FOR ALL JOBS) Cmax

27. TYPICAL OBJECTIVES MINIMIZE AVERAGE FLOW TIME MINIMIZE MAKESPAN
MINIMIZE AVERAGE TARDINESS
MINIMIZE MAXIMUM TARDINESS
MINIMIZE NUMBER OF TARDY JOBS

28. NOTATION
SCHEDULING N JOBS IN M MACHINES ACCORDING TO JOB FLOW PATTERN A AND PERFORMANCE MEASURE B
N/M/A/B
EXAMPLE: MINIMIZE AVERAGE FLOW TIME WITH ARBITRARY FLOW PATTERN G --> N/M/G/Fave

29. PERMUTATION SCHEDULE ALL JOBS VISIT MACHINES IN SAME SEQUENCE
ALL MACHINES PROCESS JOBS IN THE SAME ORDER
Example 4.3 and Fig. 4.5

30. GANTT CHARTS

31. LOWER BOUND ON SCHEDULE MAKESPAN
Each machine supplies a lower bound
A lower bound based on machine j is
LBj = min i {  r (pir)} +
 i ->j-1 (pij) +
min i { r (pir) }
Example 4.4 and Fig. 4.6

32. SINGLE MACHINE SCHEDULING
LET M = 1
GOAL: MINIMIZE AVERAGE JOB FLOW TIME (i.e. MINIMIZE AVE. WIP)
SHORTEST PROCESSING TIME (SPT) SCHEDULING
EARLIEST DUE DATE (EDD) SCHEDULING
Example 4.5 ; Example 4.6; Example 4.7

33. TWO MACHINE FLOW SHOPS
JOBS WITH SHORT PROCESSING TIME IN MACHINE 1 GO EARLY
JOBS WITH SHORT PROCESSING TIME IN MACHINE 2 GO LATE
JOHNSON’S ALGORITHM (p. 111)
Example 4.8; Example 4.9 and Fig. 4.8

34. JOB SHOP SCHEDULING
GENERAL PROBLEM: TO SCHEDULE PRODUCTION TIMES FOR N JOBS ON M MACHINES
FOR EACH JOB, MACHINE SEQUENCE and PROCESSING TIMES ARE KNOWN
POSSIBLE OBJECTIVES
MINIMIZE MAKESPAN, OR
MINIMIZE NUMBER OF TARDY JOBS, ...

35. DISPATCHING RULES
DISPATCHING: SELECTING OF A JOB FROM INPUT QUEUE FOR PROCESSING WHEN PROCESSOR BECOMES AVAILABLE
STANDARD DISPATCHING RULES
STATIC RULES VS. DYNAMIC RULES
SLACK BASED RULES
MYOPIC VS GLOBAL RULES
Table 4.7 (p. 115); Example 4.10

36. SCHEDULE GENERATION
FULLY ACTIVE SCHEDULE: NEVER MAKE A JOB WAIT IN QUEUE WHEN IT CAN BE COMPLETED BEFORE THE NEXT JOB IS SCHEDULED TO START
NONDELAY SCHEDULE: MACHINE IS NEVER IDLE WHEN ITS QUEUE IS NON-EMPTY
Table 4.9 (p. 117) and Fig. 4.9