MODELING AND ANALYSIS OF MANUFACTURING SYSTEMS Session 6

							MODELING AND ANALYSIS OF
MANUFACTURING SYSTEMS
        Session 6
     SCHEDULING
      E. Gutierrez-Miravete
          Spring 2001
 TYPES OF FLOW SYSTEMS
• PRODUCT LAYOUT
 – ASSEMBLY LINES
 – TRANSFER LINES
• PROCESS LAYOUT
 – FLOW SHOP (jobs go through same sequence)
 – JOB SHOP (each job has its own route)
• CELLULAR LAYOUT
  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
 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
 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
  THROUGHPUT TIME

THE TIME BETWEEN WHEN
THE JOB IS RELEASED TO
THE SHOP AND WHEN IT IS
COMPLETED AND READY
FOR DELIVERY
    COMPONENTS OF
   THROUGHPUT TIME
• PROCESSING TIME
• SETUP TIME
• MATERIAL HANDLING
  TIME
• WAITING TIME
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
  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)
      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?
      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
 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
     THROUGHPUT TIME

T = S{i} ( pij + wj + mj)
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
  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?)
     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)
    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)
   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
       BOTTLENECKS
• WORKCENTER WITH THE HIGHEST
  UTILIZATION
• UTILIZATION = PROCESSING
  TIME/AVAILABLE TIME
• BOTTLENECK SCHEDULING GOAL:
  TO MAXIMIZE THE PRODUCTIVE
  UTILIZATION OF BOTTLENECKS
          UTILIZATION
•   FOR PART i AND WORKCENTER m
•   DEMAND OF i Di
•   SCHEDULABLE TIME Pm
•   LOAD PROFILE pim
•   UTILIZATION um
          um =  pimDi/ Pm
       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?
        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
 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
 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
FLOW SHOP SEQUENCING
REGULAR MEASURES OF
PERFORMANCE (nondecreasing in job
completion times)
–   AVERAGE COMPLETION TIME
–   MAXIMUM COMPLETION TIME
–   FLOW TIME
–   LATENESS
–   TARDINESS
        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)
        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
      TYPICAL OBJECTIVES
•   MINIMIZE AVERAGE FLOW TIME
•   MINIMIZE MAKESPAN
•   MINIMIZE AVERAGE TARDINESS
•   MINIMIZE MAXIMUM TARDINESS
•   MINIMIZE NUMBER OF TARDY JOBS
           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
 PERMUTATION SCHEDULE
• ALL JOBS VISIT MACHINES IN SAME
  SEQUENCE
• ALL MACHINES PROCESS JOBS IN
  THE SAME ORDER
• Example 4.3 and Fig. 4.5
GANTT CHARTS
      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
       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
    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
  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, ...
       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
  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