MODELING AND ANALYSIS OFMANUFACTURING 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