MODELING AND ANALYSIS OF
MANUFACTURING SYSTEMS
Session 12
MACHINE SETUP AND
OPERATION SEQUENCING
E. Gutierrez-Miravete
Spring 2001
INTRODUCTION
• WHOLE SYSTEM DESIGN
STRATEGIES VS INDIVIDUAL
CELL/WORKSTATION DESIGN
STRATEGIES
• QUESTION: HOW TO TOOL THE
MACHINE AND THEN SEQUENCE
PRODUCTION ACTIVITIES IN IT?
• GOAL: MAXIMIZE PRODUCTIVITY
OPORTUNITIES
• SEQUENCE BATCHES SO AS TO
MINIMIZE TOOLING
CHANGEOVERS
• SEQUENCE ACTIVITIES SO AS TO
MINIMIZE IDLE TIMES
• OPTIMIZE CELL LAYOUT SO AS TO
MINIMIZE ASSEMBLY TIME
SEQUENCING AND
OPTIMIZATION
MANY SEQUENCING
PROBLEMS IN
MANUFACTURING CELL
PLANNING ARE CLASSIC
OPTIMIZATION PROBLEMS
CELL VS SYSTEM
• BOTH, CLEVER SEQUENCING OF
OPERATIONS AND OVERALL SYSTEM
DESIGN ARE IMPORTANT FOR
SUCCESS IN MANUFACTURING
• TIME FRAMES
– FOR OVERALL SYSTEM DESIGN: WEEKS
OR MONTHS (LONG TERM)
– FOR SEQUENCE DESIGN:
MINUTES/HOURS (SHORT TERM)
TASK ASSIGNMENT
LINEAR ASSIGNMENT
PROBLEM
• GOAL:
– TO DISTRIBUTE N TASKS
AMONG N WORKERS SO AS TO
MINIMIZE COST
• CONSTRAINTS:
– 1 TASK PER WORKER
– 1 WORKER PER TASK
COST MATRIX C
• ROWS: WORKERS
• COLUMNS: MACHINES
• SUMMARIZES THE
ASSIGNMENT COSTS
LAP: MATHEMATICAL
FORMULATION
• minimize
Ci j cij xij
• subject to:
i xij = 1 (for all tasks)
j xij = 1 (for all workers)
Facts
• IF A CONSTANT IS ADDED TO EVERY
ELEMENT OF A ROW OR COLUMN OF
C, THE OPTIMAL SOLUTION DOES
NOT CHANGE BUT ITS VALUE
CHANGES BY THE ADDED CONSTANT
• IF ALL cij > 0, ANY SOLUTION WITH
COST = 0 MUST BE OPTIMAL
Hungarian Algorithm
• Proceeds by adding and substracting
constants from rows and columns so as to
maintan a non-negative cost matrix.
When a feasible solution is found using
only 0 cost cells, optimum has been
found.
HA Steps
• STEP 1: COST REDUCTION BY
CONSTRUCTION OF THE REDUCED
COST MATRIX. THE RCM IS
OBTAINED BY SUBSTRACTING
FIRST THE MINIMUM ELEMENT IN
EACH ROW FROM ALL ELEMENTS
IN THE ROW THEN DOING
LIKEWISE WITH COLUMNS
HA Steps cont’d
• STEP 2: SEARCH FOR A FEASIBLE
SOLUTION USING ONLY THE 0’S IN
THE RCM . IF THIS SUCCEEDS,
OPTIMAL SOLUTION HAS BEEN
FOUND. IF ALL 0’S CAN BE
COVERED WITH LESS THAN n
HORIZONTAL AND VERTICAL
LINES, CONTINUE.
HA Steps cont’d
• STEP 3: FURTHER REDUCTION.
FIND THE MINIMUM UNCOVERED
ELEMENT. SUBSTRACT THIS
REDUCED COST FROM EACH
UNCOVERED ELEMENT AND ADD IT
TO EACH TWICE-COVERED
ELEMENT. GO TO 2.
• Example 8.1, Table 8.1, Fig. 8.1, pp. 263-
TASK SEQUENCING
TWO CLASSES OF
PROBLEMS
• EVALUATE CHANGEOVER COSTS
WHEN COSTS ARE COMPLETELY
DETERMINED BY THE CURRENT
JOB SETUP AND THE NEXT JOB TO
BE LOADED
• EVALUATE COSTS WHEN THE
ENTIRE SEQUENCE OF JOBS MUST
BE KNOWN
COMPLETE CHANGEOVERS
• N JOBS ARE TO BE PERFORMED ON
ONE MACHINE
• UNIT PROCESSING TIME AND BATCH
SIZE DETERMINE TOTAL
PROCESSING TIME
• CHANGEOVER TIMES DEPEND ONLY
ON CURRENT AND NEXT PRODUCT
• TOTAL SETUP TIME DEPENDS ON JOB
SEQUENCE
TRAVELING SALESMAN
PROBLEM
• A SALESMAN MUST VISIT EVERY
CITY IN HIS/HER TERRITORY THEN
RETURN HOME IN SUCH A WAY
THAT THE SMALLEST POSSIBLE
TOTAL DISTANCE IS TRAVELLED.
• TSP CAN BE VISUALIZED WITH A
GRAPH OF NODES (CITIES) AND
ARC LENGTHS (DISTANCES)
TRAVELING SALESMAN
PROBLEM
• DISTANCE BETWEEN CITIES i & j =
cij
• ALL ARCS ARE BIDIRECTIONAL
• NO SUBTOURS ALLOWED
• FIVE CITY COMPLETE TSP GRAPH
Fig 8.2a
• FIVE CITY POSSIBLE TOUR GRAPH
Fig 8.2b
SOLUTION OF THE TSP
• CLASSICAL OPTIMIZATION
TECHNIQUES ARE HARD TO APPLY
WHEN N IS LARGE (See Eqn 8.5-)
• HEURISTIC METHODS ARE MOST
FREQUENTLY USED
– NO SUBTOUR CONSTRAINT IS
TEMPORARILY RELAXED
– SOLVE RESULTING OPTIMIZATION
PROBLEM
TSP BY CLOSEST
INSERTION ALGORITHM
1.- SELECT A STARTING CITY
2.- PROCEED THROUGH N-1 STAGES
ADDING A NEW CITY AT EACH STAGE.
THE NEW CITY IS SELECTED FROM
THOSE CURRENTLY UNASSIGNED SUCH
THAT IT IS CLOSEST TO ANY CITY IN
THE ACCUMULATED PARTIAL
SEQUENCE
• Example 8.2; Fig 8.3, pp. 268-
TSP BY MINIMUM
SPANNING TREE
• A MST IS ANY SET OF N-1 ARCS
THAT TOUCH EACH NODE AND
HAVE THE SMALLEST SUM OF
COSTS FOR ANY SUCH SET
• BY MODIFYING THE MST SO THAT
EACH NODE IS CONNECTED
EXACTLY BY TWO ARCS IN A
CONNECTED TREE OBTAIN TSP
SOLUTION
TSP BY SUBTOUR
INTEGRATION
• START WITH A SOLUTION TO THE
ASSIGNMENT PROBLEM
• TRY TO CONNECT TWO SUBTOURS
AT A TIME BY SWITCHING ARCS
• ONCE ALL LAP SUBTOURS ARE
COMBINED, GOT TSP SOLUTION
• Fig 8.4
PARTIAL CHANGEOVERS
• N JOBS ARE TO BE PERFORMED ON ONE
MACHINE CAPABLE OF HOLDING M
TOOLS
• JOB j REQUIRES TOOLS Aj
• TOTAL NUMBER OF TOOLS REQUIRED
EXCEEDS M (TOOL CHANGES REQUIRED)
• NO JOB REQUIRES MORE THAN M TOOLS
• AT EACH JOB COMPLETION SOME TOOLS
MAY HAVE TO BE REMOVED AND NEW
TOOLS ADDED
• Fig 8.5
OBJECTIVE
TO ORDER JOBS AND TOOL
CHANGEOVERS TO MINIMIZE
THE TOTAL NUMBER OF TOOLS
CHANGED ON THE MACHINE
NOTES
• ALWAYS KEEP M TOOLS ON
MACHINE
• THE ORDERING FOR JOBS ON THE
MACHINE IS GIVEN
• KEEP TOOL NEEDED SOONEST
(KTNS) RULE IS OPTIMAL
• REMOVE ONLY “LONGEST UNTIL
NEXT USE” TOOLS
JOB ORDERING
• IF JOB r USES ONLY A SUBSET OF
TOOLS USED BY ITS PREDECESOR s
CHANGEOVER IS NOT INCREASED
(i.e. OPTIMAL SEQUENCE)
• JOB SEQUENCING PROBLEM IS
SIMILAR TO GROUP FINDING IN GT
• THE TOOL-JOB MATRIX
JOB ORDERING
• SOLUTION METHODS
– BINARY CLUSTERING
• Ex 8.3, Tables 8.3, 8.4
– TSP
• Table 8.5
SOLUTION OF THE
PARTIAL CHANGEOVER
PROBLEM
• STEP 1: JOB COMBINATION
(REDUCTION)
• STEP 2: JOB ORDERING
• STEP 3: TOOL SETUP PLANNING
BY KTNS
INTEGRATED ASSIGNMENT
AND SEQUENCING
QUESTION
• WHAT TO DO WHEN CELL SETUP
(TOOLING) AND JOB SEQUENCING
ARE RELATED BY NEITHER
DICTATES THE OTHER?
• NEED TO:
– MAKE A SEQUENCING DECISION and
– MAKE A SETUP DECISION
NOTES
• PROBLEM 1: PLAN SETUP AND
OPERATION OF ASSEMBLY CELLS
• PROBLEM 2: SETUP AND SEQUENCE
OF A MACHINE (INTERDEPENDENT
TOOLS)
• GOAL: TO MINIMIZE CYCLE TIME
• SOLUTION TECHNIQUES:
HEURISTICS
ASSEMBLY CELL LAYOUT
AND SEQUENCING
• ASSEMBLY ENVIRONMENTS
– MASS PRODUCED SINGLE PRODUCT
– MULTIPLE PRODUCTS PRODUCED IN
ALTERNATING LOTS WITH
CHANGEOVER REQUIRED
– MIX OF PART TYPES ASSEMBLED
SIMULTANEOUSLY IN CELL WITHOUT
CHANGEOVER
REQUIRED
• FIND HOW TO PERFORM THE SET
OF TASKS THAT HAVE BEEN
ASSIGNED TO A WORKSTATION
SINGLE PART TYPE
• A SINGLE PRODUCT FRAME
• PRODUCT FRAME HAS N
LOCATIONS WHERE PARTS ARE TO
BE ADDED
• WORKSTATION HAS N BINS WHERE
PART FEEDERS ARE PLACED
• Fig 8.6
REQUIRED
• ASSIGN FEEDERS TO BINS
• DETERMINE THE ORDER IN
WHICH PARTS ARE TO BE
ADDED TO FRAME
• PROBLEM CAN BE MODELED
AS A 2N-CITY TSP
BIN ASSIGNMENT AND
INSERTION SEQUENCING
• BIN ASSIGNMENT GOAL: MINIMIZE
THE LOADED TRAVEL TIME
(DISTANCE) FOR THE ASSEMBLER
• INSERTION SEQUENCING GOAL:
MINIMIZE THE UNLOADED TRAVEL
TIME (DISTANCE) FOR THE
ASSEMBLER
• Ex 8.4, Tables 8.6 , 8.7; Ex 8.5, Table 8.8
MIXED PRODUCTS
• TYPICALLY, SEVERAL PRODUCT
TYPES ARE BEING PRODUCED
SIMULTANEOUSLY IN THE SAME
CELL
• DEMAND PROPORTIONS
DETERMINED BY BILL OF
MATERIALS FOR END PRODUCTS
MIXED PRODUCT:
UNPACED LINE
• ASSUME
– RELATIVE DEMANDS ARE KNOWN
– M FRAMES TO BE MADE
– pm IS THE PROPORTION OF TYPE m
FRAMES
– BINS KEPT ON SAME PLACE
• GOAL: MINIMIZE AVERAGE
ASSEMBLY TIME OF PRODUCT
MIXED PRODUCT:
UNPACED LINE
• FOR EACH PART TYPE COMPILE TABLE
OF TRAVEL TIMES (Table 8.7)
• COMBINE TABLES BY WEIGHTED
AVERAGE
cij = m pm cijm
– pm proportion of type m frames
– cijm total travel time per type m frame if
part i is assigned to bin j
– Ex. 8.6, Tables 8.9, 8.10
CELL LAYOUT AND
SEQUENCING:
INTERDEPENDENT TOOLS
• THE NC PUNCH PRESS
– 36 TOOL TOOL TURRET (Fig 8.7)
– PARTS MAY REQUIRE UP TO 200 HITS
– HIT SEQUENCE MAY BE SUBJECT TO
PRECEDENCE CONSTRAINTS
• GOAL: LOAD TOOLS AND SEQUENCE
HITS TO MINIMIZE PRODUCTION CYCLE
• Ex 8.7, Fig. 8.8, Tables 8.11, 8.12