MODELING AND ANALYSIS OF
MANUFACTURING SYSTEMS
Session 9
FACILITY LAYOUT
E. Gutierrez-Miravete
Spring 2001
FACILITY LAYOUT
THE ARRANGEMENT OF
MANUFACTURING
RESOURCES
IN A PLANT
COMMENTS
• WHICH RESOURCES SHOULD BE
ADJACENT?
• GOAL: TO PRODUCE A BLOCK
PLAN SHOWING THE RELATIVE
POSITIONING OF ALL
DEPARTMENTS
• CAN CAD HELP?
CRITERIA FOR BLOCK PLAN
EVALUATION
• MINIMIZATION OF MATERIAL
HANDLING COST (FREQUENCY AND
LENGTH OF MOVES)
• MINIMIZATION OF THROUGHPUT
AND WIP
• SIMPLIFICATION OF MATERIAL
CONTROL AND SCHEDULING
• REDUCTION IN AISLE SPACE
SOLVING THE FACILITY
LAYOUT PROBLEM
• OFTEN VIA DETERMINISTIC MODELS
• DESIRABLE FEATURES OF SOLUTIONS
•
•
•
•
•
FLEXIBILITY
MODULARITY
MAINTAINABILITY
RELIABILITY
EMPLOYEE MORALE
THE SPINE APPROACH TO
FACILITY DESIGN
• SPINE: CENTRAL CORE OR
PASSAGEWAY TO CONDUCT
MATERIAL FLOW
• DEPARTMENTS EXPAND OUT FROM
CENTRAL CORE
• UTILITIES: CARRIED OVERHEAD
• MATERIAL STORAGE: ALONG SPINE
FACILITY LAYOUT
PROBLEM AND QUESTIONS
• HOW TO ASSIGN EACH DEPARTMENT
TO A SPECIFIC LOCATION IN THE
FACILITY?
• IS THERE A DOMINANT FLOW
PATTERN IN THE PROCESS?
• HOW CAN FLOW DOMINANCE BE
MEASURED?
FLOW DOMINANCE
• CONSIDER DEPARTMENTS i AND
j OUT OF A SET M
• HANDLING SYSTEM COST
• FLOW fij
hij
FLOW COST PARAMETER
• WEIGHTS FOR MATERIAL FLOW
BETWEEN DEPARTMENTS i AND j
(FLOW COST PARAMETER)
wij = fij hij
STATISTICS OF wij
• AVERAGE OF COST FLOW
PARAMETER
wave = i j wij /M2
• STANDARD DEVIATION OF COST
FLOW PARAMETER (FLOW
DOMINANCE MEASURE)
 = [i j (wij2 - M2 wave2)/(M2-1)]1/2
FLOW DOMINANCE
MEASURE
f =  / wave
• UPPER BOUND ( ONE wij DOMINATES)
• LOWER BOUND (ALL wij ARE EQUAL)
• See Eqns 7.3, Table 7.1 and Example 7.1
LAYOUT PROBLEMS VS
LOCATION PROBLEMS
• LAYOUT: MACHINES OCCUPY
SPACE
• LOCATION: MACHINES ARE
POINTS
DISTANCE METRICS (Fig. 7.3)
• RECTILINEAR DISTANCE
• EUCLIDEAN DISTANCE
• lp NORM
dij = [ |xi - xj|p + |yi - yj|p ]1/p
• ADJACENCY INDICATOR
ij
SYSTEMATIC LAYOUT
PLANNING
STEPS IN SYSTEMATIC
LAYOUT PLANNING (Fig 7.4)
STEP 0: DATA COLLECTION
STEP 1: FLOW ANALYSIS
STEP 2: QUALITATIVE ASPECTS
STEP3: RELATIONSHIP DIAGRAM
STEP 4: SPACE REQUIREMENTS
STEP 5: SPACE AVAILABILITY
STEP 6: SPACE RELATIONSHIP DIAGRAM
STEPS 7&8: MODIFYING CONSIDERATIONS &
LIMITATIONS
STEP 9: EVALUATION
STEP 0: DATA COLLECTION
• PRODUCT (WHAT)
• QUANTITY (HOW MUCH)
• ROUTING (HOW)
• SUPPORT SERVICES (WITH
WHAT)
• TIMING/TRANSPORT (WHEN)
S0: DATA COLLECTION
• PARETO CHARTS (Fig 7.5)
• WHAT PERCENT OF ITEMS
CONSTITUTE THE BULK OF
DEMAND?
• WHAT ARE OBJECTIVE
ESTIMATES OF SPACE
REQUIREMENTS?
STEP 1: FLOW ANALYSIS
• TO SPECIFY PHYSICAL
WORKCENTERS WHICH WILL BE
SPATIALLY ARRANGED
• DEPARTMENT DEFINITIONS BASED
AROUND PRODUCTS, PROCESSES OR
CELLS OF SIMILAR PARTS
• FLOW VOLUMES AND PATTERNS
ESTABLISHED
S1: FLOW ANALYSIS
• OPERATION PROCESS CHARTS (Fig 7.6)
– MAJOR OPERATIONS
– INSPECTIONS
– MOVES
– STORAGES
• FLOW PROCESS CHARTS (Fig 7.7)
• FLOW PATTERNS BETWEEN
DEPARTMENTS (Figs 7.8, 7.9, 7.10)
S1: FLOW ANALYSIS
• QUANTITATIVE FLOW DATA VIA
FROM-TO CHARTS (See Table 7.2)
• HOW CAN THE TOTAL FLOW
VOLUME BETWEEN WORKCENTERS
BE OBTAINED?
• HOW CAN THE TOTAL COST BE
OBTAINED?
S1: FLOW ANALYSIS
• COST OF MATERIAL MOVEMENT
FROM WORKCENTER i TO j
cij = wij dij
• TOTAL COST
C = i j cij
S1: FLOW ANALYSIS.
FROM-TO CHARTS (Table 7.2)
• FLOW VOLUMES
• MOVEMENT COST
• DISTANCE BETWEEN
WORKCENTERS
S1: FLOW ANALYSIS.
BASIC FLOW PATTERNS
• STRAIGHT-LINE
• U-SHAPED
• S-SHAPED
• W-SHAPED
• Fig 7.8
S1: FLOW ANALYSIS.
FLOW PATTERNS
• PLANT STRAIGHT SPINE-DEPARTMENT
U PATTERN (Fig 7.9)
• PLANT U SPINE - DEPARTMENT U
• ASSEMBLY FLOW PATTERNS (Fig 7.10)
• KEY: DESIGN A RATIONAL FLOW
PATTERN THAT AVOIDS CONFUSION
AND INTERFERENCE
STEP 2: QUALITATIVE
CONSIDERATIONS
OFTEN, IMPORTANT INFORMATION
CAN NOT BE QUANTIFIED.
– RECEIVING AND SHIPING NEEDING TO
SHARE COMMON FACILITIES
– PURCHASING AND ENGINEERING
NEEDING TO COMMUNICATE
– DELICATE TESTING NEEDING TO BE
FAR FROM HEAVY VIBRATION
S2: QUALITATIVE DATA
• REL CHARTS (Fig 7.11; Table 7.2)
• RATE THE DEGREE OF
DESIRABILITY OF LOCATING
TWO DEPARTMENTS ADJACENT
(A,E,I,O,U,X)
STEP 3: RELATIONSHIP
DIAGRAM
A RELATIONSHIP DIAGRAM
COMBINES QUANTITATIVE AND
QUALITATIVE INFORMATION
TO INITIATE THE
DETERMINATION OF RELATIVE
LOCATION OF FACILITIES (Fig
7.12)
Fig. 7.12
S&R
PC
AT
IC
XT
PS
S3: RELATIONSHIP
DIAGRAM
1.- DEPARTMENTS REPRESENTED BY
SQUARE TEMPLATES
2.- TEMPLATES ARRANGED IN LOGICAL
ORDER
3.- TEMPLATES CONNECTED BY LINES
COMMUNICATING THE RELATIONSHIP
BETWEEN DEPARTMENT PAIRS
4.- ITERATE
S3: RELATIONSHIP
DIAGRAM
TWO BASIC STEPS IN HEURISTICS
– CONSTRUCTION:
DETERMINING THE INITIAL
ARRANGEMENT OF TEMPLATES
– IMPROVEMENT: SEARCH FOR
BETTER ARRANGEMENTS THAN
THE INITIAL CONSTRUCTION
S3: REL DIAGRAM.
CLOSENESS RATING
• ADJACENCY FUNCTION Vij
• TOTAL CLOSENESS RATING (TCR)
TCRi = j Vij
• WHAT IS THE MEANING OF A LARGE
VALUE OF TCRi ?
• WHERE SHOULD A DEPARTMENT WITH
LARGE TCRi BE LOCATED?
S3: REL DIAGRAM.
CONSTRUCTION
1.- CALCULATE TCRi FOR ALL
DEPARTMENTS AND RANK FROM
HIGHEST TO LOWEST
2.- PLACE HIGHEST RANKED
DEPARTMENT AT CENTER
3.- ADD DEPARTMENTS ITERATIVELY SUCH
THAT THE ADJACENCY SCORE (OR
DISTANCE) IS MAXIMAL/MINIMAL
• See Example 7.2 and Fig. 7.13
S3: REL DIAGRAM.
IMPROVEMENT
• IS THE INITIAL CONSTRUCTION
OPTIMAL?
• WHAT IS A k-OPT SOLUTION?
• CRAFT : COMPUTER BASED
IMPROVEMENT PROCEDURE
– STEEPEST DESCENT PAIRWISE EXCHANGE
– PAIRS ARE SWITCHED WHICH LEAD TO THE
LARGEST IMPROVEMENT
S3: REL DIAGRAM.
IMPROVEMENT
• PROSPECTIVE DEPARTMENTS FORM
A GRID OF EQUAL SIZED SQUARES
• A FEASIBLE SOLUTION TO THE
LAYOUT PROBLEM IS THE
ASSIGNMENT OF GRID SQUARES TO
DEPARTMENTS (THE a VECTOR)
a = (a1,a2,a3,...,aM)
S3: REL DIAGRAM.
IMPROVEMENT
• NOW TRY EXCHANGING
DEPARTMENTS u AND v . WHAT IS
THE COST INVOLVED IN GOING
FROM LAYOUT a TO a’?
Cuv(a) = C(a) - C(a’)
• WHAT IS THE CHANGE IN ADJACENCY
MEASURE? (Example 7.3 and Fig. 7.14)
STEP 4: SPACE
REQUIREMENTS
• USE OF INDUSTRIAL STANDARDS
• ROUGH SKETCHES + LOCAL
STANDARDS
• USE OF CURRENT SPACE NEEDS
• USE OF X SQUARE FEET PER UNIT
PRODUCED
STEP 5: SPACE
AVAILABILITY
• EXISTING FACILITY
• NEW FACILITY
• GOAL: FIND THE MINIMUM
SPACE REQUIRED
STEP 6: SPACE
RELATIONSHIP DIAGRAM
• DEPARTMENTS OFTEN HAVE
DIFFERENT SIZES!
• A SPACE RELATIONSHIP DIAGRAM
REPLACES THE EQUAL SIZE
TEMPLATES OF A RELATIONSHIP
DIAGRAM WITH TEMPLATES OF SIZE
PROPORTIONAL TO ACTUAL SPACE
REQUIREMENTS (Fig 7.15; Table 7.3)
S 6: SWITCHES IN A SRD
• IF DEPARTMENTS ARE OF EQUAL
SIZE, SWAP GRID SQUARES
• IF DEPARTMENTS ARE ADJACENT
AND OF DIFFERENT SIZE, SELECT
ENOUGH GRID SQUARES FROM
LARGE DEPT FARTEST FROM SMALL
ONE, THEN MOVE SMALL DEPT INTO
SELECTED SQUARES (Fig 7.16)
STEPS 7 & 8:
MODIFYING CONSIDERATIONS
AND LIMITATIONS
• SITE-SPECIFIC AND
OPERATION-SPECIFIC
CONDITIONS MAY AFFECT
THE LAYOUT
• EXAMPLES
STEP 9: EVALUATION
• AVAILABLE ALTERNATIVES MUST BE
COMPARED
– PICTORIAL DISPLAYS
W/SUPERIMPOSED FLOWS
– ADVANTAGES/DISADVANTAGES
– COSTS
– QUALITATIVE FACTOR RATINGS
QUADRATIC ASSIGNMENT
PROBLEM APPROACH
OBJECTIVE OF QAP
FIND THE MINIMUM COST
ASSIGNMENT OF M DEPARTMENTS
TO M LOCATIONS WHERE THE COST
TO ASSIGN DEPARTMENT i TO
LOCATION k AND DEPARTMENT j
TO LOCATION
l IS cijkl
OBJECTIVE
min ijkl cijkl xik xjl
with
and
i xik = 1 for all locations
k xik = 1 for all depts.
NOTE: PROBLEM IS HARD TO SOLVE.
IT’S BETTER TO USE HEURISTICS (See
Eqns 7.13, 7.14)
PAIRWISE EXCHANGE
• MEASURE OF IMPORTANCE: TOTAL
FLOW
• START WITH A SOLUTION
• PROCEED TO SWITCH PAIRS OF
DEPARTMENTS THAT IMPROVE TOTAL
FLOW UNTIL NO IMPROVING
SWITCHES EXIST
• Warning: No guarantees! (Fig. 7.17, Table 7.4)
VNZ HEURISTIC
• RANK DEPARTMENTS BY THEIR COST
(INSTEAD OF THEIR CLOSENESS)
• SELECT THE TWO MOST IMPORTANT
DEPARTMENTS
• CONSIDER SEQUENTIALLY ALL
POSSIBLE EXCHANGES INVOLVING
THE TWO DEPARTMENTS
VNZ HEURISTIC
• MAKE TWO PASSES THROUGH THE
PAIRS OF DEPARTMENTS MAKING
SWITCHES WHENEVER
IMPROVEMENT IS ENCOUNTERED
• See Example 7.4
BRANCH AND BOUND
• Francis & White method
• Steps (see p. 230)
• See Example 7.5 and Fig. 7.18
GRAPH THEORETIC
APPROACH
• BOTH QUANTITATIVE AND QUALITATIVE
DATA NEEDED
• HOW ABOUT MAXIMIZING THE
ADJACENCY SCORE?
• PHYSICAL MAP OF DEPARTMENTS =
PLANAR GRAPH G(N,A)
• PLANAR GRAPHS HAVE DUALS
– NODES>REGIONS - ARCS>BOUNDARIES
• See Fig. 7.19
GRAPH PROPERTIES
1.- THE DUAL OF A PLANAR GRAPH IS
PLANAR
2.- THE MAXIMUM NUMBER OF ARCS
IN A PLANAR GRAPH IS 3M-6
3.- A MAXIMALLY PLANAR GRAPH HAS
2M-4 FACES AND EACH FACE IS
TRIANGULAR
MAXIMALLY PLANAR
WEIGHTED GRAPH
• A MAXIMALLY PLANAR WEIGHTED
GRAPH (MPWG) IS A MPG WHOSE
SUM OF ARC WEIGHTS IS AT LEAST
AS LARGE AS THE SUM FOR ALL
OTHER MPG’S
• MAXIMIZING THE ADJACENCY
SCORE IS EQUIVALENT TO FINDING A
MPWG
GRAPH THEORY APPROACH
1.- FIND A MPWG BASED ON REL
CHART WEIGHTS. ADD A PSEUDODEPARTMENT VERTEX TO FORM THE
BUILDING EXTERIOR.
2.- FIND THE DUAL OF THE MPWG
3.- CONVERT THE DUAL INTO A BLOCK
PLAN
FINDING THE MPWG
• GOAL: FIND A MPWG IN WHICH
NODES ARE DEPARTMENTS AND
EDGE WEIGHTS ADJACENCY
DESIRABILITY
• CONSTRUCTION (See Example 7.6 and
Figs. 7.21, 7.22)
• EDGE REPLACEMENT (Fig. 7.23)
• VERTEX RELOCATION (Fig. 7.24)
WHAT TO DO WITH LARGE
FACILITIES?
• Strategy: Decompose into nearly
independent entities.
• FORMING SUBGROUPS OF
DEPARTMENTS WITH HIGH
INTERACTION
• GRAPHS AND SUBGRAPHS
NET AISLE AND
DEPARTMENT LAYOUT
• ONCE BASIC FLOW PLAN IS
FORMULATED, DETAILED FLOW
PATTERNS MUST BE ESTABLISHED
• NEED TO DETERMINE AISLES AND I/O
LOCATIONS
• TRAVEL RESTRICTED TO AISLES AND
FROM OUTPUT(1) TO INPUT(2)
• FLOW WILL FOLLOW SHORTEST PATHS
MONTREUIL NET LAYOUT
MODEL
• INPUTS: RELATIVE DEPT. LOCATIONS,
ADJACENCIES, AISLE CORRIDORS,
DEPT. DIMENSION BOUNDS
• OUTPUTS: AISLE WIDTHS,
COORDINATES OF DEPT.
BOUNDARIES AND I/O LOCATIONS
• Example 7.7; Tables 7.5, 7.6 and Fig 7.25
LOCATING NEW FACILITIES
• HOW ABOUT ADDING NEW
ENTITIES TO AN EXISTING
FACILITY?
• TWO POSSIBILITIES
– SINGLE ENTITY ADDITION
– MULTIPLE ENTITY ADDITION
SINGLE FACILITY LOCATION
• LOCATIONS OF EXISTING FACILITIES
ARE KNOWN (Pi)
• COST PARAMETERS (wi) FOR NEW
MACHINE ARE KNOWN
• PROBLEM STATEMENT
min f(x,y) = i wi d(X,Pi)
SINGLE FACILITY LOCATION
• IF LINEAR DISTANCE IS USED f(x,y)
BECOMES SEPARABLE INTO f1(x)
AND f2(y)
• IF THERE ARE NO CONSTRAINS, THE
MEDIAN LOCATION SOLVES THE
PROBLEM
• Example 7.8; Fig. 7.26
SINGLE FACILITY LOCATION
• WHAT TO DO WHEN THE MEDIAN
LOCATION IS NOT FEASIBLE?
• USE OF ISOCOST (CONTOUR)
LINES
• Example 7.9; Fig. 7.27
MULTIFACILITY LOCATION
• WHAT TO DO WHEN SEVERAL
MACHINES ARE TO BE ADDED?
• See Sect. 7.7.2