MODELING AND ANALYSIS OFMANUFACTURING SYSTEMS

Session 9 FACILITY LAYOUT

E. Gutierrez-MiraveteSpring 2001

FACILITY LAYOUT

THE ARRANGEMENT OF MANUFACTURING

RESOURCES

IN A PLANT

COMMENTS

• WHICH RESOURCES SHOULD BE ADJACENT?

• GOALGOAL: 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 hij

• FLOW fij

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 wave

2)/(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 SYSTEMATIC LAYOUT PLANNINGPLANNING

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 XT

PSATPC

IC

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 ijkl cijkl xik xjl

with i xik = 1 for all locations

and 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 PSEUDO-DEPARTMENT VERTEX TO FORM THE BUILDING EXTERIOR.

2.- FIND THE DUAL OF THE MPWG3.- 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