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? 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 h ij FLOW f ij

FLOW COST PARAMETER WEIGHTS FOR MATERIAL FLOW BETWEEN DEPARTMENTS i AND j (FLOW COST PARAMETER) w ij = f ij h ij

STATISTICS OF w ij AVERAGE OF COST FLOW PARAMETER w ave =  i  j w ij /M 2 STANDARD DEVIATION OF COST FLOW PARAMETER (FLOW DOMINANCE MEASURE)  = [  i  j (w ij 2 - M 2 w ave 2 )/(M 2 -1)] 1/2

FLOW DOMINANCE MEASURE f =  / w ave UPPER BOUND ( ONE w ij DOMINATES) LOWER BOUND (ALL w i j 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 l p NORM d ij = [ |x i - x j | p + |y i - y j | 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 P RODUCT (WHAT) Q UANTITY (HOW MUCH) R OUTING (HOW) S UPPORT SERVICES (WITH WHAT) T IMING/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 c ij = w ij d ij TOTAL COST C =  i  j c ij

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 S&R XT PS AT PC 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 V ij TOTAL CLOSENESS RATING ( TCR ) TCR i =  j V ij WHAT IS THE MEANING OF A LARGE VALUE OF TCR i ? WHERE SHOULD A DEPARTMENT WITH LARGE TCR i 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 ’?  C uv ( 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 c ijkl

OBJECTIVE min  i  j  k  l c ijkl x ik x jl with  i x ik = 1 for all locations and  k x ik = 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 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 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 ( P i ) COST PARAMETERS ( w i ) FOR NEW MACHINE ARE KNOWN PROBLEM STATEMENT min f(x,y) =  i w i d(X,P i )

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