Facility Layout 6

MULTIPLE, Other algorithms, Department Shapes

MULTIPLE

• MULTI-floor Plant Layout

Evaluation (MULTIPLE)– Improvement type

– From-To chart as input

– Distance based objective function

(rectilinear distances between

centroids).

– Improvements: Two way exchanges

and steepest descent

Stores

Milling

Turning

Press

Plate

Assembly

Warehouse

– 12 6 9 1 4 –

– – – – 7 2 –

– 3 – – 4 – –

– – – – 3 1 1

– 3 1 – – 4 3

1 – – – – – 7

– – – – – – –

Sto

res

Mill

ing

Tur

ning

Pre

ss

Pla

te

Ass

embl

y

War

ehou

se

MULTIPLE (cont.)

• MULTIPLE can exchange departments that are not adjacent to each other.

• The layout is divided into grids

• Space Filling Curves are generated so that the curve touches each grid in the layout.

MULTIPLE (cont.)

• A layout vector (DEO) is specified and the departments are added to the layout using the layout vector.

• To exchange departments, the positions of the departments in the layout vector are exchanged.

Depts: 1 = 12 grids2 = 4 grids3 = 6 grids

Order = 1, 2, 3

Order = 2, 3, 1

Example - MULTIPLE

6 departments, Each grid 10 ft by 10 ft.All cij = $0.1/ftNo locational restrictions

F 1 2 3 4 5 61 - 100 10 52 - 253 - 254 - 105 - 1006 -

Dist A B C D E FA - 10 20 10 20 30B - 10 20 10 10C - 30 20 10D - 10 20E - 10F -

Space Filling Curve = A - D - E - B - C - F

Initial Layout Vector = 6-2-3-4-5-1

2 3 1

6 4 5

(Draw the initial layout)

Example – Multiple (2) Initial Layout Vector = 6-2-3-4-5-1

2 3 16 4 5

Layout 6-2-3-4-5-1

Pair Flow Cost Dist Total1-2 100 0.1 20 2001-3 10 0.1 10 101-5 5 0.1 10 52-6 25 0.1 10 253-4 25 0.1 10 254-5 10 0.1 10 105-6 100 0.1 20 200

Total 475

Cost = 100*20*0.1

+ 10*10*0.1

+ 5*10*0.1

+ 25*10*0.1

+ 25*10*0.1

+ 10*10*0.1

+ 100*20*0.1

= 475

Example – Multiple – Exchanges (3)

1 3 26 4 5

2 1 36 4 5

2 3 46 1 5

2 3 56 4 1

2 3 61 4 5

3 2 16 4 5

4 3 16 2 5

5 3 16 4 2

6 3 12 4 5

2 4 16 3 5

2 5 16 4 3

2 6 13 4 5

2 3 16 5 4

2 3 14 6 5

2 3 15 4 6

$535

$405

$475

$695

$315

$435

$495

$315

$675

$495

$475

$495

$405

$435

$535

First IterationFirst Iteration

Selected

Example – Multiple – Exchanges (3)

$335

$315

$435

$715

$475

Second IterationSecond Iteration

Exchange 1-2

Exchange 1-6

Exchange 1-3

Exchange 1-4

Exchange 1-5

$405

$335

$495

$715

$315

Exchange 2-3

Exchange 3-4

Exchange 2-4

Exchange 2-5

Exchange 2-6

$315

$425

$435

$315

$355

Exchange 3-5

Exchange 5-6

Exchange 3-6

Exchange 4-5

Exchange 4-6

No more exchanges ! Final Layout. Is it optimal?

Multi-Floor Objective Function

Indices:i,j for departmentsm for floorsl for lifts

where:

Area Constraint:

i j

Vij

Vij

Hij

Hijij cdcdf MIN

0 if min

0 if Vijljill

VijijH

ij ddd

ddd

mi

mi Aa

MULTIPLE objective function

i j

Vij

Vij

Hij

Hijij cdcdf MIN

0 if min

0 if Vijljill

VijijH

ij ddd

ddd

MULTIPLE vs. CRAFT

• Multi-floor capabilities• Accurate cost savings• Exchange any two departments• Considers exchanges across floors

MULTIPLE review

1. The result of running MULTIPLE is a 2-opt solution with respect to the initial layout.

• True or False

2. The advantage(s) of MULTIPLE over CRAFT is(are):a) Exchange any two departments

b) Exchanges departments that are unequal in size and non-adjacent

c) Checks the cost of all exchanges before making the selection

d) All of the above

e) (a) and (b)

Department Shapes

Measure 1 =

Enclosing rectangle area

Department area

Measure 1 = for all shapes 25

16

Are all these shapes equally good?

Department Shapes (2)

Measure 2 =

Enclosing rectangle Length

Enclosing rectangle Width

Measure 2 = for all shapes 5

5

Are all these shapes equally good?

Normalized Shape Factor ()

Shape Factor = Perimeter/Area

Ideal Shape Factor = Perimeter/Areafor a square with the same area

= Shape Factor / Ideal Shape Factor

= Perimeter / Perimeter for a squarewith same area

= P / P*

P = 20

P* = 16

= 1.25

P = 24

P* = 16

= 1.5

P = 26

P* = 16

= 1.625

Other Methods and Tools

• MIP: – formulate the facility layout problem as a

mixed integer programming (MIP) problem by assuming that all departments are rectangular.

• SABLE:– Like MULTIPLE, but instead of steepest

descent pair-wise exchanges, it uses simulated annealing to search for exchanges.

– Less likely to get “stuck” in a local optima

Other Methods and Tools (Cont.)

• Simulated Annealing (SA) and Genetic Algorithms (GA)

– All methods/tools based on steepest descent approach (forces an algorithm to terminate the search at the first two-opt or three-opt solution it encounters), result in a solution which is likely locally optimal.

– Steepest descent algorithms are highly dependent on the initial solution (path dependent).

– SA-based procedure may accept non-improving solutions several times during the search in order to “push” the algorithm out of a solution which may be only locally optimal.

– GA is originated from the “survival of the fittest” (SOF) principle, which works with a family of solutions to obtain the next generation of solutions (good ones propagate in multiple generations)