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Facility Layout 6

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).

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Facility Layout 6

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  1. Facility Layout 6 MULTIPLE, Other algorithms, Department Shapes

  2. 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

  3. 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.

  4. MULTIPLE (cont.) Order = 1, 2, 3 • 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. Order = 2, 3, 1 Depts: 1 = 12 grids 2 = 4 grids 3 = 6 grids

  5. Example - MULTIPLE 6 departments, Each grid 10 ft by 10 ft. All cij = $0.1/ft No locational restrictions A - D - E - B - C - F Space Filling Curve = Initial Layout Vector = 6-2-3-4-5-1 (Draw the initial layout)

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

  7. Example – Multiple – Exchanges (3) First Iteration $535 $435 $475 $495 $405 $495 $315 $475 $405 $675 $435 $695 $495 Selected $535 $315

  8. Example – Multiple – Exchanges (3) Second Iteration $335 $405 $315 Exchange 1-2 Exchange 2-3 Exchange 3-5 $315 $335 $425 Exchange 1-3 Exchange 2-4 Exchange 3-6 $435 $495 $435 Exchange 1-4 Exchange 2-5 Exchange 4-5 $715 $715 $315 Exchange 1-5 Exchange 2-6 Exchange 4-6 $475 $315 $355 Exchange 1-6 Exchange 3-4 Exchange 5-6 No more exchanges ! Final Layout. Is it optimal?

  9. Multi-Floor Objective Function Indices: i,j for departments m for floors l for lifts where: Area Constraint:

  10. MULTIPLE objective function

  11. MULTIPLE vs. CRAFT • Multi-floor capabilities • Accurate cost savings • Exchange any two departments • Considers exchanges across floors

  12. MULTIPLE review • The result of running MULTIPLE is a 2-opt solution with respect to the initial layout. • True or False • The advantage(s) of MULTIPLE over CRAFT is(are): • Exchange any two departments • Exchanges departments that are unequal in size and non-adjacent • Checks the cost of all exchanges before making the selection • All of the above • (a) and (b)

  13. Department Shapes Enclosing rectangle area Measure 1 = Department area Are all these shapes equally good? 25 Measure 1 = for all shapes 16

  14. Department Shapes (2) Enclosing rectangle Length Measure 2 = Enclosing rectangle Width Are all these shapes equally good? 5 Measure 2 = for all shapes 5

  15. Normalized Shape Factor (W) Ideal Shape Factor = Perimeter/Area for a square with the same area W = Perimeter / Perimeter for a square with same area W = P / P* P = 20 Shape Factor = Perimeter/Area P* = 16 W = 1.25 P = 24 P* = 16 W = 1.5 W = Shape Factor / Ideal Shape Factor P = 26 P* = 16 W = 1.625

  16. 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

  17. 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)

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