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Models for the Layout Problem

Models for the Layout Problem. Chapter 7. Models. Physical Analog Mathematical. Analog Model. Algorithms. Computation time requirement comparison of polynomial and nonpolynomial algorithms [1]. [1] Based on data in Garey and Johnson (1979). Server(s). Arrival Process.

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Models for the Layout Problem

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  1. Models for the Layout Problem Chapter 7

  2. Models • Physical • Analog • Mathematical

  3. Analog Model

  4. Algorithms Computation time requirement comparison of polynomial and nonpolynomial algorithms[1] [1] Based on data in Garey and Johnson (1979).

  5. Server(s) Arrival Process Departure Process Queue Generic Modeling Tools • Mathematical Programming • Queuing and Queuing Network • Simulation

  6. Single-row layout

  7. Multi-row layout

  8. Terminal Gates Airport terminal gates

  9. Department shape approximation

  10. li lj Dept i Dept j xi xj Single-row layout modeling

  11. Parameters and variables for the single-row layout model Parameters: • n number of departments in the problem • cij cost of moving a unit load by a unit distance between departments i and j • fij number of unit loads between departments i and j • li length of the horizontal side of department i • dij minimum distance by which departments i and j are to be separated horizontally • H horizontal dimension of the floor plan Decision Variable: • xi distance between center of department i and vertical reference line (VRL)

  12. li lj . . . Dept i Dept j xi xj ABSMODEL 1 Subject to

  13. Customer service General repair area Parts display area Do Example 1 in LINGO

  14. LMIP 1? Minimize Subject to

  15. LMIP 1 Minimize Subject to

  16. LINGO • Do Example 2 in LINGO without integer variables • Do Example 2 in LINGO with integer variables Machine Dimensions Horizontal Clearance Matrix Flow Matrix

  17. QAP Parameters: n total number of departments and locations aij net revenue from operating department i at location j fik flow of material from department i to k cjl cost of transporting unit load of material from location j to l Decision Variable:

  18. QAP i=1,2,...,n Subject to j=1,2,...,n i, j=1,2,...,n

  19. Do Example 3 in LINGO Office Site

  20. ABSMODEL 2 Minimize |xi – xj| + |yi – yj|> 1 i=1,2,...,n–1; j=i+1,...,n xi, yi = integeri=1,...,n Subject to

  21. Do Example 4 in LINGO Office Site

  22. ABSMODEL 3 Minimize |xi – xj| +Mzij> 0.5(li+lj)+dhiji=1,2,...,n–1; j=i+1,...,n |yi – yj| +M(1-zij)> 0.5(bi+bj)+dviji=1,2,...,n–1; j=i+1,...,n zij(1-zij)= 0 i=1,2,...,n–1; j=i+1,...,n xi, yi>0 i=1,...,n Subject to

  23. Do Example 5 in LINGO Office Trips Matrix

  24. LMIP 2 Subject to

  25. LP for generating blockplan Parameters Upper and lower bounds on the length of department i Upper and lower bounds on the width of department i Upper and lower bounds on the perimeter of department i Set of department pairs adjacent in the horizontal and vertical dimensions, respectively Decision Variables x, y coordinates of upper right corner of department i x, y coordinates of lower left corner of department i

  26. LP for generating blockplan (cont.) Subject to

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