Airport Terminal Layout Modeling Algorithm Comparison

1. Models for the Layout Problem Chapter 10

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