Chapter 9 Mixed-Integer Programming. Chapter 9. Chapter 9. Enumeration approach for 20 objects (0,1): 2 20 possibilities, evaluate each case for satisfying constraint. The traveling salesman problem . The problem is to assign values
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Enumeration approach for 20 objects (0,1): 2 20 possibilities, evaluate each case for satisfying constraint.
subject to the 2n constraints
Example: Austin/San Antonio/El Paso/Dallas/Houston
for Binary Variables
The variables. Each pipeline segment has associated with it five variables:
pipe diameter and length, but are assumed to be $870/(in.)(mile)(year).
The rate of work of one compressor is
The inequality constraints. The operation of each compressor is constrained so that the
discharge pressure is greater than or equal to the suction pressure
and the compression ratio does not exceed some prespecified maximum limit K
In addition, upper and lower bounds are placed on each of the four variables
Compressor Compression cost
station ratio ($/year)
1 1.44 70.00
2 1.40 70.00
3 1.12 70.00
4 1.00 70.00
5 1.00 70.00
6 1.00 70.00
7 1.00 70.00
8 1.26 70.00
9 1.00 70.00
10 1.00 70.00
Costs reduced from $14 million/yr (initial guess) to $7 million/yr at optimum
six projects to improve operations as well as profitability.
Due to expenditure limitations and engineering staffing
constraints, however, not all of these projects can be
implemented. The following table gives projected cost,
staffing, and profitability data for each project
A new or modernized production line must be provided
(project 1 or 2). Automation is feasible only for the new line.
Either project 5 or project 6 can be selected, but not both.
Determine which projects maximize the net present value
subject to the various constraints.