Computing Information

Use the CS Unix Labs on the first floor of CS&S: Locations here.

For new users of Unix and the CS Unix facilities, orientation sessions will be held in CS&S 1325 according to the following schedule.

CS Unix Environment: You can develop models for any homework assignment or project on your Windows PC (see below) or some other non-unix environment. Ultimately, however, your programs must be runnable on the CS Unix systems and must be submitted through these systems.

You need to set up your unix paths properly in order to run GAMS and the handin utility for homework submission. We have created a .cshrc file that does this for you. To obtain and run it, login to your CS Unix account and type

cp ~cs635-1/public/.cshrc.local  ~/.cshrc.local
source ~/.cshrc 

GAMS for the PC: Limited versions of GAMS can be downloaded for many platforms. The Windows version is particularly nice, as it includes an Integrated Development Environment. We cannot give support for installation on your own personal computers.

Thanks to GAMS, I have obtained a license for the full version of GAMS for Windows PCs for the duration of the class. When you download and install GAMS on your PCs, it will ask you for the license file during installation. Please save this file somewhere on your PC, and tell GAMS its whereabouts during installation.

Texts

GAMS - A User's Guide is electronically available.

The following should be on 2-hour reserve at the Wendt Library.

• Model Building in Mathematical Programming, H.P. Williams, Wiley, (4th Edition) 1999.
• Introduction to Mathematical Programming, W. Winston and M. Ventataraman, Duxbury, (4th Edition) 2003.
• Optimization in Operations Research, R. Rardin, Prentice Hall, 1998.
• Practical Management Science, Winston and Albright, Duxbury Press, 1997.

• A GAMS Tutorial (by Rick Rosenthal). This will be used for several introductory class lectures.
• GAMS Solver Manuals, etc
• GAMS/Cplex Manual is electronically available.
• gdx utils manual is electronically available.
• gdxviewer.exe, a PC based viewer for gdx files.
• NEOS Optimization Tree

Examples (some will be used in class)

• Top Brass Example (Rardin). Variants with
  • upper bounds specified via .up,
  • use of set
  • use of set, parameter, scalar, sum.
  • adds postprocessing of the results, use of alias, display. Here is the listing file also.
• MoBrass Example: modified version of topbrass, with costs included.
• Transport Model (GAMS Library)
• Examples with sets, subsets, ord() and card():
  • Ordered one-dimensional sets and use of card() and ord(). Also listing file
  • Subsets and multidimensional sets including listing file
  • Subsets and their use in defining equations (Fibonacci example) including listing file
• Examples showing logical conditions and conditional assignments:
  • Set membership logical condition and conditional assignment (listing file);
  • Fibonacci example with ord() and conditional assignment (listing file);
  • Fibonacci example with sameas() and conditional assignment (listing file);
  • Fibonacci example with set membership condition and conditional assignment (listing file);
  • Sum of squares, using ord(), cond(), and conditional assignment;
• Drugco Example (Winston and Albright).
• Tyco Example (Winston and Albright, p.116).
• Mighty Steel Example, and listing file.
• Simple unbounded and infeasible linear programs.
• Use of options in display statements, and listing file
• Fibonacci example using dynamic sets, and listing file.
• Establishing static and dynamic sets, and listing file.
• Using dynamic sets to find leaves and root nodes of a directed graph, and listing file.
• Minimum cost network flow example and listing file. Also a modified version with capacity constraints, and listing file.
• Larger random minimum-cost network flow example and listing file.
• The same minimum-cost network flow example, with different options contained in the cplex.opt file. Here are listing files for primal simplex (lpmethod 1; takes about 71 seconds), dual simplex (lpmethod 2, which is the default; takes about 18 seconds), network simplex (lpmethod 3; takes about 15 seconds to execute, since it's best suited to the problem structure).
• Sailco example: application of min-cost network flow.
• Shortest-path problem with lake and listing file.
• Repeated shortest-path, illustrating solves within loops, conditional (if) statement, interrogation of model attributes. Here's an edited listing file.
• Gandhi example: Fixed-cost model: LP with binary variables.
• Modified Gandhi example: Includes capacity constraints on each machine, more than one machine of each type can be used.
• Dorian Auto: Either-Or Constraints. See the following more concise formulation with semiint variables.
• Pitcher: If-Then Constraints.
• Happy Class: Assignment Problem.
• Kilroy County Fire Department: Set-covering problem.
• More set covering: Aggregate, Warehouse.
• How many female IE undergrads?: Modeling logical conditions.
• Happy Class Revisited: Assignment Problem with Logical Constraints.
• Multicast Server Location: Piecewise linear concave cost function, with integer variables representing location of servers.
• Happy Milk Description and Solution. Version with a concave cost function. The latter illustrates the use of SOS2 variables to model such a cost function. Here is the edited listing file.
• Basketweavers University: Precedence constraints.
• stars.gms: use of $include statement. See also the listing file.
• qp1.gms, Portfolio Optimization problem, as formulated in the GAMS Model Library. Uses the data file qpdata.inc.
• Transport example, with reports written by the put statement. Here are the report files: factors.dat, results.dat
• largenet3.gms, modification of largenet2.gms, modified to write its own cplex.opt file.
• qp1rho.gms, Modified (standard) version of portfolio optimization, in which the parameter rho is used to weight between risk and return. Try values rho=0.1, 1, 10.
• translcp.gms, transport problem, LCP model.
• lqr.gms, linear-quadratic regulator optimal control. Try varying Ubound and see the effect on optimal objective and solution. This example writes an output file lqr.out.
• ngon.gms, calculating the N-gon of radius 1 with maximum area. (A nonlinear model.)
• ngon_betterstart.gms: improved starting point leads to better robustness. (ngon.gms fails for N>8). But this model still produces some nonoptimal "solutions"; e.g. the area obtained for N=25 is smaller than for N=20.
• ngon_alt.gms: An alternative model due to Vanderbei.
• ngon_prieto.gms: A model due to prieto which seems to do well up to quite large values of N.
• unitcircle.gms, calculating the N-gon inscribed in a unit circle of maximum area. (A nonlinear model.) (The solutions are regular polygons, with smaller areas than those in the previous model.)
• Use of scaling options: scaling.gms and scaling_alt.gms. See User Guide Section 17.3.
• ex1.gms, simplot1.m: Generating and plotting some simple random data using Matlab. See also the variants simplot1a.m and simplot1b.m.
• ex2.gms, simplot2.m: The same data, done in a slightly nicer way. (The plot is slightly different.)
• ngonplot.gms, ngon.m: plots the optimal N-gon of radius 1 with maximum area. Here is the fancier program ngon_wedges.m, which divides the polygon into "pie slices" and plots them each in a different color.
• mincostplot.gms: Mininum cost network flow problem from mincost.gms, but uses put facility to write arcs and computed flows to a file mincost.dat. The file is read and plotted by mincostplot.m.
• Some simple examples illustrating the use of the Matlab Optimization Toolbox routine linprog: lp1.m, lp2.m
• Some examples illustrating the use of the Matlab Optimization Toolbox routine quadprog, on convex and nonconvex problems: qp1.m, qp2.m, qp3.m, qp4.m, qp5.m.
• translcp.gms: Transportation Problem expressed as an LCP.
• matchingpennies.gms: The matching pennies problem, a two-person game. We find the Nash equibrium by using a complementarity formulation.
• matchingsavant.gms: Variant on the matching pennies game, in which one of the players has an edge.
• Natural gas planning (2 stages) , a stochastic linear program.
• Natural gas planning (3 stages), a stochastic linear program.