Time Dependent Queueing Analyer
Software that
accompanies my book:
The SITATION software as well as the other programs that accompany
Daskin's text (Network and Discrete Location: Models, Algorithms,
and
Applications) have been updated to run under Windows 95.
The following enhancements have been made to the original version of
the
program:
- The programs are entirely menu-driven
and run under Windows 95 and later versions of Windows.
- SITATION now solves five classes of
location problems including: P-median, P-center, Set Covering,
Maximal Covering, and Uncapacitated Fixed Charge Problems.
- SITATION includes branch and bound
capabilities to allow the user to obtain very tight (usually provably
optimal) solutions.
- Additional mapping
capabilities have been added to SITATION.
- SITATION allows the user to zoom
in on portions of the tradeoff curves and maps.
- SITATION allows the user to specify alphanumeric
(text-based) node names.
- SITATION solves the Covering-Median
tradeoff problem using the weighting method. (See section 8.2 of my
book)
- The newest version of SITATION will solve problems with up to 300 nodes and the program does not expire!
To learn more about the
software, click here
(for a PDF document about the
software).
The latest version of
this software
is available by clicking here
You will receive a zipped file that is about 7 MB long.
The file contains the zipped version of four programs and another 13
data
files.
Documentation is
available here
Note that
there were minor errors with earlier versions
You should download the current version which I hope is bug free.
Version 5.5.0.15 and above now
allows you
to map EUROPEAN data and comes with
a dataset representing the 150 largest cities in Europe.
It also allows you to save maps in various formats for use in other
programs.
It also includes the ability to solve joint LOCATION/INVENTORY problems.
Finally it includes a Powerpoint presentation as an introduction to SITATION.
Spreadsheet for
the Traveling Salesman Problem
You can download an EXCEL©
spreadsheet that allows you to try your hand at solving a 49-node
traveling salesman problem. You have to list the two character state
abbreviation for the 48 capitals in the continental United States plus
Washington, DC in an order to solve the traveling salesman problem. The
spreadsheet will automatically compute the (great circle) distance
between each pair of cities as well as the total distance of the tour.
The spreadsheet will also provide error messages if a state
abbreviation is spelled incorrectly and/or if a state is used more than
once. Finally, the spreadsheet includes a map showing the outline of
the United States as well as the tour that you have identified.
Have fun with it.
Click here
to download a Zip file that contains this spreadsheet.
Here is a good (but NOT the best)
solution...
Spreadsheet for
Facility Location Problems
You can download an EXCEL©
spreadsheet that allows you to try your hand at solving a variety of
facility location problems on a 49-node dataset. The dataset corresponds
to the capitals of the 48 states in the continental United States
plus Washington, D.C. The spreadsheet is pre-loaded with the 1990 state
populations as demands and initial fixed costs. You can change these
numbers as you see fit.
The problems that you can try to solve include Maximal Covering,
P-Median, and Uncapacitated Fixed Charge location problems. For each
problem, you can locate as many facilities as you want. To locate a
facility, you simply specify the two character state abbreviation for
the capital of the state. The spreadsheet provides error messages in
the event you spell a state abbreviation incorrectly or in the event
that you list a location twice. The spreadsheet will automatically
compute the objective function values for the three problems identified
above and will show the results in a spreadsheet as well as on a
dynamically updated map built into the spreadsheet.
Have fun with it.
Click here
to download a Zip file that contains this spreadsheet.
Time Dependent Queueing Analyzer
This program allows you to explore the differences between steady-state
and time-dependent queueing problems. The model uses a sinusoidal
pattern for the mean of a Poisson arrival process. The problem
you are faced with is that of determining the starting time and shift
duration for full time and part time
employees to attain various objectives. The program solves for
the steady-state state probabilities (assuming they exist) at each
instant of time. The program also solves the Chapman-Kolmogorov
first-order differential equations for the time-dependent state
probabilities and reports such measures as the time-dependent number in
the system and the time-dependent probability of waiting for service.
The figure below
shows the mean arrival rate (in blue), the number on duty (in black) ,
the steady-state expected number in the system (in red) and the
time-dependent expected number in the system in green. Note that
the number on duty can be less than the number needed for steady state
(for short periods of time). During these times, the expected
number in the system in steady state is reported as 0, since the number
is not defined.
The graph below
shows the steady-state (red) and time-dependent (green) probability of
waiting for service. Again, if the steady-state conditions do not
exist at a particular instant in time, the probability of waiting is
reported as 1 (as is the case for times before time 60. For times
between 0 and 60, 5 serves are needed and only 4 are available.
The figure below shows the distribution of the number in the system in
steady-state (red) and in the time-dependent (green) cases at time 750.
Note that the distributions are quite different and that the mean
of the number in the system at time 750 assuming steady state operation
is quite a bit larger than is the mean accounting for the
time-dependent nature of the arrival and service processes.
Click here to download a zipped file containing this program.
Click here to download a PDF version of a Powerpoint presentation explaining this program in greater detail.