Senior Design Project
Systems Science Engineering

    Start Date: Fall 2006
    End Date: Spring 2007



Steven R. Vogl
Senior Design Project
Washington University, St. Louis
 

Project Supervisors:

Dr. Michael S. McCoy
Boeing Technical Fellow
Operations Analysis

Martin Netherton
Engineer
Operations Analysis
 

Abstract:

The goal of the Supply Distribution Model is to develop a computer program in Microsoft Excel that reduces the cost of distributing supplies from a single origin to many independent drop-off locations.  In route, the supplies must pass through a system of three intermediate warehouses, known as regional staging areas.  In addition to placing the regional staging areas, the program must also determine how to assign delivery vehicles to each staging area in order to satisfy the set of deliveries.  Once all this information has been determined, the results must be output to the user in a user-friendly, graphical way so that s/he can implement the solution.
 

Constraints:

This project was a constrained simulation of supply distribution from a single origin to many destinations.  Constraints on the system include:

  1. Supply Types:
        a.)  Power Generators
        b.)  Chainsaws
        c.)  Plywood
  2. Supply Sizes:
        a)  Length
        b)  Width
        c)  Height
  3. Vehicle Types:
        a)  Pick-Up Truck
        b)  Bread Truck
        c)  Tractor-Trailer Truck
  4. Vehicle Sizes:
        a)  Length
        b)  Width
        c)  Height
  5. Vehicle Speeds
  6. Drop-Off Region:  25-mile-radius region about the origin (central warehouse)
     

Program Outputs:

In the end, the information that the company hopes to extract from running the computer program are the

  1. locations of the regional staging areas (for all three RSAs), the
  2. vehicle assignments (the number of each type of vehicle per RSA), and the
  3. cost information – Fixed-costs and transportation-costs.
     

RSA Placing Algorithm:

The method used by this program to calculate the locations of the RSAs is most accurately described as a “sweeping” algorithm.  An algorithm is essentially a procedure for solving a mathematical problem.  In this case, the solution is reached by progressing through a series of steps to produce a simple, effective, and meaningful solution:

Step 1:  Access the queue and all information contained within.
Step 2:  For each order, convert the rectangular (x,y) coordinate pairs into polar (r,θ) coordinate pairs.
Step 3:  Sort the queue according to the angular (θ) coordinate of each location.
Step 4:  Divide the queue into equal sets of orders; the number of sets is equal to the number of RSAs to be used (3).
Step 5:  Convert the polar coordinates back to rectangular coordinates.
Step 6:  For each set (each 1/3 of the queue), calculate the statistical mean of the x-coordinates of all orders in that set.
Step 7:  Calculate the statistical mean of the y-coordinates of all orders in the set.
Step 8:  Assign the calculated mean values of each set to each regional staging area.

The result is that the RSAs are placed at the statistical center of each cluster of orders.
 

Examples (Microsoft Excel):

(1) (2) (3)


Counter-Examples (Microsoft Excel):

(1) (2)


Examples/Counter-Examples (MATLAB):

(Example 1) (Example 2) (Counter-Example 1)


Conclusion:

The simulation that was created for this project satisfies all the requirements set forth by the project advisor:

“The model which you produce should allow for the following key points in a user friendly manner:

·   Input of numbers of each supply that needs to end up at each store

·   Output of total cost of moving all supplies

·   Graphical display of the cost of delivering each needed supply to each store”

The ability to input the “numbers of each supply that needs to end up at each store” in a “user friendly manner” is satisfied using the “Order Form” in the simulation.  This form allows the user to input information on the number of each type of supply requested, and the location where the delivery is to be made.  Submitting this form places the order into the queue for delivery on the following day.

Also, the total cost information is output to the user on the simulation interface, as well as a breakdown of the fixed-costs and transportation-costs.  This information is then used to “create a graphical display” of the cost of delivering the needed supplies to their final destinations.

The method used to generate locations of the RSAs generates (what some may consider) a “Quick-and-Dirty” solution.  The final output is not necessarily an “optimal” solution, but provides a quick and useful solution to most conceivable scenarios.  In developing this model, the project advisor repeatedly emphasized the concept of a “quick tool,” which is a product that a vendor can take to a customer and quickly produce insightful results to a problem.  The overall goal of the project was to produce such a quick tool that any company (in this specific case, the Boeing Company) can run on any MAC or PC running Microsoft Excel.  This goal was achieved by this project.

I am happy with the product that I produced over the past 8 months and I look forward to assisting the next student who expands upon my work to solve the issues that arose during the creation of this product.

 

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