SCMN3710 Logistics Bonus Quiz. Management Coursework

Please explain all the solution in detailed.

SCMN3710 LOGISTICS BONUS QUIZ #1 FALL 2019    

The LeafBarrow Co., inventor of a new type of wheelbarrow that makes it possible to rake leaves directly into it so you don’t have to bend over to collect them, has decided to build its first factory and will use the grid technique to identify the geographic location where their total inbound and outbound transportation costs are minimized.

The inbound grid coordinates, transportation rates and volumes are as follows:

Source             Horizontal         Vertical             Rate ($/ton-mile)           Tons/yr.

Buffalo             700                  1,125                $1.25                           275

Memphis          250                  600                  $1.10                           550

St. Louis          225                  825                  $1.15                           800

The outbound grid coordinates, transportation rates and volumes are as follows:

Market              Horizontal         Vertical             Rate ($/ton-mile)           Tons/yr.

Atlanta             600                  500                  $1.75                           475

Boston             1,050                1,200                $1.95                           300

Jacksonville     800                  300                  $1.65                           350

Philadelphia      925                  975                  $2.05                           250

New York         1,000                1,080                $2.00                           225

1. What is the horizontal (x) coordinate of the geographic center where total inbound and outbound transportation costs are minimized? (4 points)

1. What is the vertical (y) coordinate of the geographic center where total inbound and outbound transportation costs are minimized? (4 points)

1. Since Atlanta is the outbound destination with the most volume, there has been some consideration to locating the factory there. What is the minimum distance (straight line) between Atlanta and the geographic center where inbound and outbound transportation costs are minimized? (2 points)

C = Ton-mile center                             

r_i = Raw materials transportation rate                            R_i = Finished goods transportation rate

d_i = Distance to RM grid location for I                          D_i = Distance to FG grid location for i

s_i = Volume (weight) of RM purchased from source I     M_i = Volume (weight) of FG sold in market i