ITSCM $306$

Chapter $15$ Problem Set: Logistics

$1$ of $2$

Problem $1\%$ Grade

Bindley Corporation has a one$-$year contract to supply motors for all washing machines

produced by Rinso Ltd$.$ Rinso manufactures the washers at four locations around the country:

New York City, Fort Worth, San Diego, and Minneapolis. Plans call for the following numbers of

washing machines to be produced at each location:

New York City $50,000$

Fort Worth $70,000$

San Diego $60,000$

Minneapolis $80,000$

Bindley has three plants that can produce the motors. The plants and production capacities are

as follows:

Boulder $100,000$

Macon $100,000$

Gary $150,000$

Shipment will be made in lots of $1,000$ motors from Bindley to Rinso. Due to varying production

and transportation costs, Bindley$$s profits depend on where the motors are produced and where

they are shipped. Based on estimates from Bindley$$s Accounting Department, the following

table provides the profit in dollars per unit.

Shipped To

Produced at New York Fort Worth San Diego Minneapolis

Boulder $$7$ $$11$ $$8$ $$13$

Macon $$20$ $$17$ $$12$ $$10$

Gary $$8$ $$18$ $$13$ $$16$

Given profit maximization as a criterion, use the Transportation Method of Linear

Programming to determine the optimum ship quantity from each Bindley location to each

Rinso location. Include the following items in your response:

$($a$)$ Submit your Excel file in Canvas, showing your solution using the Excel Solver add$-$

in$.($As an alternative, you can use the Solver add$-$on in Google Sheets, but in that

case, you must share file permissions and submit the URL link in Canvas.$)(40\%)$

$($b$)$ Demonstrate your understanding of the Excel solution by answering the following

questions:

ITSCM $306$

Chapter $15$ Problem Set: Logistics

$2$ of $2$

Problem $1($b$)$ continued $\%$ Grade

i$.$ How many motors should be shipped from Gary to Minneapolis? $(10\%)$

ii$.$ Note that Bindley$$s total production capacity exceeds Rinso$$s total

demand. Based on your solution, how much production capacity is still

available at each of Bindley$$s three locations?

$($Hint: Subtract planned shipments from factory capacity.$)(10\%)$

Problem $2$:

Santa Cruz Bottling is a soft drink manufacturer on the coast of central California. The company

is planning to build an additional manufacturing plant due to increased demand for its products.

The new plant will primarily serve the states of New Mexico and Arizona. A key concern is to

minimize transportation costs in these markets. Following is a list of cities where its main

wholesale customers are located, along with estimated annual demand in each city.

City x$-$coordinate y$-$coordinate Number of

cases

Phoenix AZ $25025025,000$

Tucson AZ $35012520,000$

Albuquerque NM $80045028,000$

Santa Fe NM $85052017,000$

Use the centroid method to identify a potential location for the new bottling plant. Round

your coordinates to one decimal place. $(40\%)$