1. Transshipment Problem
STRATEGIC
RESOURCE
ALLOCATION
and
PLANNING
MGMT E-5050
Bamm Mining Company
Transshipment Problem

2. Bamm Mining Company Bamm Mining Company is currently extracting
rock from two mines. Once it is taken from the
ground and loaded on a truck, it is sent to one
of two plants for processing.
The processed rock is then shipped to one of
three builders’ supply stores, where it is sold
for landscaping purposes.
The cost of transportation, the supply available
at each mine, and the processing capacity of each
plant are given on the following table:

3. Daily Process Capacity
Bamm Mining Company
Cost per Ton for Shipping
To Plant
From Mine #1 #2
Daily Supply A
$6.00
$8.00
320 tons B
$7.00
$10.00
450 tons
Daily Process Capacity
500 tons

4. Bamm Mining Company To From Plant #1 $13.00 $17.00 $20.00 #2 $19.00
The cost of shipping from each processing plant to each
store and the daily demand are as follows:
Cost per Ton for Shipping To
From Plant
Supply Store A
Supply Store B
Supply Store C #1
$13.00
$17.00
$20.00 #2
$19.00
$22.00
$21.00
Daily Demand
200
240
330

5. Bamm Mining Company REQUIREMENT:
Formulate a linear program that can be used to
determine how to meet the demands of the 3
supply stores at the least cost.
Solve this by computer. How many tons should
be shipped from each mine to each plant?
How many tons should go from each plant to
each store?

6. Bamm Mining Company Assume that the cost of processing the rock is
$22.00 per ton at Plant 1 and $18.00 per ton at
Plant 2.
REQUIREMENT:
Formulate a linear program to minimize the
total processing and transportation cost.
Solve this by computer. What is the optimal
solution?

7. Solution Let : A1 = tons of ore from mine A to plant 1
B1 = tons of ore from mine B to plant 1
B2 = tons of ore from mine B to plant 2

8. Solution Let : X1 = tons shipped to Builder’s Home from plant 1
Y1 = tons shipped to Homeowners’ Hdqtrs from plant 1
Y2 = tons shipped to Homeowners’ Hdqtrs from plant 2
Z1 = tons shipped to Hardware City from plant 1
Z2 = tons shipped to Hardware City from plant 2

9. Solution Minimize cost = 6A1 + 8A2 + 7B1 + 10B2 + 13X1 + 19X2
+ 17Y1 + 22Y2 + 20Z1 + 21Z2
subject to :
A1 + A2 = 320 ( supply at mine A )
B1 + B2 = 450 ( supply at mine B )
A1 + B1 =< 500 ( capacity at plant 1 )
A2 + B2 =< 500 ( capacity at plant 2 )

10. Solution X1 + X2 = 200 ( demand at Builder’s Home )
Y1 + Y2 = 240 ( demand at Homeowners’ Hdqtrs )
Z1 + Z2 = 330 ( demand at Hardware City )
A1 + B1 = X1 + Y1 + Z1
Units shipped into plant 1 must equal units shipped out of plant 1
A2 + B2 = X2 + Y2 + Z2
Units shipped into plant 2 must equal units shipped out of plant 2
All variables => 0

11. Solution A1 = 50 tons of ore from mine A to plant 1
B1 = 450 tons of ore from mine B to plant 1
X1 = 200 tons shipped to Builder’s Home from plant 1
Y1 = 240 tons shipped to Homeowners’ Hdqtrs from plant 1
Z1 = 60 tons shipped to Hardware City from plant 1
Z2 = 270 tons shipped to Hardware City from plant 2
All other variables = 0
Minimum total cost = $19,160.00