ENGRI 1101
Engineering Applications of OR
Fall ’09
Homework 6
The Transportation Problem
•
Due date: 4:00pm on Friday, October 16, 2009 in the ENGRI 1101 box at the west end of the corridor
on the second floor of Rhodes Hall, where it connects to Upson.
•
Reading assignment: Pages 14 in Handout 7 on the transportation problem.
•
Make sure to put your name, netid, and lab section on the first page and staple the problems in order.
1. (50 points) Consider the following problem: there are
m
warehouses, where warehouse
i
has supply
s
i
, for each
i
= 1
, . . . , m
; there are
n
stores, where store
j
has demand
d
j
, for each
j
= 1
, . . . , n
;
however, for the first
n
i
units(where
n
i
≤
s
i
) shipped from warehouse
i
, there is a perunit shipping
charge from warehouse
i
to store
j
of
c
ij
dollars, for each
i
= 1
, . . . , m
,
j
= 1
, . . . , n
, whereas for
the remaining
s
i

n
i
units there is a surcharge of
p
i
>
0 dollars per unit shipped. Our aim is to find
the shipments that incur the least total cost (that is, the sum of both shipping and shortfall costs).
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 Fall '09
 TROTTER
 Shipping, Rhodes Hall, ﬁrst ni units

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