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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).
The input is not necessarily balanced; that is, it is possible (and most likely) that
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This note was uploaded on 09/07/2011 for the course OR 1101 taught by Professor Trotter during the Fall '09 term at Cornell University (Engineering School).
 Fall '09
 TROTTER

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