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A problem of a company that has 3 factories producing 5 different products with varying costs and inventory levels. It discusses how to compute the cost for a factory to fill a purchase order, check if a factory has enough inventory, and find the cheapest factory to fill the order. It also introduces the concept of positive infinity and the use of a true/false function to check if a factory can fill the order.
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^ Previous Lecture:
^ 2-d array—matrix ^ Today’s Lecture:
^ More examples on matrices ^ Contour plot (Read 7.2, 7.3) ^ Announcements:
^ Project 3 due tonight at 11pm ^ Prelim 2 on Thurs Mar 12. Email [email protected] if you have a prelim conflict ^ Review session next week
March 5, 2009
Lecture 14
Initialize vectors/matrices if dimensions are known…instead of “building” the array one component ata time
% Build y on the flyx=linspace(a,b,n);for k=1:n
y(k)=myF(x); end
% Initialize yx=linspace(a,b,n);y=zeros(1,n);for k=1:n
y(k)=myF(x); end Much faster for large n!
March 5, 2009
Lecture 14
function A = RandomLinks(n)% A is n-by-n matrix of 1s and 0s% representing n webpagesA = zeros(n,n);for i=1:n
for j=1:n r = rand(1);if i~=j && r<= 1/(1 + abs(i-j));
A(i,j) = 1; end end end
March 5, 2009
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Random web^ N
March 5, 2009
Lecture 14
Line black as it leaves page j, red when it
arrives at page i
Represent the web pages graphically…
March 5, 2009
Lecture 14
ShowRandomLinks.m
March 5, 2009
Lecture 14
ProblemsA customer submits a purchase order thatis to be filled by a single factory.1. How much would it cost a factory to fill the order?2. Does a factory have enough inventory to fillthe order?3. Among the factories that can fill the order,who can do it most cheaply?
March 5, 2009
Lecture 14
Cost Array
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The value of
C(i,j)
is what it costs
factory i to make product j.
March 5, 2009
Lecture 14
Purchase Order
The value of
PO(j)
is the number of
product j’s that the customer wants
March 5, 2009
Lecture 14
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Cost forfactory 1:
March 5, 2009
Lecture 14
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Cost forfactory 2:
s^
%Sum
of
cost
for
j=1:5s =
s
C(2,j)*PO(j)
end
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Lecture 14
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Cost forfactory i:
s^
%Sum
of
cost
for
j=1:5s =
s
C(i,j)*PO(j)
end
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Lecture 14
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Finding the Cheapest
1019930 1040 As computedby
iCost
March 5, 2009
Lecture 14
iBest = 0;
minBill = inf;
for i=1:nFact
iBill = iCost(i,C,PO);if iBill < minBill
% Found an ImprovementiBest = i; minBill = iBill; end end Finding the Cheapest
