Download ENGR-25_Prob_4-28_Dense_Road_Solution

Engineering 25
Chp4
Tutorial:
Prob 4.28
Solution
Bruce Mayer, PE
Licensed Electrical & Mechanical Engineer
[email protected]
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
[email protected] • ENGR-25_HW-01_Solution.ppt
The Situation
 Optimize Distribution Center
Location for Customers:
ENGR25 Problem 4.25 * 23Feb06
35
NOTES
• Size of Bubbles denotes relative shipping Volume
30

25

North Distance (Ymiles)
20

15

10

5

0
-5
0
5
10
15
20
25
file = P4-25_Dense-Road_Bubble-Chart_0602.xls
-5
East Distance (Xmiles)
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[email protected] • ENGR-25_HW-01_Solution.ppt
30
35
WhareHouse Location
Optimization
N
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[email protected] • ENGR-25_HW-01_Solution.ppt
E
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
[email protected] • ENGR-25_HW-01_Solution.ppt
Engineering/Math/Physics 25: Computational Methods
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Bruce Mayer, PE
[email protected] • ENGR-25_HW-01_Solution.ppt
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Bruce Mayer, PE
[email protected] • ENGR-25_HW-01_Solution.ppt
The Final Hand Notes
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GamePlan Illustrated
 Set x-value (m-index)
 Test 31 y-values (n-index)
 Increment x-value (m = m+1)
 Test 31 new y-values
 Repeat
N
E
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[email protected] • ENGR-25_HW-01_Solution.ppt
The MATLAB Program
% Bruce Mayer, PE * 8Sep11 * Rev 26Feb12
% ENGR25 * Problem 4-28
% file = Prob4_28_Dense_Road_1109.m
% Find Optimum Location for Shipping Distribution Center
%
% INPUT SECTION - Data For Six Shipping Destinations
xloc = [1,7,8,17,22,27]; % X-CoOrd in Miles
yloc = [28,18,16,2,10,8]; % Y-CoOrd in Miles
V = [3,7,4,5,2,6]; % Shipping Volume in Tons/Week
%
% Initialize Low-Cost Location & CoOrds Collection Vectors
%=> Units for Collection Vectors: [$-Cost, X-miles, Y-Miles]
C_Lo = [1e6, 31, 31];
C_L1 = [1e6, 31, 31];
C_L2 = [1e6, 31, 31];
%
% CALCULATION SECTION
% vary X&Y for Dist Cntr; calc cost at each location
for m = 0:30 % vary X-CoOrd in Miles
for n = 0:30 % vary Y-CoOrd in Miles
for k = 1:6 % Calc Dist & Cost for 6 Destinations
d(k) = sqrt((m-xloc(k))^2 + (n-yloc(k))^2);
cost(k) = 0.5*d(k)*V(k);
end
% Sum the 6 costs for location (m,n)
Cmn = sum(cost);
LcnCost(m+1, n+1) = Cmn; % Store all Cost-Tests for later inspection
%* Note: Array indices are NATURAL No'.s; they canNOT Start a Zerot
% Compare to Previous value for Low-Cost
if Cmn < C_Lo(1) % replace ALL THREE previous if new CHAMPION
C_L2 = C_L1;
C_L1 = C_Lo;
C_Lo = [Cmn, m, n];
elseif Cmn < C_L1(1) % Replace TWO RunnersUp if new 1st RunnerUp
C_L2 = C_L1;
C_L1 = [Cmn, m, n];
elseif Cmn < C_L2(1) % Replace ONE RunnerUp if new 2nd RunnerUp
C_L2 = [Cmn, m, n];
end
end
end
%
% REPORT RESULTS
display('The LOWEST-Cost Option in [$-cost, X-miles, Y-miles]')
disp(C_Lo)
display('The 1st "RunnerUp" Low-Cost Option in [$-cost, X-miles, Y-miles]')
disp(C_L1)
display('The 2nd "RunnerUp" Low-Cost Option in [$-cost, X-miles, Y-miles]')
disp(C_L2)
%
% Make SURF plot to show Cost vs Location
E = [0:30];
N = [0:30];
surfc(E, N, LcnCost), xlabel('miles North'), ylabel('miles East'), zlabel('$Cost
per Week'
Bruce Mayer, PE
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The Number Results
The LOWEST-Cost Option in [$-cost,
X-miles, Y-miles]
147.2551
9.0000
16.0000
The 1st "RunnerUp" Low-Cost Option
in [$-cost, X-miles, Y-miles]
147.3513
8.0000
16.0000
The 2nd "RunnerUp" Low-Cost Option
in [$-cost, X-miles, Y-miles]
148.0319
10.0000
16.0000
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The Graph Results
400
$Cost per Week
350
300
250
200
150
100
30
20
10
0
30
25
15
20
10
miles East
miles North
 Note the Fairly Large
Optimum Region
@ 10mi-E & 16mi-N
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0