Chapter 5-Suggested Problems and Solution
# 14
a. This is a transportation problem. Note that demand exceeds supply by 20 units.
You need to draw three supply nodes (the warehouses) and four demand nodes (the stores, along
with the arcs, costs on each arc, and supply and demand numbers corresponding to each node.
b. MIN 5 X11 + 4 X12 + 6 X13 + 5 X14
+3 X21 + 6 X22 + 4 X23 + 4 X24
+4 X31 + 3 X32 + 3 X33 + 2 X34
ST -X11 - X12 - X13 - X14 = -30
-X21 - X22 - X23 - X24 = -30
-X31 - X32 - X33 - X34 = -30
+X11 + X21 + X31 + XD1
≤
+20
+X12 + X22 + X32 + XD2
≤
+25
+X13 + X23+ X33 + XD3
≤
+30
+X14 + X24+ X34 + XD4
≤
+35
X
ij
≥
0
c. See file: Prb5_23.xls
The optimal solution is: X12 = 25, X14 = 5, X21 = 20, X23 = 10, X34 = 30, XD3 = 20.
Minimum total cost = $285.
Note that store 3 receives 20 units less than demanded.
d. Assign arbitrarily large costs (such as $999) to the arcs representing these flows.

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