6. Lab Week 6 Problem Solutions - Lab Week 6 Problem...

Lab Week 6 Problem Solutions
CHAPTER 5
DISTRIBUTION AND NETWORK FLOW MODELS
1.
1a.
Let Xij = the number of units shipped from plant i to warehouse j.
Where i = A, B, C
j= 1, 2, 3
Objective Function (Minimize):
Min. Z = 50X
A1
+ 32X
A2
+ 40X
A3
+ 16X
B1
+ 30X
B2
+ 20X
B3
+ 35X
C1
+ 28X
C2
+ 42X
C3
Subject to
Supply Constraints: Non-negativity Constraints
X
A1
+ X
A2
+ X
A3
= 700 All variables ≥0
X
B1
+ X
B2
+ X
B3
= 200
X
C1
+ X
C2
+ X
C3
= 200
Demand Constraints:
X
A1
+ X
B1
+ X
C1
= 300
X
A2
+ X
B2
+ X
C2
= 400
X
A3
+ X
B3
+ X
C3
= 400

1b. When using solver, make sure “assume linear model” and “assume non-negativity” are
checked under the options menu. Excel formatting:

1c. To make sure route 3-A is unacceptable, change the cost to a very high number (e.g.,
ten times the next highest cost). Note the cost of $500 from plant A to warehouse 3.
The solver constraints are the same.

15.
15a.
Objective Function (minimize cost):
Min. Z = 9X
13
+ 11X
14
+ 10X
23
+ 12X
24
+ 8X
35
+ 4X
36
+ 6X
45
+ 7X
46
Subject to
Supply Constraints: Non-Negativity Constraint:
X
13
+ X
14
= 200 All variables ≥ 0
X
23
+ X
24
= 300
Transshipment Constraints :
X