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Supply Chain Logistics Help
Consider the following example that demonstrates optimization of transportation.
There are production facilities in Battle Creek, Cherry Creek, and Dee Creek with annual capacities of 500 units, 400 units, and 600 units, respectively. The annual demands at warehouses in Worchester, Dorchester, and Rochester are 300 units, 700 units, and 400 units, respectively. The table below gives the unit transportation costs between the production facilities and the warehouses.
Worchester Dorchester Rochester
Battle Creek
$20/unit
$30/unit
$13/unit
Cherry Creek
$10/unit
$5/unit
$17/unit
Dee Creek
$15/unit
$12/unit
$45/unit
How much of the demand at each of the warehouses must be met by each of the production facilities?
This problem can be modeled as a linear programming model as follows:
Decision Variables
Xbw = # of units to be transported from Battle Creek to Worchester
Xcw = # o
f units to be transported from Cherry Creek to Worchester
Xdw = # of units to be transported from Dee Creek to Worchester
Xbd = # of units to be transported from Battle Creek to Dorchester
Xcd = # of units to be transported from Cherry Creek to Dorchester
Xdd = # of units to be transported from Dee Creek to Dorchester
2
QSO 635 Module
Seven
Xbr = # of units to be transported from Battle Creek to Rochester
Xcr = # of units to be transported from Cherry Creek to Rochester
Xdr = # of units to be transported from Dee Creek to Rochest
er
Objective Function
Minimize total annual transportation cost ($):
= 20*Xbw + 10*Xcw + 15*Xdw + 30*Xbd + 5*Xcd + 12*Xdd + 13*Xbr + 17*Xcr + 45*Xdr
Constraints
Demand Constraints
Xbw + Xcw + Xdw ≥ 300
(demand at Worchester)
Xbd + Xcd + Xdd ≥ 700
(demand at Dorchester)
Xbr + Xcr + Xdr ≥ 400
(demand at Rochester)
Capacity Constraints
Xbw + Xbd + Xbr ≤ 500
(capacity at Battle Creek)
Xcw + Xcd + Xcr ≤ 400
(capacity at Cherry Creek)
X
dw + Xdd + Xdr ≤ 600
(capacity at Dee Creek)
Non

Negativity Constraints
Xbw, Xcw, Xdw, Xbd, Xcd, Xdd, Xbr, Xcr, and Xdr are ≥ 0
Integer Constraints
Xbw, Xcw, Xdw, Xbd, Xcd, Xdd, Xbr, Xcr, and Xdr are integers
The above model can be solved using the Microsoft Excel Solver tool. Refer to the tutorial on how to use the Solver tool (click on each image for a better display).
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