QUESTION

# 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).

Files: QSO635_Module7_Lecture.pdf
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