# Optimal transportation of goods in a supply chain

*label*Business

*timer*Asked: May 20th, 2013

**Question description**

Optimal transportation of goods in a supply chain is

essential because it is important that:

• The total transportation cost is minimized

• The demand at warehouses is satisfied

• The capacity at production facilities is not exceeded

Read this article that describes in detail the role of

transportation in a supply chain.

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 = # of 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

Refer to the example in the

Module Seven lecture document. Solve the linear programming model using the

Microsoft Excel Solver tool