Introduction: This is a type of constrained optimization problem using the linear programming methods introduced in Chapter 5. This is what is known as a transshipment problem. It uses three tiers of operations: factories, distribution centers, and customers.

The scenario is that a company operates three factories. They are in Atlanta, Denver, and Phoenix. There are five distribution centers: Philadelphia, Atlanta, Indianapolis, Boise, and Las Vegas. The distribution centers are the transshipment nodes. These three factories and Distribution Centers supply six customers in Hartford, Pensacola, St. Louis, Chicago, Los Angeles, and Duluth. The processing capacities of the factories and distribution centers are shown below.

Factory Capacity:

• Atlanta 5000
• Denver 8000
• Phoenix 8000

Distribution Center Capacity:

• Philadelphia 3000
• Atlanta 5000
• Indianapolis 6000
• Boise 4000
• Las Vegas 7000

The demand for the six customers is also shown here.

Customer Plant Demand:

• Hartford 2500
• Pensacola 1500
• St. Louis 2000
• Chicago 2500
• Los Angeles 2500
• Duluth 1500

The costs to ship from each factory to each distribution center are shown below:

	Philadelphia	Atlanta	Indianapolis	Boise	Las Vegas
Atlanta	18	0	10	XXXXXX	XXXXXX
Denver	XXXXXX	XXXXXX	20	12	10
Phoenix	XXXXXX	25	XXXXXX	10	5

Similarly, the costs to ship from each DC to each customer is shown below:

	Hartford	Pensacola	St. Louis	Chicago	Los Angeles	Duluth
Philadelphia	3	10	XXXXXX	XXXXXX	XXXXXX	XXXXXX
Atlanta	8	2	XXXXXX	XXXXXX	XXXXXX	XXXXXX
Indianapolis	XXXXXX	8	4	2	XXXXXX	6
Boise	XXXXXX	XXXXXX	XXXXXX	7	6	5
Las Vegas	XXXXXX	XXXXXX	XXXXXX	XXXXXX	3	6

Costs are given per unit.

The objective of this problem is to satisfy all customer demand at lowest cost! Assume for this problem that factories produce only in bulk and that the DCs are performing a breakbulk operation, where the bulk shipments are separated out into individual orders. Therefore, customers cannot buy direct from factory in this model and can only purchase through the DCs.