OPTNET is a program for identifying the minimumcost solution of network flow problems. The user enters a model title and list of arcs in the network. Pressing the Solve LP button runs OPTNET and displays the generated reports
Model input format. The title of the model is entered into the indicated form field. A network flow problem is given in circularized form (see below) and is entered in the Model Input Field as series of directed arcs, one per line.
Each model arc is given in one of the following forms:
 fromnode tonode unitcost upperbound lowerbound
 fromnode tonode unitcost upperbound
 fromnode tonode unitcost
 fromnode tonode
where:
 fromnode: name of the arc’s originating node, 18 letters and digits, beginning with letter
 tonode: name of the arc’s terminating node, 18 letters and digits, beginning with letter
 unitcost: (integer) cost per unit of flow across or through the arc (assumed to be 0 in Form 4)
 upperbound: (integer) maximum possible flow through the arc (assumed to be 9999999 in Forms 3 and 4)
 lowerbound: (integer) minimum required flow through the arc (assumed to be 0 in Forms 2, 3, and 4)
Model limits. The model cannot exceed 400 nodes and 2000 arcs. All numerical values must be specified as integers.
Example model. (This model can be cut and pasted into the input form)
SOURCE A 0 100 100 SOURCE B 0 200 200 A D 30 A C 10 B C 5 B E 25 C D 18 C E 20 D SINK 0 150 150 E SINK 0 150 150 SINK SOURCE
Circularized network models. OPTNET requires that networks be described in a circularized network form, which does not use supplies and demands on nodes. Instead it requires that all flow that enters a node must leave, hence the net supply and demand at a node is zero. This is a circularized network graph for the above example model.
Any network with supplies and demands at the nodes can be converted into circularized form by adding two new nodes and a few arcs. The figure above shows a circularized form of the following network graph with supplies and demands at the nodes.
Example 2: Stuart Furniture network
Formulation of the Stuart Furniture case, with costs given in cents and the units of flow are chairs or chairsworth of wood.
source s1 200 10000 400 source s2 150 10000 400 s1 p1 20 s1 p2 40 s1 p3 80 s1 p4 80 s2 p1 80 s2 p2 60 s2 p3 20 s2 p4 20 p1 p1a 500 500 p1 p1a 600 250 p2 p2a 700 750 400 p2 p2a 900 250 p3 p3a 300 1000 500 p3 p3a 400 400 p4 p4a 400 250 250 p4 p4a 500 100 p1a ny 100 p1a dal 100 p1a sf 200 p1a chi 0 p2a ny 300 p2a dal 600 p2a sf 700 p2a chi 300 p3a ny 300 p3a dal 100 p3a sf 500 p3a chi 300 p4a ny 800 p4a dal 200 p4a sf 100 p4a chi 400 ny sink 2000 2000 500 dal sink 1500 400 100 sf sink 2000 1500 500 chi sink 1800 1500 500 sink source
Example 3: Ryan Electronics
Formulation of the Ryan Electronics transshipment network example in Anderson text, 15th ed, Chapter 6:
SOURCE DENVER 0 600 SOURCE ATLANTA 0 400 DENVER KANCITY 2 DENVER LVILLE 3 ATLANTA KANCITY 3 ATLANTA LVILLE 1 KANCITY DETROIT 2 KANCITY MIAMI 6 KANCITY DALLAS 3 KANCITY NEWORL 6 LVILLE DETROIT 4 LVILLE MIAMI 4 LVILLE DALLAS 6 LVILLE NEWORL 5 DETROIT SINK 0 200 200 MIAMI SINK 0 150 150 DALLAS SINK 0 350 350 NEWORL SINK 0 300 300 SINK SOURCE 0
