Balancing Total Supply and Total Demand

The TRANS Procedure

Balancing Total Supply and Total Demand

When Total Supply Exceeds Total Demand

When total supply of a transportation problem exceeds total demand, PROC TRANS can add an extra destination node (called the excess node) to the problem and set the demand at that node equal to the difference between total supply and total demand. There are two ways that this extra destination node can be added to the transportation network.

When the NOTHRUNET option is specified, the sum of flows that reach the destination nodes equals the total demand of the transportation problem. For some source nodes, supply can be conveyed through real arcs but can also be drained away to the excess node. The supply of each source node is really an upper bound of the number of flow units such a node can actually supply.

When the THRUNET option is used, the sum of flows that reach the destination nodes equals the total supply of the transportation problem. For some destination nodes, the amount of flow can exceed that node's demand. The demand of destination nodes is a lower bound of the number of flow units a destination node can demand.

When Total Demand Exceeds Total Supply

When total demand exceeds total supply, PROC TRANS can add an extra source node (the excess node) to the problem. This node is able to supply to the network the difference between total demand and total supply. There are two ways this extra source node can be added to the transportation network.

When the NOTHRUNET option is specified, the sum of flows that leave the source nodes equals the total supply of the transportation problem. For some destination nodes, demand will be satisfied by flow through real arcs and can be satisfied by flows through arcs directed from the excess node. The demand of each destination node is really an upper bound of the number of flow units such a node can actually receive.

When the THRUNET option is specified, the sum of flows that leave the source nodes equals the total demand of the transportation problem. For some source nodes, the sum of flow that is conveyed through arcs originating at that node can exceed the node's supply capability. The supply of source nodes is a lower bound of the number of flow units a source node is able to supply to the network.

If total supply does not equal total demand and either the THRUNET or NOTHRUNET option is specified, PROC TRANS automatically creates the excess node and the arcs incident to it. When the optimization is complete, these ancillary parts of the network are erased. Information about these parts will not be found in the OUT= data set.

Chapter Contents
Previous
Next
Top