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In this model, we have a network with seven node. Three of the nodes are source nodes and four of the nodes are destination nodes. Each of the source nodes can ship to any of the destination nodes. The problem is the more product you send down and are, the longer it takes for it to arrive. This might be the case if the underlying network were a railroad, for instance. We assume that shipping times obey the following relationship:
Time=Rate/(1-Flow/Limit)where,
Time is the time to ship one unit of product down a route,Based on this relationship, we see shipping times go to infinity as the capacity of an arc is approached. The goal of the model is to determine how much product to ship from each source to each destination so as to minimize total shipping times.
Rate is the time required to transport one unit down a route with no congestion along the route,
Flow is the amount of product shipped down a route, and
Limit is the maximum limit of product flow down a route.