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Operations Research Models and Methods
Problems Section
Network Flow Programming Models
 - Military Aircraft Routing

A military commander wants to allocate his resources of airplanes to targets over the next two days. At present the planes are located at several bases. In particular, there are 10 bases and the number of planes currently at base i is .

There are 12 targets. Six of the targets, numbered 1 through 6, are identified for day 1. The rest of the targets, numbered 7 through 12, are identified for day 2. Analysts have estimated a dollar value of the damage caused by each plane that is sent to a target. For target j, that damage value is for the first five planes sent. For each additional plane up to 10 planes the damage is 0.75. There is no value to sending more than 10. Of the planes sent to a target j, a certain proportion will be lost due to the target defenses. That proportion is .

A plane will leave its current base in the morning of day 1, attack the target assigned to it. If it is not lost it will land at one of the 10 bases and spend the night. On the next day, it will leave the overnight base and attack the target assigned for day 2. At the end of day 2, remaining planes will return to one of the bases. Each base can accommodate no more than 20 planes overnight. Part of the problem concerns travel cost. The cost for a plane to travel between base i and target j is .

One additional parameter that the commander must consider is the cost of lost planes (and pilots). The cost of a lost plane is k.

a. Set up the network model that will determine how many planes to be sent from each base to each target in the two day time horizon. The goal is to maximize the damage to the targets minus the cost of travel and the cost of lost planes lost. Show the conceptual model. You may neglect the integrality of the number of planes.

b. How would you change the model to determine which targets should be attacked in each the two days? A target may be assigned to either day. A target can only be attacked once. (You may have to use integer variables and side constraints.)

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Operations Research Models and Methods
by Paul A. Jensen
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