# A rent-a-car company operating in New York City serves the three major airports—Kennedy, La…

A rent-a-car company operating in New York City serves the three major airports—Kennedy, La Guardia, and Newark—and has two downtown distribution centers. On Sunday evenings most of the cars are returned to the downtown locations by city residents returning from weekend travels. On Monday morning, most of the cars are needed at the airports and must be ‘‘deadheaded’’ by company drivers. The two downtown distribution centers have ai (i = 1, 2) excess cars available. The three airports must be supplied with cars at a transportation cost of ci j (i = 1, 2; j = 1, 2, 3) for deadheading from distribution center i to airport j. The Monday morning demand rj for cars at airport j is uncertain and is described by the probability distribution p j (rj). If the demand exceeds supply at airport j, the unsatisfied demand is lost, with an average lost contribution per car of u j .

a) Formulate a mathematical program to minimize total deadheading transportation cost plus expected lost contribution.

b) Suppose now that the manager of fleet allocation is also concerned with supply over demand. All cars in excess of 50 cars above demand must be parked in an overflow lot at a cost of sj per car. Reformulate the program to include these expected average costs.

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