Based on Denardo et al. (1988). Three fires have just broken out in New York. Fires 1 and 2 each require two fire engines, and fire 3 requires three fire engines. The “cost” of responding to each fire depends on the time at which the fire engines arrive. Let t ij be the time in minutes when the engine j arrives at fire i (if it is dispatched to that location). Then the cost of responding to each fire is as follows: fire 1, 6 t 11 + 4 t 12 ; fire 2, 7 t 21 + 3 t 22 ; fire 3, 9 t 31 + 8 t 32 + 5 t 33 . There are three fire companies that can respond to the three fires. Company 1 has three engines available, and companies 2 and 3 each have two engines available. The time (in minutes) it takes an engine to travel from each company to each fire is shown in the file P05_66.xlsx. a. Determine how to minimize the cost associated with assigning the fire engines. ( Hint : A network with seven destination nodes is necessary.) b. Would the formulation in part a still be valid if the cost of fire 1 were 4 t 11 + 6 t 12 ?

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Practical Management Science

6th Edition
WINSTON + 1 other
Publisher: Cengage,
ISBN: 9781337406659
BuyFind

Practical Management Science

6th Edition
WINSTON + 1 other
Publisher: Cengage,
ISBN: 9781337406659

Solutions

Chapter
Section
Chapter 5, Problem 66P
Textbook Problem

Based on Denardo et al. (1988). Three fires have just broken out in New York. Fires 1 and 2 each require two fire engines, and fire 3 requires three fire engines. The “cost” of responding to each fire depends on the time at which the fire engines arrive. Let tij be the time in minutes when the engine j arrives at fire i (if it is dispatched to that location). Then the cost of responding to each fire is as follows: fire 1, 6t11 + 4t12; fire 2, 7t21 + 3t22; fire 3, 9t31 + 8t32 + 5t33. There are three fire companies that can respond to the three fires. Company 1 has three engines available, and companies 2 and 3 each have two engines available. The time (in minutes) it takes an engine to travel from each company to each fire is shown in the file P05_66.xlsx.

  1. a. Determine how to minimize the cost associated with assigning the fire engines. (Hint: A network with seven destination nodes is necessary.)
  2. b. Would the formulation in part a still be valid if the cost of fire 1 were 4t11 + 6t12?

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Chapter 5 Solutions

Practical Management Science
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