Consider the equipment replacement problem presented in the chapter. Recall that in the network model formulation of this problem a node represents a year when the equipment was purchased. An arc from node i to node j indicates that the equipment purchased in year i can be replaced at the beginning of year j. How could the network model below be modified to depict an equipment purchase in year 4 and operating costs only through the remainder of the planning window?
A) Modify the cost on arc 4-5 to account for only operating costs.
B) Add a second arc 4-5 to represent just the operating costs.
C) Add a dummy node, 6, so that arc 4-6 represents just the operating costs.
D) Add a dummy node, 6, so that arc 4-5 represents operating costs and 5-6 represents new equipment purchase.

Question

Consider the equipment replacement problem presented in the chapter. Recall that in the network model formulation of this problem a node represents a year when the equipment was purchased. An arc from node i to node j indicates that the equipment purchased in year i can be replaced at the beginning of year j. How could the network model below be modified to depict an equipment purchase in year 4 and operating costs only through the remainder of the planning window? ​  ​
A) Modify the cost on arc 4-5 to account for only operating costs. 
B) Add a second arc 4-5 to represent just the operating costs. 
C) Add a dummy node, 6, so that arc 4-6 represents just the operating costs. 
D) Add a dummy node, 6, so that arc 4-5 represents operating costs and 5-6 represents new equipment purchase.

Quizplus · Accepted Answer

Adding a dummy node, 6, and having arc 4-6 represent just the operating costs will allow the network model to depict an equipment purchase in year 4 and operating costs only through the remainder of the planning window. This avoids the need for modifying existing arcs, adding extra arcs, or adding costs to arcs that do not accurately reflect the scenario described.

Consider the Equipment Replacement Problem Presented in the Chapter