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, is the best choice because it allows us to have a separate arc, 4-6, that represents just the operating costs without affecting the existing arcs in the network. This keeps the network structure intact and allows us to easily modify the costs without changing the underlying logic of the problem.

Consider the Equipment Replacement Problem Presented in the Chapter