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 creating a new arc from node 4 to node 6 would allow for the representation of operating costs only through the remainder of the planning window. This new arc would represent the costs associated with operating the equipment purchased in year 4 until the end of the planning period. The original arc from node 4 to node 5 would still represent the option to replace the equipment at the beginning of year 5, but the cost associated with this arc would only include the cost of purchasing new equipment and not the operating costs.

Consider the Equipment Replacement Problem Presented in the Chapter