19 Time_Cost_Tradeoff - Time Cost Tradeof Activity-On-Arc N...

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Time Cost Tradeof Time Cost Tradeof
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Activity-On-Arc Activity-On-Arc N : the event (node) set representing the numbers of the node A : the activity set (arc set) represented by a collection of pairs of nodes enclosed in parentheses and separated by a comma
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Example Example N = {1, 2, ….. , 7} and A ={(1,2), (1,3), (2,3), (1,4), (2,5), (3,5), (3,6), (4,6), (5,7), (6,7)}. Note that activity (2,3) is a "dummy" activity. It merely helps represent the precedence relationships. It takes 0 time units and consumes no resources 1 2 3 4 5 6 7
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Notation Notation d ij c = shortest achievable (crash) duration for activity (i , j). d ij n = normal duration for activity (i , j). NC ij = direct cost of activity (i, j) if performed at normal duration. CC ij = direct cost of activity (i, j) if performed at crash duration. c ij = additional direct cost of crashing activity (i, j) by one time unit. Note: CC ij = NC ij + c ij (d ij n - d ij c ) d ij = a decision variable, representing the duration of activity (i, j) With each activity (i , j) A
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Notation Notation With each event i N of the project i = partial payment to be received when event i is realized.
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