10 3. 7. 8. 2.
Examine the network below.
Write the complete LP formulation for this problem. Please include the Objective Function and the complete set of constraints.
Consider the provided diagram,
In order to analyze the network given above by linear programming.
let xi (>=0) represent the cost at which we start activity i.
This time is our choice and hence is a decision variable.
- the xi can be constrained to take integer (whole number) values if we so wish using integer programming.
- the xi are NOT necessarily the same as the earliest times.
Considering the precedence relationship between activity 1 and activity 2, it is clear that we must have,
That means, the starting time for activity 2 must be at least as great as the cost for an immediate predecessor activity plus the cost for this predecessor activity. Note that we do not put here. This is because the inequality () gives us more flexibility than the equality (=).
we must also have
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