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Minimizing the Project Cost with Generalized Precedence Relations

Zhi-Xiong Su, Han-Ying Wei, Xue Min Yu

2016
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Journal of Software
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Minimizing the project cost is a task of project scheduling, and usually is a starting point in the optimization about cost, for example the time-cost tradeoff is to compress the project duration from the one with minimum cost. Project cost can be minimized by letting all activities choose their minimum cost durations only when strict precedence relations exist between activities. But if generalized precedence relations (GPRs) exist between activities, letting all activities choose their
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... choose their minimum cost durations may not satisfy the given precedence relationships and result in a unfeasible project. In minimizing the project cost with GPRs, we transformed the mathematical programming model into two equivalent special models: a minimum cost -maximum flow model and a transportation model with balanced supply and demand. The two special models can be solved by using any current efficient algorithms. [5] first proposed a simple and applicable model to represent them based on Roy's concept. The works of Wiest [6] and Elmaghraby and Kamburowski [7] can be regarded as a milestone in the development of the activity network under GPRs. For Wiest [6], he found abnormal critical activity under some GPRs, in which the project duration will be prolonged if the duration of the activity is shortened, and vice versa. This overturned the traditional view of critical activity and opened up a new area of activity network under GPRs investigation. For Elmaghraby and Kamburowski [7], firstly, they cleverly represented all precedence relations in a network by adding reverse arcs with negative lengths, and proposed a perfect activity network under GPRs; secondly, they further studied the anomalies under GPRs, and described them as two manifestations that, the one refers to the reduction (increase) in project completion as a consequence of prolonging (shortening) an activity, and the other one occurs when diminishing the duration of an activity results in infeasibility of the activity network; in addition, they studied the time-cost tradeoff problem with GPRs and transformed it as a special case of the uncapacitated minimum cost flow problem. On the basis of the above works, Qi and Su [8] and Su et al. [9], [10] focused on noncritical activities and time floats under GPRs, and discovered new anomalies such as the invariability and increase in time float following consumption. In these works, they have pointed out that there was a project feasibility problem, which may be caused by GPRs. A number of scholars have researched a variety of problems with GPRs, and the most important of these, with respect to the current paper, are those dealing with project scheduling problems [11]-[17]. They mainly emphasized resource conflicts and minimized the project duration under conditions of constrained resources, rather than minimized the project cost. The time-cost tradeoff problem with GPRs is an important project scheduling problem, and Elmaghraby and Kamburowski [7] have been instrumental in presenting the problem. They transformed the problem into a minimum cost flow problem and devised a 163 Journal of Software 1 K kk k gx , and the objective function of the minimum project cost model is 165

doi:10.17706/jsw.11.2.162-181
fatcat:yk7pbcgysnhl7kr22sdqf6ekoi