Project management in a competitive environment: interdicting a CPM based project and its implications

Abstract

There are two opponents in a classic network interdiction problem, network owner/defender and interdictor/attacker. Each side has enough information about the other's possible courses of action. While the network user wishes to run the network in an optimal way, the attacker with the limited resources tries to prevent the optimal operation of the network by interdicting the arcs/nodes of the network. In this study, we investigate project management in a competitive environment using a network interdiction approach. We assume that the project owner/manager strives to minimize the completion time of a Critical Path Method (CPM) based project while an opponent attempts to maximize the minimum completion time by inflicting some delays on project activities with available interdiction resources. Considering both discrete and continuous delay times, we develop two bi-level mixed-integer programming models for the interdictor. Using duality, we then convert the bi-level models to standard single-level models, which are solvable through standard optimization packages. We extend these models to find efficient solutions in terms of project completion time and interdiction resources from the interdictor's perspective. In this respect, we develop an algorithm to find an efficient solution set for the interdictor. Next, from project manager's standpoint, we discuss the earliest and latest scheduling times of activities in case of interdiction. Finally, we apply the developed techniques in a marketing project aiming at introducing a new product. The findings may enhance a better project management in an environment where an opponent can adversely affect the project management process by delaying some activities.