The problem we investigate deals with the optimal assignment of resources to the activities of a stochastic project network. We seek to minimize the expected cost of the project include sum of resource utilization costs and lateness costs. We assume that the work content required by the activities follows an exponential distribution. The decision variables of the model are the allocated resource quantities. We construct a continuous time Markov chain model for the activity network and use the PhaseType distribution to evaluate the project completion time. Then we use Fibonacci search over the interval of permissible allocations to the activity to seek the minimum expected cost. Manuscript profile

Extensive research has been devoted to resource constrained project scheduling problem. However, little attention has been paid to problems where a certain time penalty must be incurred if activity preemption is allowed. In this paper, we consider the project scheduling problem of minimizing the total cost subject to resource constraints, earliness-tardiness penalties and preemption penalties, where each time an activity is started after being preempted; a constant setup penalty is incurred. We propose a solution method based on a pure integer formulation for the problem. Finally, some test problems are solved with LINGO version 8 and computational results are reported. Manuscript profile

In this paper we consider the non-preemptive variant of a multi-mode resource constrained project scheduling problem (MRCPSP) withmode identity, in which a set of project activities is partitioned into disjoint subsets while all activities forming one subset have to beprocessed in the same mode. We present a depth-first branch and bound algorithm for the resource constrained project scheduling problemwith mode identity. The proposed algorithm is extended with some bounding rules to reduce the size of branch and bound tree. Finally,some test problems are solved and their computational results are reported. Manuscript profile