REDUCING PROJECT DURATION IN STOCHASTIC ENVIRONMENTS BY OPTIMAL RESOURCE ALLOCATION USING A PROBABILISTIC MODEL

Many models have been developed for the resource-constrained project scheduling problem (RCPSP). In the deterministic type of problems, limited resources are assigned to the project’s activities, where each activity has a fixed duration and resource requirements. The aim is to find an optimal or close to optimal assignment schedule of the resources in order to achieve minimal duration, subject to the precedence relations among the activities, to the resource requirements of each activity and to the availability of the resources.

Project activities in real-world scenarios are commonly subject to considerable uncertainty during the execution stage, which often leads to schedule disruptions and project slippage. The uncertainties during project execution can stem from various sources such as human and/or machine failures, external disturbances etc.

This paper presents a model for project’s resource allocation that considers the probability distributions of each activity, and its effect on the entire duration. According to the proposed model, the probability of a successful completion of an activity in a specific duration is governed by the resources allocated to that activity. The model considers serial activities where resources that are allocated to a specific activity cannot be transferred to another activity. Each activity in the project is characterized by an expected duration E(d_i) that is related to the amount of resources allocated to that activity – r_i, such that As the project’s total amount of resources is limited, and that a resource that is allocated to a specific activity cannot be transferred to a different activity, the goal is to assign the resources to all activities such that the duration of the entire project is minimized. The effect of the resource allocation on the expected duration of the activities (given by F) is determined in a probabilistic manner according to the specific resource and activity type.

The duration of the entire project d_p is given by where is the duration of activity i. Since the expected value operator is linear, and since the duration of the entire project is the sum of all the expected durations of the project’s activities (assuming no parallel activities are allowed), the expected duration of the entire project is given by Given that the expected duration of each activity is determined by the amount of resources allocated to that activity, the expected duration is determined by the resource allocation of all activities in the project. Initial simulation results show how different resource allocation schemes affect the expected duration of the entire project. Further analysis is required in order to determine an analytical solution for this type of the resource-constrained project scheduling problem (RCPSP).