Development and analysis of a resource cost minmization model for parallel project scheduling and human resource allocation problem

In today's world, effective project management is an important subject matter for almost all companies. The two most important aspects of project management are project scheduling and allocation of human resources. In this study, a two-staged stochastic optimization problem, including simultaneous project scheduling and resource allocation problems is discussed. In the first stage, the project activities, whose workforce are considered stochastic, are scheduled along the project planning horizon, while in the second stage, resource assignments are made to these activities. If the required workforce for certain activities exceeds the capacities of internal resources, external human resources are used. With the proposed mathematical model, it is aimed to minimize the expected costs of the external human resources used. Within the scope of the problem, two scenarios are considered. In the first scenario, partial assignment of activities are not accepted. Thus, the decision variable that controls whether the project activities are assigned in a certain period is accepted as binary. In the second scenario, partial assignment of activities are accepted. In this case, corresponding decision variable is accepted as float. For both cases, the required workforce for activities are considered stochastic and the probability distributions are considered as both uniform and triangular. The data set designed in MATLAB, is tested with Constraint Programming (CP) Optimizer in CPLEX OPL environment and different sensitivity analyses for both mathematical models are presented.