Abstract
This paper presents two stochastic optimization approaches for simultaneous project scheduling and personnel planning, extending a deterministic model previously developed by Heimerl and Kolisch. For the problem of assigning work packages to multi-skilled human resources with heterogeneous skills, the uncertainty on work package processing times is addressed. In the case where the required capacity exceeds the available capacity of internal resources, external human resources are used. The objective is to minimize the expected external costs. The first solution approach is a “matheuristic” based on a decomposition of the problem into a project scheduling subproblem and a staffing subproblem. An iterated local search procedure determines the project schedules, while the staffing subproblem is solved by means of the Frank–Wolfe algorithm for convex optimization. The second solution approach is sample average approximation where, based on sampled scenarios, the deterministic equivalent problem is solved through mixed-integer programming. Experimental results for synthetically generated test instances inspired by a real-world situation are provided, and some managerial insights are derived.
Highlights
In project management, the two important tasks of project scheduling on the one hand and of personnel planning on the other hand are usually not faced separately from each other, but rather in a simultaneous or interleaved manner
The resources have different efficiency values ηsk for each skill k they own; these efficiency values are drawn from a truncated normal distribution with an expected value of μ = 1, a standard deviation of σ = 0.25, and minimum and maximum threshold values of 0.5 and 1.5, respectively
We developed two solution approaches for a stochastic project scheduling and staffing problem under uncertainty on required efforts
Summary
The two important tasks of project scheduling on the one hand and of personnel planning on the other hand are usually not faced separately from each other, but rather in a simultaneous or interleaved manner. The project scheduling and staffing model proposed by Heimerl and Kolisch (2010) deals with the problem of assigning multi-skilled human resources to work, while taking into account resource-specific and heterogeneous skill efficiencies. The articles Heimerl and Kolisch (2010), Kolisch and Heimerl (2012), Felberbauer et al (2016), and Gutjahr and Froeschl (2013) constitute the starting point for the present paper In line with these articles, we assume that in the case where the work time demand exceeds the available capacity, external capacity is used, e.g., by hiring external personnel.
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