# Stochastic project management: Multiple projects with multi-skilled human resources

## TL;DR

This paper introduces two stochastic optimization methods for joint project scheduling and personnel planning with multi-skilled human resources, addressing uncertainty in work durations and external staffing costs.

## Contribution

It extends a deterministic model to incorporate stochastic processing times and external resource costs, proposing a matheuristic and a sample average approximation approach.

## Key findings

- The methods effectively handle uncertainty in project scheduling.
- External staffing costs are minimized under stochastic conditions.
- Experimental results demonstrate practical applicability and managerial insights.

## 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.