Mixed-Integer Linear Programming Formulation and Priority-Rule Methods for a Preemptive Project Staffing and Scheduling Problem

Abstract

This chapter presents a generic model for an industrial project scheduling problem. The problem addressed here is an extension of the Resource-Constrained Project Scheduling Problem (RCPSP) and the Multi-Skill Project Scheduling Problem (MSPSP). The main specificities of this problem are the following: We considered both preemptive activities and non-preemptive activities, resource requirements of activities are given in terms of skills, and different durations exist in terms of both activities and skills. This model and its resolution methods are to be used in the Apache Open For Business (OFBiz) open source Enterprise Resource Planning (ERP) system, and must therefore satisfy some industrial constraints. We first propose a general model for this problem. Then, we propose a Mixed Integer Linear Program (MIP) formulation and a heuristic algorithm based on priority rules. The originality of the model lies in the fact that it simultaneously considers skill synchronization, preemption and precedence relationships. Experimental results performed on adapted instances from the PSPLIB benchmark are provided.