# Resource-constrained multi-project scheduling with activity and time flexibility

## TL;DR

This paper introduces a new resource-constrained multi-project scheduling problem that incorporates activity and time flexibility, proposing models to optimize makespan, activity balance, and resource utilization in manufacturing.

## Contribution

It presents a novel integrated flexible project scheduling problem with new objectives and develops mixed integer and constraint programming models for it.

## Key findings

- Models solve benchmark instances to optimality.
- Proposed models are effective for large industry cases.
- New problem formulation enhances scheduling flexibility.

## Abstract

Project scheduling in manufacturing environments often requires flexibility in terms of the selection and the exact length of alternative production activities. Moreover, the simultaneous scheduling of multiple lots is mandatory in many production planning applications. To meet these requirements, a new resource-constrained project scheduling problem (RCPSP) is introduced where both decisions (activity flexibility and time flexibility) are integrated. Besides the minimization of makespan, two new alternative objectives are presented: maximization of balanced length of selected activities (time balance) and maximization of balanced resource utilization (resource balance). New mixed integer and constraint programming (CP) models are proposed for the developed integrated flexible project scheduling problem. Benchmark instances on an already existing flexible RCPSP and the newly developed problem are solved to optimality. The real-world applicability of the suggested CP models is shown by additionally solving a large industry case.