Resource-constrained multi-project scheduling: benchmark datasets and decoupled scheduling

Abstract

In this paper, we propose a new dataset for the resource-constrained multi-project scheduling problem and evaluate the performance of multi-project extensions of the single-project schedule generation schemes. This manuscript contributes to the existing research in three ways. First, we provide an overview of existing benchmark datasets and classify the multi-project literature based on the type of datasets that are used in these studies. Furthermore, we evaluate the existing summary measures that are used to classify instances and provide adaptations to the data generation procedure of Browning and Yassine (J Scheduling 13(2):143-161, 2010a). With this adapted generator we propose a new dataset that is complimentary to the existing ones. Second, we propose decoupled versions of the single-project scheduling schemes, building on insights from the existing literature. A computational experiment shows that the decoupled variants outperform the existing priority rule heuristics and that the best priority rules differ for the two objective functions under study. Furthermore, we analyse the effect of the different parameters on the performance of the heuristics. Third, we implement a genetic algorithm that incorporates specific multi-project operators and test it on all datasets. The experiment shows that the new datasets are challenging and provide opportunities for future research.

Appendix: Summary measures

Measure	Formula	Notes
Network measures
C	$\frac{A' - A'_\mathrm{min}}{A'_\mathrm{max^*}-A'_\mathrm{min}}$
NC	$\frac{A^n_j}{|I_j|+2}$	The average number of non-redundant arcs per node, including dummies${}^\mathrm{a}$
NPL	$\frac{|I_j|}{L_j}$	The average number of activities in parallel
OS	$\frac{A^r_j}{|I_j|*(|I_j|-1)/2}$	The ratio of the number of arcs (excluding dummies) and the theoretical number of arcs${}^\mathrm{b}$
SP	$\frac{L_j - 1}{|I_j|-1}$	The ratio of the longest chain in the network and the total number of activities
Resource measures
ARLF	$\frac{1}{CP_{j}}\sum _{t = r_j}^{r_j+CP_{j}}\sum _{i \in I_j}\sum _{k \in H_{ij}}Z_{ijt}X_{ijt}\left( \frac{r_{ijk}}{|H_{ij}|} \right)$
AUF	$\frac{1}{S} \sum _{s=1}^S \frac{W_{sk}}{l_sR_k}$	S is the number of intervals, $W_{sk}$ the total resource demand for resource k in interval s and $l_s$ the length of the interval
Load	$\frac{R_k}{|J|\cdot d_k}$	$d_k$ is the duration of an activity with resource demand for type k
MAUF	$\frac{1}{M_{ES}} \sum _{s=min_{j\in J}r_j}^{M_{ES}} \frac{W_{sk}}{l_sR_k}$	Similar to AUF, with $l_s = 1$
$\sigma ^2_\mathrm{UF}$	$\frac{\sum _{k\in K} (\text {UF} - \text {UF}_k)^2}{|K|}$
MUF	$\max _{k\in K} \frac{\sum _{j\in J}\sum _{i\in I_j} r_{ijk}d_{ij}}{R_k M_{ES}}$	The ratio of the earliest start schedule resource requirements and the available resources
NARLF	$\frac{1}{|J| * CP_\mathrm{max}}\sum _{j\in J}\sum _{t = r_j}^{r_j+CP_{j}}\sum _{i \in I_j}\sum _{k \in H_{ij}} Z_{ijt}X_{ijt}\left( \frac{r_{ijk}}{|H_{ij}|} \right)$
NARLF$'$	$\frac{1}{|J| * CP_\mathrm{max}}\sum _{j\in J}\sum _{t = r_j}^{r_j+CP_{j}}\sum _{i \in I_j}\sum _{k \in H_{ij}} Z'_{t}X_{ijt}\left( \frac{r_{ijk}}{|H_{ij}|} \right)$
RC	$\frac{1}{|K|}\sum _{k\in K}\frac{\overline{r_k}}{R_k}$	Where $\overline{r_k}$ is the average resource requirement, when it is required by an activity
RF	$\frac{\sum _{j\in J}\sum _{i\in I_j} |H_{ij}|}{|K|\sum _{j\in J}|I_j|}$	The average percentage of resource types that an activity requires
RS	$\frac{R_k - r_k^\mathrm{min}}{r^\mathrm{max}_k - r_k^\mathrm{min}}$	The resource strength. $r_k^\mathrm{min}$ is the maximum demand for resource k over all activities, $r_k^\mathrm{max}$ the peak demand for type k in the unconstrained earliest start schedule

1. ${}^\mathrm{a}A^n_j$ is the number of non-redundant arcs in the network of project j, including dummy arcs
2. ${}^\mathrm{b}A^r_j$ is the total number of redundant and non-redundant arcs in de network of project j, excluding dummy arcs