Bottleneck Identification in Resource-Constrained Project Scheduling via Constraint Relaxation

TL;DR

The paper tackles bottleneck identification in resource-constrained project scheduling to reduce project tardiness by relaxing specific capacity constraints. It introduces two methods: untargeted relaxations (iira) that adapt Job-Shop bottleneck indicators to RCPSP, and targeted relaxations (ssira) that use suffix-relaxed schedules to focus on a chosen target project. Empirical results show untargeted relaxations perform comparably to targeted ones, with ssira generally delivering more consistent improvements across instances. The work provides practical decision-support tools for computer-aided scheduling and highlights the potential of instance-specific relaxations to improve production plans.

Abstract

In realistic production scenarios, Advanced Planning and Scheduling (APS) tools often require manual intervention by production planners, as the system works with incomplete information, resulting in suboptimal schedules. Often, the preferable solution is not found just because of the too-restrictive constraints specifying the optimization problem, representing bottlenecks in the schedule. To provide computer-assisted support for decision-making, we aim to automatically identify bottlenecks in the given schedule while linking them to the particular constraints to be relaxed. In this work, we address the problem of reducing the tardiness of a particular project in an obtained schedule in the resource-constrained project scheduling problem by relaxing constraints related to identified bottlenecks. We develop two methods for this purpose. The first method adapts existing approaches from the job shop literature and utilizes them for so-called untargeted relaxations. The second method identifies potential improvements in relaxed versions of the problem and proposes targeted relaxations. Surprisingly, the untargeted relaxations result in improvements comparable to the targeted relaxations.

Figures (4)

• Figure 1: Example of an original and relaxed schedule with 8 jobs and a single resource. The Jobs segments show the (overlapping) scheduling of jobs in time. The Resource 1 segments show the cumulative consumption of the single resource by the scheduled jobs. In the Relaxed schedule the Capacity constraint relaxation refers to the temporary increase of the resource capacity.
• Figure 2: Illustration of the iira. Starting with the original schedule, the bottleneck resource is identified using the identification indicator, granular resource load is computed for the resource, utilizing convolution, a specific improvement period is chosen for capacity relaxation, and a modified schedule is obtained.
• Figure 3: Illustration of the ssira. Starting with the original schedule, improvement intervals are found in suffix-relaxed schedules, the best improvement intervals are selected, corresponding capacities are relaxed, and a new schedule is obtained.
• Figure 4: An example evaluation displays schedule differences versus achieved improvement. Surprisingly, the iira often finds better solutions than ssira.

Theorems & Definitions (2)

• Definition 1: Suffix-relaxed schedule
• Definition 2: Left-shift closure