The multi-mode resource investment problem: a benchmark library and a computational study of lower and upper bounds

The multi-mode resource investment problem (MRIP) is the multi-mode extension of the resource investment problem, which is also known under the name resource availability cost problem. It is a project scheduling problem with a given due date as well as precedence and resource constraints. The goal is to find a precedence feasible schedule that minimises the resource costs of the allocated resources. To compute these costs, the maximum resource peak is considered regarding renewable resource types, whereas the sum of allocated nonrenewable resource units is used in the case of nonrenewable resources. Many practical and complex project scheduling settings can be modelled with this type of problem. Especially with the usage of different processing modes, time and cost compromises can be utilised by the project manager. In the literature, some procedures for the MRIP have been investigated; however, the computational experiments in these studies have not been carried out on common benchmark instances. This makes a fair comparison of methods difficult. Therefore, we generated novel instances specifically designed for this problem and published them on the website https://riplib.hsu-hh.de. On this website, the instances as well as best-known solution values are available and researchers can also contribute their findings. We investigate these novel instances by proposing and evaluating lower bounds for the MRIP. Additionally, we analyse the proposed instances by applying heuristic as well as exact methods. These experiments suggest that most of the instances are challenging and further research is needed. Finally, we show some computational complexity properties of the NP-hard MRIP.

A flexible resource investment problem based on project splitting for aircraft moving assembly line

Purpose In response to the station design and flexible resources allocation of the aircraft moving assembly line, a new problem named flexible resource investment problem based on project splitting (FRIP_PS), which minimizes total cost of resources with a given deadline are proposed in this paper. Design/methodology/approach First, a corresponding mathematical model considering project splitting is constructed, which needs to be simultaneously determined together with job scheduling to acquire the optimized project scheduling scheme and resource configurations. Then, an integrated nested optimization algorithm including project splitting policy and job scheduling policy is designed in this paper. In the first stage of the algorithm, a heuristic algorithm designed to get the project splitting scheme and then in the second stage a genetic algorithm with local prospective scheduling strategy is adopted to solve the flexible resource investment problem. Findings The heuristic algorithm of project splitting gets better project splitting results through the job shift selection strategy and meanwhile guides the algorithm of the second stage. Furthermore, the genetic algorithm solves resources allocation and job schedule through evaluation rules which can effectively solve the delayed execution of jobs because of improper allocation of flexible resources. Originality/value This paper represents a new extension of the resource investment problem based on aircraft moving assembly line. An effective integrated nested optimization algorithm is proposed to specify station splitting scheme, job scheduling scheme and resources allocation in the assembly lines, which is significant for practical engineering applications.

Multi-agent Learning by Trial and Error for Resource Leveling during Multi-Project (Re)scheduling

In a multi-project context within enterprise networks, reaching feasible solutions to the (re)scheduling problem represents a major challenge, mainly when scarce resources are shared among projects. The multi-project (re)scheduling must achieve the most efficient possible resource usage without increasing the prescribed project constraints, considering the Resource Leveling Problem (RLP), whose objective is to level the consumption of resources shared in order to minimize their idle times and to avoid overallocation conflicts. In this work, a multi-agent solution that allows solving the Resource Constrained Multi-project Scheduling Problem (RCMPSP) and the Resource Investment Problem is extended to incorporate indicators on agents’ payoff functions to address the Resource Leveling Problem in a decentralized and autonomous way, through decoupled rules based on Trial-and-Error approach. The proposed agent-based simulation model is tested through a set of project instances that vary in their structure, parameters, number of resources shared, etc. Results obtained are assessed through different scheduling goals, such as project total duration, project total cost and leveling resource usage. Our results are far better compared to the ones obtained with alternative approaches. This proposal shows that the interacting agents that implement decoupled learning rules find a solution which can be understood as a Nash equilibrium.