The multi-mode resource investment problem: a benchmark library and a computational study of lower and upper bounds
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The multi‑mode resource investment problem: a benchmark library and a computational study of lower and upper bounds Patrick Gerhards1 Received: 10 April 2019 / Accepted: 25 June 2020 © The Author(s) 2020
Abstract 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. Keywords Project scheduling · Resource investment problem · Multi-mode · Benchmark instances · Mixed-integer programming
* Patrick Gerhards patrick.gerhards@hsu‑hh.de 1
Helmut Schmidt University, Hamburg, Germany
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P. Gerhards
1 Introduction Project scheduling is an important part of project management. Often, projects have a deadline or a due date and the tasks of the project compete against each other in the use of scarce resources. In the resource investment problem (RIP), the decision maker can determine how many units of each resource are allocated to the project in order to find a schedule that meets the due date. This schedule needs to respect the allocated resources as well as the precedence relations among the activities of the project. The goal is to minimise the project costs that are defined by the allocated units of resources. In this work, we consider two types of resources: renewable and nonrenewable resources. The amount of available renewable resource units is replenished after each time period. So, for the cost calculation of the renewable resource costs, the maximum resource usage
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