Abstract
The amount of resources assigned to a task highly influences its processing time. Traditionally, different functions have been used in the literature in order to map the processing time of the task with the amount of resources assigned to the task. Obviously, this relation depends on several factors such as the type of resource and/or decision problem under study. Although in the literature there are hundreds of papers using these relations in their models or methods, most of them do not justify the motivation for choosing a specific relation over another one. In some cases, even wrong justifications are given and, hence, infeasible or nonappropriated relations have been applied for the different problems, as we will show in this paper. Thus, our paper intends to fill this gap establishing the conditions where each relation can be applied by analysing the relations between the processing time of a task and the amount of resources assigned to that task commonly employed in the production and project management literature.
Highlights
The completion time of a project has turned out to be one of the main sources of competitive advantage for companies
This lead time depends on the processing time of each task in the project and, traditionally, these processing times have been assumed to be fixed data. In real life, they are usually dependent on the amount of resources assigned to the tasks [3]. They are denoted as controllable processing times, and it is assumed that jobs can be accomplished in shorter or longer durations by increasing or decreasing the available resources, such as manpower and equipment [4]
The assumption of controllable processing times acquires great importance when looking at the completion time of the project
Summary
The completion time of a project (project lead time) has turned out to be one of the main sources of competitive advantage for companies (see, e.g., [1, 2]). In real life, they are usually dependent on the amount of resources assigned to the tasks [3] In this case, they are denoted as controllable processing times, and it is assumed that jobs can be accomplished in shorter or longer durations by increasing or decreasing the available resources, such as manpower and equipment [4]. Properly speaking, resource-dependent processing times have been usually classified depending on the level of skill of the assigned resources and on the amount of resources In the former case, a task is performed by a resource (typically an employee) with a given level of skill or experience, and the processing times of that task are different depending on such level (examples can be found in [9,10,11,12,13]).
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