Toward a scalable type-2 fuzzy model for resource-constrained project scheduling problem

Highlights

• A new solution for RCPSP under uncertain activity time span.

• A scalable type-2 fuzzy Dijkstra algorithm and simplex algorithm.

• Run-time optimization using type-2 fuzzy simplex algorithm.

• Different permutation in type-2 Dijkstra algorithm.

• The largest cover of uncertainty through type-2 fuzzy.

Abstract

This paper develops a scalable method for the Resource-Constrained Project Scheduling Problem (RCPSP) with a type-2 fuzzy uncertain activity time-span. The objective of this method is the project completion time minimization. This problem has been solved through a scalable type-2 fuzzy Dijkstra algorithm inside different activities rules. The Dijkstra algorithm produces a different permutation of activities alongside each selected path that should be examined in optimization function using the type-2 fuzzy simplex algorithm. This method generates the best permutation using run-time optimization which significantly satisfies lower project completion time inside the project cost minimization. Also, the method proposed a resource workload for both tactical and operational levels of planning. The presented approach is conducted by the gas-related industry project and a case on satellite design of the aerospace industry on 3 different Resource/Process/Environment strategies. The results convey the defined method has a better performance compared to type-1 fuzzy for covering the largest uncertainty domain. This method could be considered in every engineering project management.

Introduction

The RCPSP is classic and well-known research that minimizes the project completion time [1], [2], [3]. In general, project scheduling with precedencies and resource limitations is in the category of the NP-hard problem [4]. This standard version includes activities scheduling with different essential renewable resources [3]. Also, resources are available in limited quantities and each activity has a known time-span with a constant quantity of resources [5]. There are different extensions of RCPSP such as generalized precedence relations, multiple objective, uncertain parameters, and multi-mode activity. In all extensions, each activity must be implemented and all of them besides the precedence constraints are known [3], [6]. Thus, there are different solutions to RCPSP which have been illustrated in Fig. 1 as the taxonomy for solving methods [7], [8]. The proposed solution of this paper can be classified as a combined method of exact solution (Mathematical programming) and heuristic one (Search based).

In this case, many types of research have determined heuristic approaches for solving the RCPSP but often need a huge computational effort to solve problems [9]. Most of the researches in RCPSP has been done in a static environment [7] but due to the dynamic nature of the environment, project scheduling may be subject to considerable uncertainties [2], [10]. These uncertainties are as following [10]:

• Uncertainties in activities,

• Uncertainties in resources demand,

• Temporal uncertainties.

Therefore, effectively dealing with the RCPSP solving method with these uncertainties is becoming an important challenge for managers [9].

Identified the crucial of developing a new approach, the authors focus on the type-2 fuzzy version of the RCPSP in this study and assume activity time-span is an uncertain variable. The reason for activity time-span parameter consideration in uncertain conditions is that the varying in activity time-span present difficult management of activity execution. Thus, confusion in activity execution may cause project delay, higher project cost, and resource insufficiency [3]. Thus, for solving this problem, the main research question is as following:

(RQ) How can we cover this uncertainty level of scheduling?

To address the RCPSP under uncertain activity time-span, the scalable type-2 fuzzy approach is formed based on the following research stages:

• Identify the network of the project,

• Identify precedence constraints of each activity,

• Identify resource constraints of each activity,

• Appropriate settings such as activity time-span in type-2 fuzzy version,

• Identify the priority of activities,

• Calculate the best path of activities execution via scalable type2-fuzzy Dijkstra algorithm.

The proposed method was conducted by two case studies, one in a gas-related industry and a case on the aerospace industry. The presented approach has handled the projects on 3 different Resource/Process/Environment strategies. Due to the wide range of uncertainty and complexity of such projects, a scalable type-2 Fuzzy model has been used for handling projects dimension. In the cases of this paper both for the gas industry and for the satellite design development, uncertainty and risk are an integral part of the projects. Section 5 indicates applying the proposed method for the uncertainty handling of high-tech project management. The proposed method has better results and covers a larger range of uncertainty and also minimizes project execution time. The solution method with a combination of type-2 simplex algorithm and the type-2 fuzzy Dijkstra algorithm provides the most optimal path to perform activities.

The novelty of the paper includes two important issues in project management, as follows:

A—The first novelty in problem formulation includes the use of triangular, trapezoidal membership functions, etc., as scalable fuzzy which can strengthen the effectiveness of dealing with uncertainty. In other words, the proposed method has better results and covers a larger range of uncertainty and also minimizes project execution time compared with traditional ones.

B—The second contribution of the paper is based on the solution method. The combination of the Simplex algorithm and the type-2 fuzzy Dijkstra algorithm provides the most optimal path to perform activities in a wide range of uncertainty-based projects.

This paper has been organized as follows: Section 2 presents the literature review. Section 3 gives a brief introduction to the basic theory of type-2 fuzzy in the proposed algorithm. Section 4 presents a formal description of the algorithm. Section 5 validates the illustrated method by two case studies in the gas-related and aerospace industry. Finally, Section 6, presents the conclusion.