Chance-Constrained Model for RCPSP with Uncertain Durations

Lei Wang,Hu Huang,Hua Ke

doi:10.1186/s40467-015-0034-8

Lei Wang, Hu Huang + Show 1 more

Open Access

https://doi.org/10.1186/s40467-015-0034-8

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Abstract

Project scheduling with uncertain durations becomes a research focus with the development of uncertainty theory. Most researches concerned aim at minimizing project makespan or project cost according to different decision criterions. However, few works considered resource constraint, which initially appeared in deterministic resource-constrained project scheduling problem (RCPSP) and reflects the reality of a project. In this paper, RCPSP with uncertain activity durations, or uncertain RCPSP (URCPSP), is explored. Our aim is to minimize project makespan with certain belief degree. A corresponding uncertain model is built based on chance-constrained programming. To solve the model, a hybrid intelligent algorithm integrating genetic algorithm and an uncertain serial schedule generation scheme is designed and tested in some numerical examples. This work may provide some advices for the risk-averse project manager.

Highlights

Project scheduling is to assign activity starting times according to scheduling objectives, such as minimal project makespan and minimal project cost [1]
The problem can be divided into many subproblems, including resource-constrained project scheduling problem (RCPSP), resource leveling problem (RLP), and time-cost trade-off problem (TCTP)
The left part of a child comes from one parent and the right part consists of those remaining activities from another parent by removing activities contained in the left part

Summary

Introduction

Project scheduling is to assign activity starting times according to scheduling objectives, such as minimal project makespan and minimal project cost [1]. A baseline schedule, a list of activity starting times, can be obtained by solving deterministic RCPSP. Zhang and Chen [32] proposed an expected makespan minimization model for project scheduling problem with uncertain durations and total cost chance constraint. As far as we know, few researches pay attention to project scheduling problem with uncertain activity durations as well as resource constraint. The project scheduling problem in this paper possesses three characteristics simultaneously: uncertain activity durations, resource constraints, and belief degree for the objective value. An uncertain model based on chance-constrained programming instead of expected value model is proposed to minimize project makespan with some belief degree, which is applicable to the risk-averse decision-maker who wants to realize the project schedule with a pretty high belief degree.

11: Take out i from W and U if

Findings

Conclusion