An Interval Programming Based Approach for fully uncertain Resource-Constrained Project Scheduling Problem Considering Project Manager’s Attitude toward Risk

Abstract

In recent years, there has been a growing attention to model and solve resource-constrained project scheduling problem (RCPSP) under uncertain environments. In most of the real-life cases, project managers may face with many uncertainties in activity durations, resource availabilities, resource requirements of the activities, the earliest and latest finishing times of the activities etc. In addition to these input parameters, project schedule which represents the starting and/or completion times of the activities should also be considered as uncertain variables in such a fully uncertain environments where all of the project data are imprecise. Based on this motivation, this paper presents an interval programming based transformation approach to overcome fully uncertain nature of the problem. In detail, classical discrete-time binary integer programming model of the deterministic problem was extended by incorporating interval-valued parameters and decision variables. Then, fully uncertain RCPSP was transformed into the crisp equivalent form by making use of interval programming, interval ranking and interval arithmetic operations. In the proposed approach, interval arithmetic operations are performed by using supplementary information obtained from the project manager. Thus, the proposed approach is also able to take into account the project managers' attitude toward risk and produces more acceptable and risk-free solutions. Finally, a real-life liquefied natural gas (LNG) storage tank construction project in a petroleum refinery is presented for testing its validity and practicality. The computational results have shown that more applicable and information efficient project schedules can be derived via the proposed approach according to the project manager's attitude toward risk.

Constraint Programming-Based Transformation Approach for a Multi-Objective & Multi-Mode Resource Investment Project Scheduling Problem Under Mixed Fuzzy-Stochastic Uncertainties

“…Because of these overlapped fuzzy numbers, precedence relations among the project activities may not be satisfied explicitly. This problematic issue has already mentioned by Subulan (2019Subulan ( & 2020 and defined as one of the risky situations in fully uncertain project scheduling applications. Actually, standard fuzzy arithmetic based solution approaches may cause these risky situations.…”

“…In this section, a literature survey on fuzzy-stochastic and fuzzy-random project scheduling problems is presented. In fact, researches in this field can be mainly classified into three parts, i.e., fuzzy, stochastic and fuzzy-random project scheduling problems according to the type of uncertainties (Subulan 2019;Subulan, 2020). Most of the previous researches handled the uncertain project parameters/input data by making use of probability or fuzzy set theories.…”

“…Moreover, project schedules or starting/completion times of the activities which correspond to the decision variables took deterministic values in most of the previously mentioned studies. However, project schedules should also be defined as uncertain variables in such fully uncertain environments where all of the project parameters are stated as fuzzy, stochastic or fuzzystochastic data (Subulan, 2019;Baykasoğlu & Subulan, 2017;2019).…”

“…Most of the classical transformation approaches in fuzzy mathematical programming literature utilized standard fuzzy arithmetic operations or Zadeh's extension principle with fuzzy ranking techniques while converting a fuzzy optimization problem into its crisp equivalent form. However, some recent studies (Subulan, 2020;Sotoudeh-Anvari, 2020;Baykasoğlu & Subulan, 2017, 2019 have proven that standard fuzzy arithmetic-based transformation approaches may cause questionable results or unrealizable solutions for many real-life engineering applications. For instance, several risky situations may arise in project scheduling and transportation applications under fully fuzzy environments 2017;2019;Subulan, 2020).…”

“…However, some recent studies (Subulan, 2020;Sotoudeh-Anvari, 2020;Baykasoğlu & Subulan, 2017, 2019 have proven that standard fuzzy arithmetic-based transformation approaches may cause questionable results or unrealizable solutions for many real-life engineering applications. For instance, several risky situations may arise in project scheduling and transportation applications under fully fuzzy environments 2017;2019;Subulan, 2020). Additionally, these standard fuzzy arithmetic-based transformation approaches are mainly developed depending upon integer linear programs (ILPs) with fuzzy parameters and variables.…”