Project scheduling and buffer management: A comprehensive review and future directions

Article history: Received: June 17, 2021 Received in revised format: July 30, 2021 Accepted: September 18, 2021 Available online: September 18, 2021 In the project management, buffers are considered to handle uncertainties that lead to changes in project scheduling which in turn causes project delivery delay. The purpose of this survey is to discuss the state of the art on models and methods for project buffer management and time optimization of construction projects and manufacturing industries. There are not literally any surveys which review the literature of project buffer management and time optimization. This research adds to the previous literature surveys and focuses mainly on papers after 2014 but with a quick review on previous works. This research investigates the literature from project buffer sizing, project buffer consumption monitoring and project time/resource optimization perspectives. © 2022 Growing Science Ltd. All rights reserved.

In the project management, buffers are considered to handle uncertainties that lead to changes in project scheduling which in turn causes project delivery delay. The purpose of this survey is to discuss the state of the art on models and methods for project buffer management and time optimization of construction projects and manufacturing industries. There are not literally any surveys which review the literature of project buffer management and time optimization. This research adds to the previous literature surveys and focuses mainly on papers after 2014 but with a quick review on previous works. This research investigates the literature from project buffer sizing, project buffer consumption monitoring and project time/resource optimization perspectives.

Introduction
Today, one of the biggest problems that companies, and organizations are faced with is that their projects take longer than the scheduled duration. Projects are often prolonged, lots of delays happen during the execution phase, and most of the time projects do not finish according to planned schedule. An effective method to improve the stability of project scheduling is to consider buffers to cope with time changes of projects using the critical chain method. In fact, a project buffer which does not have any float is considered at the end of a critical chain to be used when there is a delay. To increase safety in project implementation and factories production in the face of possible and unpredictable events, time buffers will be placed in different parts of projects and activities to prevent the negative effects of fluctuations in activities on the project's critical chain which will otherwise lead to a delay in the whole project. Three types of buffers are used, called the Project Buffer, Feeding Buffer, and Resource Buffer (Vanhoucke et al., 2016). The project buffer is placed at the end of the project's critical chain to maintain the project delivery date (Goldratt, 1997). Buffer management can be considered as the most important measure in implementing the critical chain scheduling, because if short buffers are allotted, we will need to re-schedule the project repeatedly until the end of the project, and if long buffers are allotted, all concepts used in scheduling will be violated . According to an extensive study by Hall (2015), project scheduling and project buffer management are among research areas with a high research potential for the next 10 years. Critical chain project management (CCPM) technique improves the accuracy of project plans by addressing variations by considering buffers in the project schedule. CCPM was originally proposed by Goldratt (1997) to improve the traditional methods of project management using a new mechanism to manage uncertainties. The Theory of Constraints (TOC) and the critical chain/buffer management are two effective approaches in project management (Goldratt, 1984). Since the introduction of the TOC, several researchers have examined its application in project management (e.g., Newbold (1998), Herroelen and Leus (2001), Leach (2005), Tukel et al. (2006), Woeppel (2006), Rabbani et al. (2007), Blackstone et al. (2009)). Project buffers and feeding buffers aggregate the protection (by removing safety from the individual tasks) that a project needs to meet its due date and allow focus on project duration (Leach, 2005) .To deliver a project within the shortest possible time, several project planning and scheduling techniques such as CCPM can typically be used in project implementation (Li et al, 2019). CCPM technique identifies the longest chain of both precedence and resource dependent tasks in the generated project schedule as the critical chain of project network schedule. CCPM is based on methods and algorithms derived from TOC. Most traditional methods of buffer sizing such as root square error method (RSEM), cut and paste method (C&PM), adaptive procedure with resource tightness (APRT), and adaptive procedure with density (APD) do not yield realistic buffer estimations under resource constraints (Vanhoucke, 2016). To improve this problem, it's better to hybrid these methods with other scheduling methods or design a new project buffer management algorithm/model. As mentioned before, there are not literally any surveys which review the literature of project buffer management and time optimization. In this paper, project buffer management is investigated from the following perspectives: project buffer sizing, project buffer consumption monitoring, project buffer sizing with buffer consumption monitoring simultaneously and project time/resource optimization. Table 1 shows all categories of literature review in this research.
The rest of the paper is structured as follows: In section 2, project buffer sizing is reviewed. Project buffer consumption monitoring is reviewed in section 3. Then, in section 4, project buffer sizing with buffer consumption monitoring simulation is reviewed. Finally, project time/resource optimization is reviewed in section 5.

Proposed algorithms/models
Bie et al. (2012) presented a technique for buffer sizing under the assumption that activities are interdependent. Ma et al. (2014) proposed a framework for using the improved CCPM method to manage construction projects. In this framework, they addressed two major challenges in CCPM-based construction planning: buffer sizing and multiple resource leveling. Peng and Huang (2014) suggested a useful approach to using the project critical chain method. In that study, they considered a float time in the non-critical chain as the main concern in determining feeding buffers, and thus, significantly simplified the process of using the project critical chain method. Russell et al. (2014) studied the addition of buffers to activities as a case study in construction projects. They added a time buffer to the project activities as an additional time to compensate for uncertainty, and to protect the project against tensions. Hu et al. (2015) introduced a new control procedure based on Critical Chain Scheduling and Buffer Management (CC/BM) that evaluates the probability of successful project completion relative to the cost of crashing and that determines when to expedite which activities in a cost-effective manner. Results of an experimental application of the proposed method presented its relative dominance over the currently widely adopted buffer management approach with respect to project time and cost performance. Hu et al. (2017) developed an improved framework for buffer management based on critical chain, which allowed for additional resources to be allocated if need be. Sarkar et al. (2018) focused on construction projects and developed a project management framework based on critical chains. Hu et al. (2019) presented six prioritization indices for selecting an optimal chain when more than one chain is possible. Then, they examined four production plans for rescheduling. She et al. (2021) proposed a new procedure for buffer sizing based on network decomposition, which offers logical advantages over previous ones. In this research, the size of a feeding buffer is determined from all associated noncritical chains. Then, the project buffer incorporates safety margins outside the critical chain by comparing feeding chains with their parallel critical counterparts. Table 2 lists the related works in the field of project buffer sizing.  (2015) studied the CCPM approach. They identified the approaches taken by researchers and suggested future research areas in this regard. Their main purpose was to describe the current state of research on the critical chain management method and to discover new directions for further research. The study covers 140 articles, journals, and conferences focusing on the CCPM method. Finally, 21 potential areas for critical chain management methods were recommended for future research. Vanhoucke (2016) investigated the traditional methods of buffer sizing and the way they are obtained and compared their respective results by an example. Bakry et al. (2016) introduced a buffer sizing algorithm to optimize project planning under uncertainty conditions. Zohrehvandi and Khalilzadeh (2019) integrated the APRT method with Failure Modes and Effects Analysis (FMEA), which resulted in a shorter project duration. Zarghami et al. (2019) presented a new step towards the sizing of buffers for CCPM by developing a probabilistic measure obtained through a reliability analysis of project resources. In addition, Zarghami et al. (2020) presented a new step towards the sizing of buffers for CCPM by developing a probabilistic measure obtained through a reliability analysis of project resources. In this method, buffer size was determined by assigning a scaling factor to the standard deviation of a chain. Sarkar et al. (2021) developed an enhanced CCPM framework for effective implementation of projects related to construction. The proposed framework improved buffer sizing by integrating the various uncertainties that affect construction scheduling. Table 3 shows the related works in the field of project buffer sizing: traditional buffer management methods.

Scheduling methods
Zhang et al. (2016) proposed a buffer sizing method based on resource tightness to better reflect the relationships between activities and improve the accuracy of project buffer sizing. They first determined resource tightness using critical quantification and resource accessibility. Then, through the design structure matrix, they analyzed the information flow between activities and the rework time resulting from information exchange and information resource tightness. Finally, the project buffer size was determined using resource tightness (both physical and information resource tightness). The results showed that the proposed method considers the effect of resource density on the project buffer, thus overcoming the shortcomings of traditional methods which consider only the physical resource tightness and ignore the information resource tightness. Zhang et al. (2017) developed a buffer sizing method based on a fuzzy resource-constrained project scheduling problem (RCPSP) to obtain an appropriate proportionality between the activity duration and the buffer size. Roghanian et al. (2018) proposed an improved critical chain approach with a fuzzy approach for project planning under uncertainty conditions. Table 4 demonstrates the related works in the field of project buffer sizing focusing on scheduling methods. Khesal et al. (2019) proposed an integrated earned value management (EVM) approach to control quality, cost, schedule and risk of projects. This study represented a new EVM framework by considering a quality control index. Particularly, some control indices and cumulative buffers defined by two proposed methods, namely the linear-and Taguchi-based methods. Zhong and Zhang (2015) addressed the RCPSP with beta distributed durations and exponential distributed resources. In this research, the resource interruptions are considered essentially to make the time buffer to compensate for the tardiness of the start time as well as to get the minimum makespan of activities in the proactive phase.

Proposed algorithms/models
Poshdar et al. (2016) considered a probabilistic-based buffer allocation method (MPBAL) in which project planners conduct buffer sizing according to preferences.  introduced a two-stage multi-objective buffer allocation approach for a more accurate project planning and scheduling. Martens and Vanhouck (2017) proposed a buffer controlling approach to determine the EVM of buffer allocation at various project phases. Zhang and Wan (2018) proposed an integrated buffer monitoring method. In their research, the prediction model based on the grey neural network was established, and the follow-up buffer consumption was predicted quantitatively according to the past and present performance data at the project monitoring points. Then, considering the relationship between the buffered consumed and the follow-up buffer consumption, a buffer integrated monitoring system was formed based on the integrated quantitative analysis on the buffer consumed and the subsequent trend information at each monitoring point. A buffer control model was presented by  which functioned in accordance with respective circumstances of different project phases. Martens and Vanhoucke (2020) improved the accuracy of project time forecasting by extending exponential smoothing for project time forecasting using EVM and earned duration management with the integration of corrective actions that are taken during project progress. According to the findings, the new heuristic was significantly useful in developing effective solutions within small CPU times. Table 5 lists the related works in the field of project buffer consumption monitoring: proposed algorithms/models.  Hu et al. (2016) proposed a new project schedule monitoring framework by introducing the activity crucial index. A buffer sizing method was introduced by , aiming at maximizing the efficiency of the project schedule. Salama et al. (2021) presented a new method for project tracking and control of integrated offsite and onsite activities in modular construction considering practical characteristics associated with this type of construction. Mahtamtama et al. (2018) proposed a dashboard for inventory monitoring that could perform cycle counting whilst also implementing a specific concept in TOC which is Buffer Time Management, this concept applies buffers on a certain period to each item inside the warehouse. Iranmanesh et al. (2016) research proposed an innovative buffer management method based on optimizing attributes to improve the efficiency of buffer management and optimize the estimation accuracy of a project buffer. The Monte Carlo simulation results showed that the buffer obtained using this method is smaller than the cut and paste method, but larger than the root square error method. Table 6 shows the related works in the field of project buffer consumption monitoring: traditional buffer management methods.  Poshdar et al. (2018) proposed a Multi-objective Probabilistic-Based Buffer Allocation method based on a goal-seeking optimization approach that uses a visual presentation of the mathematical optimization results to involve the preference of the project decision-makers in the final solution.  introduced a heuristic algorithm to determine the sizes of project buffers and feeding buffers as well as dynamically control buffer consumption, named as Fuzzy Overlapping Buffer Management Algorithm (FOBMA). In the research, the pentagonal fuzzy numbers were used to determine the appropriate amount of project activity resources. Also, an overlapping method was applied to obtain more realist activity durations. Another shortcoming of those methods is the lack of control over the consumption of buffers . In this research, buffer consumption is controlled by using a dynamic method. Due to varying circumstances in different phases of the project in terms of the duration of each phase, the amounts of activities' resources, and the complexity of the activities network, it is essential that buffer consumption be controlled dynamically. In this way, the amount of buffers which remains unconsumed in each phase of the project, will be transferred to the next phase. In addition, Zohrehvandi et al. (2021) proposed a project time optimization algorithm for calculating project buffer and feeding buffers as well as dynamic controlling of buffer consumption in different phases of a wind power plant project for finding a more realistic project duration. The author is currently working deeply on this topic and has several articles under review that will develop this topic. Table 7 demonstrates the related works in the field of project buffer sizing with buffer consumption monitoring: proposed algorithms/models and scheduling methods. Bevilacqua et al. (2015) examined a real problem consisting of a multi-objective optimization of planning a project's activities by taking resource constraints and prioritization into account. They used the CCPM method in this study. A scenariobased optimization method based on CCPM was suggested by Ma et al. (2015) with the aim of improving the robustness of schedules in construction projects. Peng et al. (2015) evaluated prioritization of critical chain scheduling issues in different execution modes. The results showed that by including the prioritization, the least number of resources was used in the project. Zhang et al. (2015) proposed a new approach for the CCPM method by considering an information-based relationship amongst project activities. Table 8 lists the related works in the field of project time/resource optimization: traditional buffer management methods.

Scheduling methods
The PERT method was first introduced by the US Navy for a large and complex submarine project (Salas-Morera et al., 2018). The PERT method is the most extensive technique for project planning, scheduling, and controlling, and a method for project evaluation and review (Malcolm et al., 1959). One assumption is the Beta distribution with a three-point estimate: optimistic (a), most probable (m), and pessimistic (b), and the mean = . The use of several distributions with other parameter estimates has been proposed (Hajdu and Bokor 2016) . Zhao et al. (2020) solved the resource conflict problems by a twostage approach combined with a feeding buffer for rescheduling. Beşikci et al. (2015) introduced a multi-project planning environment which included several projects with specific dates. They presented three scheduling problems to explore this multi-project environment. In their research, they integrated this multi-project environment as one model, and presented it as a resource portfolio problem. Leyman and Vanhoucke (2015) introduced a scheduling approach that improved the project's net present value. Almeida et al. (2016) investigated one of the latest approaches for project scheduling under resource constraints. Rueda-Velasco et al. (2017) presented an algorithm for multi-project scheduling with respect to dynamic resource allocation. Bruni et al. (2017) proposed an RCPSP with uncertain activity durations. Kadri and Boctor (2018) presented an RCPSP with transferable times. Kadri and Boctor (2018) included transfer times in their proposed resourceconstrained project scheduling problem. Chen et al. (2018) examined the performance of 17 priority rule-based heuristics and the justification technique on the stochastic RCPSP. Vanhoucke and Coelho (2019) presented a new solution algorithm to solve the RCPSP with activity splitting and setup times. Wang et al. (2019) considered an RCPSP with a single shared resource. Liu et al. (2020) investigated an energy-efficient integration of process planning and scheduling based on RCPSP. Rahman et al. (2020) proposed an algorithm based on genetic algorithms to solve a resource-constrained project planning problem. They implemented the proposed algorithm in the critical path of the project. It was a heuristic algorithm based on the critical path. Coelho and Vanhoucke (2020) created insight and understanding into what makes an RCPSP instance hard, and proposed a new dataset that consists of a small set of instances that are impossible to solve with the algorithms currently existing in the literature. Project planning and control are critical functions in project management. These functions involve a host of decision problems for scheduling projects, identifying and reporting the status of the project, comparing it with the baseline plan, analyzing the deviations, detecting out-of-control situations, and taking appropriate corrective actions (Hazir 2015). Hammad et al. (2018) presented a new framework for estimating, allocating, and managing planning probabilities using the TOC and the obtained value. Naeni et al. (2014) presented a new fuzzy-based earned value model with the advantage of developing and analyzing the earned value indices, and the time and the cost estimates at completion under uncertainty. Dehghan and Ruwnapura (2013) introduced an algorithm based on overlap among activities to optimize time and cost in activities and projects. Dehghan et al. (2015) improved an algorithm by using the activities overlapping method and utilizing genetic algorithms to optimize durations of projects' activities.  introduced a reconfigurable model that is a combination of a schedule model and a queuing system M/M/m/K to reduce the duration of the wind turbine construction project closure phase and reduce the project documentation waiting time in the queue. Also, Zohrehvandi et al. (2017) presented an algorithm for sequencing and scheduling of the activities in the project completion phase and reduced the duration of the phase. Table 9 shows the related works in the field of project time/resource optimization: scheduling methods.

Conclusion
The purpose of this study was to discuss the state of the art on models and methods for project buffer management and time optimization in construction projects and manufacturing industries. This research investigated the literature from project buffer sizing, project buffer consumption monitoring and project time/resource optimization perspectives with respect to traditional buffer management methods, algorithms/models and scheduling methods. According to the literature review, research carried out so far in the field of project buffer management and time optimization generally concentrated on traditional buffer management methods. Although, in some cases, scheduling methods have been employed to manage the buffer of a project, most of the research have used traditional methods of buffer management. The focus of this study has been on introduction and application of hybrid algorithms and models of simultaneous Buffer sizing and Buffer consumption. Scholars and researchers can study each of the mentioned papers and see the changing trend of the subjects from the scratch so that they can perceive the need for developing new algorithms and models in project buffer management and time optimization. For this purpose, for each area the authors tried to have a quick review on early works and for each classification some of the prominent works in the literature have been introduced so that the interested readers can refer and find other related papers to study.