Evaluating the efficiency of the recovery strategies on the integrated project and personnel scheduling problem

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EVALUATING THE EFFICIENCY OF THE

RECOVERY STRATEGIES ON THE

INTEGRATED

PROJECT

AND

PERSONNEL SCHEDULING PROBLEM

Aantal woorden / Word count: 32.311

Nele Lettens

Stamnummer / student number : 01509495

Promotor / supervisor: Prof. Dr. Broos Maenhout

Masterproef voorgedragen tot het bekomen van de graad van:

Master’s Dissertation submitted to obtain the degree of:

Master in Business Engineering: Operations Management

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PERMISSION

I declare that the content of this Master’s Dissertation may be consulted and/or reproduced,

provided that the source is referenced.

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PREFACE

This dissertation was the last step necessary to obtain a master’s degree in Business Engineering with the main subject Operations Management. Writing this dissertation was a very insightful task that enabled me to both integrate myself in the academic literature on project and personnel scheduling as well as to develop and execute a study in this field of research. This process was however not all plain sailing and the end results would not be the same without the help, guidance and inspiration of several people.

First of all, I would like to thank my supervisor Prof. Dr. Broos Maenhout for offering me this interesting yet challenging topic that pushed me beyond my limits. I’m grateful for his fast responding to my never-ending questions as well as constructive feedback and guidance to ensure this dissertation turns out to be its best possible version.

Furthermore, I would like to thank Eva for both proofreading and helping me with the lay-out of this dissertation. Additionally, I am sincerely thankful for her friendship and encouragement during this dissertation as well as during the past five years of this study programme.

Finally, I could not end this dissertation as well as my career as a student without thanking my family and friends as well as Robbe for their unconditional support. As this dissertation was written during the COVID-19 pandemic, their support was more than ever helpful to reduce the stress-level experienced.

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1.2Uncertainty ...19 1.2.1 Uncertainty of arrival ...19 1.2.2 Uncertainty of capacity ...20 1.2.3 Uncertainty of demand ...20 1.3Recovery strategies ...21 1.3.1 Rescheduling framework ...22 1.3.1.1 Rescheduling environments ...22 1.3.1.2 Rescheduling strategy ...22 1.3.1.3 Rescheduling methods ...23

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1.3.1.4 Framework applied ...24

1.3.2 Recovery strategies in the project scheduling problem ...26

1.3.2.1 Right-shift rescheduling ...26

1.3.2.2 Partial rescheduling...27

1.3.2.3 Complete regeneration ...29

1.3.3. Recovery strategies in the personnel scheduling problem ...33

1.3.3.1 Proactively dependent reactive methods ...34

1.3.3.2 Pure reactive methods ...35

2. RESEARCH METHODOLOGY ...37

2.1 Inserting uncertainty ...38

2.2 Repairing disrupted schedules ...42

2.2.1 Method 1: Right-shift scheduling of project and personnel schedule ...43

2.2.2 Method 2: Complete regeneration of project + right-shift scheduling of the personnel schedule ...56

2.2.3 Method 3: Right-shift scheduling of project schedule + complete regeneration of personnel schedule ...58

2.2.4 Method 4: Complete regeneration of project and personnel schedule ...61

2.3 Analyzing the performance measures ...63

2.3.1 Schedule cost ...64

2.3.2 Schedule stability ...65

2.3.2.1 Project schedule stability ...65

2.3.2.2 Personnel schedule stability ...65

3. COMPUTATIONAL EXPERIMENTS: TEST DESIGN ...67

3.1Project and personnel characteristics...67

3.1.1 Project characteristics ...67

3.1.2 Personnel characteristics ...68

3.2 Objective function weights and baseline mathematical model ...69

3.2.1 Objective function weights ...69

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3.4 Reactive methods ...72

3.5 Performance evaluation ...73

4. RESULTS ...75

4.1 Uncertainty of capacity...75

4.1.1 Schedule cost increase ...76

4.1.2 Project stability ...77

4.1.3 Personnel stability ...79

4.2 Uncertainty of demand ...81

4.3 Uncertainty of arrival ...87

4.4Summary...91

5. CONCLUSION ...95

5.1 General conclusion ...95

5.2 Limitations and future research...97

6. REFERENCES ... x

7. APPENDIX ... xvi

A.1. Uncertainty of capacity – Cost increase – PP ... xvi

A.2. Uncertainty of capacity – Cost increase – PS ... xviii

A.3. Uncertainty of capacity – Project stability – PP ...xx

A.4. Uncertainty of capacity – Project stability – PS ... xxii

A.5. Uncertainty of capacity – Personnel stability – PP... xxiv

A.6. Uncertainty of capacity – Personnel stability – PS... xxvi

B.1. Uncertainty of demand – Cost increase – PP ... xxviii

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B.3. Uncertainty of demand – Project stability – PP ... xxxiv B.4. Uncertainty of demand – Project stability – PS ... xxxvi B.5. Uncertainty of demand – Personnel stability – PP ...xxxviii B.6. Uncertainty of demand – Personnel stability – PS ... xl C.1. Uncertainty of arrival – Cost increase – PP ... xlii C.2. Uncertainty of arrival – Cost increase – PS ... xlv C.3. Uncertainty of arrival – Project stability – PP ... xlviii C.4. Uncertainty of arrival – Project stability – PS ... l C.5. Uncertainty of arrival – Personnel stability – PP... lii C.6. Uncertainty of arrival – Personnel stability – PS... liv

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LIST OF ABBREVIATIONS

ANOVA = Analysis of Variance

AOR = Affected operations rescheduling CRS = Complete rescheduling

EBST = Earliest baseline starting time

ILP = Integer linear programming

LAN = Lowest activity number

LRS = Local rescheduling

LST = Latest starting time

LW = Largest activity weight

MUP = Matchup scheduling

PP = Preempt-repeat

PS = Preempt-resume

RAN = Random

RCPSP = Resource-constrained project scheduling problem

RCPSP-WET = Resource-constrained project scheduling problem with weighted earliness/tardiness cost

RCJAP = Resource-constrained job assignment problem RSS = Right-shift scheduling

SD = Standard Deviation

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LIST OF FIGURES

Figure 1.1: A) AoA representation of link between activities i & j; B) AoN representation of link between

activities i & j ... 6

Figure 1.2: Rescheduling framework (Adapted from Viera et al., 2003) ...25

Figure 1.3: Right-shift scheduling ...27

Figure 1.4: LRS algorithm (Kuster et al., 2007) ...29

Figure 1.5: Modified Serial Schedule Generation Scheme ...30

Figure 2.1: Research methodology...37

Figure 2.2: Uncertainty simulation flowchart...38

Figure 2.3: Baseline project and personnel schedule ...39

Figure 2.4: Disrupted schedule - Uncertainty of capacity ...39

Figure 2.5: Disrupted schedule - Uncertainty of demand ...40

Figure 2.6: Disrupted schedule - Uncertainty of arrival ...41

Figure 2.7: Right-shift scheduling due to uncertainty of capacity – PREEMPT-REPEAT ...45

Figure 2.8: Right-shift scheduling due to uncertainty of capacity – PREEMPT-RESUME ...46

Figure 2.9: Completely right-shifted schedule - Uncertainty of capacity ...47

Figure 2.10: Right-shift scheduling due to uncertainty of demand - personnel schedule adaption ...48

Figure 2.11: Completely right-shifted schedule - Uncertainty of demand ...49

Figure 2.12: Project right-shift scheduling due to uncertainty of capacity – PREEMPT-REPEAT ...50

Figure 2.13: Project right-shift scheduling due to uncertainty of capacity – PREEMPT-RESUME ...51

Figure 2.14: Completely right-shifted schedule - Uncertainty of arrival ...51

Figure 2.15: Personnel right-shift scheduling due to uncertainty of capacity – PREEMPT-REPEAT...54

Figure 2.16: Personnel right-shift scheduling due to uncertainty of capacity – PREEMPT-RESUME ...56

Figure 4.1: Average cost increase due to uncertainty of capacity - PP ...76

Figure 4.2: Average cost increase due to uncertainty of capacity - PS ...77

Figure 4.3: Average project stability due to uncertainty of capacity - PP ...78

Figure 4.4: Average project stability due to uncertainty of capacity - PS ...79

Figure 4.5: Average personnel stability due to uncertainty of capacity - PP ...80

Figure 4.6: Average personnel stability due to uncertainty of capacity - PS ...81

Figure 4.7: Average cost increase due to uncertainty of demand - PP ...82

Figure 4.8: Average cost increase due to uncertainty of demand - PS ...83

Figure 4.9: Average project stability due to uncertainty of demand - PP ...84

Figure 4.10: Average project stability due to uncertainty of demand - PS ...84

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Figure 4.12: Average personnel stability due to uncertainty of demand - PS ...86

Figure 4.13: Average cost increase due to uncertainty of arrival - PP ...87

Figure 4.14: Average cost increase due to uncertainty of arrival - PS ...88

Figure 4.15: Average project stability due to uncertainty of arrival - PP...89

Figure 4.16: Average project stability due to uncertainty of arrival - PS...89

Figure 4.17: Average personnel stability due to uncertainty of arrival - PP ...90

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LIST OF TABLES

Table 1.1. Relevant activity characteristics ... 9

Table 1.2: Personnel scheduling characteristics ...14

Table 2.1: Reactive methods applied ...42

Table 3.1: Objective function weights ...70

Table 3.2: Objective function weights ...73

Table 3.3: Performance measures ...74

Table 3.4: Violation weights ...74

Table 4.1: Relative schedule cost increase improvement - RSS compared to CRS (project) + RSS (personnel)...92

Table 4.2: Relative schedule cost increase improvement - RSS compared to RSS (project) + CRS (personnel)...92

Table 4.3: Relative schedule cost increase improvement - RSS compared to CRS ...92

Table 4.4: Relative project stability improvement - RSS compared to CRS ...93

Table 4.5: Relative personnel stability improvement - RSS compared to RSS (project) + CRS (personnel) ...93

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0. INTRODUCTION

Planning a project with scarce resources is a widely recognized problem domain in project management. A subfield of this problem is where the needed resources are human resources. These resources are one of the most valuable as they account for 30-50% of the total project cost (Adrian, 1987; Larson & Gray, 2011). Despite their importance, human resources complex the project planning problem such that both the topic of project planning and personnel rostering are generally studied separately in literature. Accordingly, in practice, both problems are also solved consequently, where first the project schedule is defined and afterwards the personnel timetable is constructed to guarantee the staffing requirements of the project. Nevertheless, Alfares and Bailey (1997) indicated already early on that integrating these two problems in to “the integrated project and personnel scheduling problem” could decrease the labor and the overhead cost. Hence, integrating these two problems become extremely relevant for today’s project managers whom try to be more and more competitive by cutting costs. Unfortunately, the relevant studies on integration of both problems are limited and the integration problem remains one of today’s challenges in planning a project with scarce resources (Vanhoucke, 2018).

An important issue that comes along with scheduling the project and personnel concerns the assumptions on the project characteristics that need to be made. A project manager makes numerous deterministic assumptions on the availability of the personnel, the duration of the project activities, the resources requirements of the activities, etc. in order to construct a baseline schedule. But, as the execution of the project deals with a stochastic environment, project disruptions and deviations from the baseline schedule occur. According to Van den Bergh, Beliën, De Bruecker, Demeulemeester, and De Boeck (2013), when dealing with the integrated problem, operational variability originates from three different sources i.e. the uncertainty of demand, the uncertainty of arrival, and the uncertainty of capacity. These three sources lead to different types of project disruptions and unfortunately these disruptions are more often the rule than the exception. In order to efficiently manage the recovery of project disruptions, a handful of reactive mechanisms are available. When dealing with the integrated project and personnel scheduling problem, the reactive mechanisms available are even broader compared to when the two problems are handled separately. When integrating these two problems, all options that stem from either adapting the project activities or adapting the personnel roster are available. However, up till now it remains unclear which recovery method would be the most applicable for which type of source of uncertainty when dealing with the integrated problem. Determining the best rescheduling solution for the integrated problem remains a gap in academic research. As project costs could dramatically increase due to these disruptions, gaining more insight on how to properly handle this uncertainty in a project becomes equally important as the

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scheduling itself. Specifically, in the field of project management dealing with uncertainty becomes valuable because each year numerous projects go over budget and drag along long after their planned completion time (Flyvbjerg, Bruzelius, & Rothengatter, 2003). Nevertheless, this determination is often considered as the most difficult part of the rescheduling process (Vieira, Herrmann & Lin, 2003).

Therefore, this master thesis analyzes the efficiency of the different reactive mechanisms available when integrating these two scheduling problems to recover from project disruptions. This efficiency forms a first performance measure. To gain more insight in the usefulness of the mechanisms, the resulted project stability and personnel roster stability is analyzed too as a second performance measure of the mechanism. This evaluation is applied to an artificial setting where a disruption happens to a single project with no more than 10 activities in a controlled environment. The baseline schedules subject to this analysis were constructed in an integrated way, which takes both the precedence constraints available in the project planning problem and the time-related calendar constraints available in the personnel scheduling problem in account. The personnel scheduling problem is embodied by the manpower days-off scheduling problem where members are scheduled in a non-cyclical way on the one hand and where the project scheduling problem on the other hand is the standard formulation of the resource-constrained project scheduling problem as formulated by Herroelen, De Reyck, and Demeulemeester (1998). After generating these baseline integrated schedules, the study is also split up according to the three types of operational variability specified in Van den Bergh et al. (2013). The different disruptions analyzed are (1) the unavailability of a project worker as uncertainty of capacity, (2) a change in the resource requirement of an activity as uncertainty of demand and, (3) a change in an activity’s duration as the uncertainty of arrival. To find out which mechanism performs better on which type of uncertainty, the different types of disruptions are not combined but analyzed separately using a single disruption case per uncertainty type.

As the aim of this dissertation is to analyze the existing recovery mechanisms, literature was reviewed to identify the relevant mechanisms available for the integrated project recovery and to gain better understanding in the scheduling environment of the problem. This research results in no real development of the ultimate recovery method, however the conclusions of this evaluation are valuable for a further development of an efficient recovery model for the integrated problem.

Overview

The outline of this dissertation is as follows: the first chapter entails a review of the relevant literature. As the dissertation concerns several varying fields of research, this chapter deals with both the scheduling problem, the uncertainty available in this problem, and covers an extensive overview of the available reactive methods in project management. The second chapter further elaborates on the research methodology used to investigate the efficiency and the stability of the different reactive mechanisms

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this dissertation. Subsequently, chapter 4 provides the reader with the results of the performance measures of the different methods as outcome of these experiments. In the last chapter, the conclusions and limitations of the dissertation are given.

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1. LITERATURE REVIEW

This first chapter highlights the most relevant topics for the dissertation. The chapter is split up in three main sections. Section 1.1 deals with the scheduling of the integrated project and personnel problem. In this section, apart from the integrated problem, both the project scheduling and the personnel rostering will be discussed too in order to better understand the environment recovery problem. Understanding both scheduling problems first will be beneficial to grasp the complexity of the integrated problem. Section 1.2 of this chapter elaborates on the uncertainty available in this problem type due to its operation in a real-life environment. This will highlight the different deficiencies that may arise in the project and personnel scheduling environment. The last section, section 1.3, covers the management of this uncertainty through the use of recovery strategies. The recovery actions help to deal with the rescheduling of the problem once a project disruption occurs.

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1.1 Scheduling problem

The quote of Benjamin Franklin (n.d.) nicely illustrates why the scheduling problem is so widely studied and relevant for project managers. Next to this argument, Aytug, Lawley, McKay, Mohan, and Uzsoy (2005) identify several other reasons why baseline scheduling remains important. They list the following purposes of scheduling:

1. Basis for communication & coordination 2. Basis of planning of external activities 3. Optimization and evaluation of performance 4. Avoidance of further problems

Therefore, even when dealing with the stochastic nature of projects and knowing that there is a high chance of deviating from this schedule, constructing baseline schedules is still beneficial. Hence, this first section of the literature review identifies the relevant literature that deals with this scheduling problem. Section 1.1.1 covers the project scheduling problem, whereas section 1.1.2. provides background information on the personnel scheduling problem, specifically applied in a project environment. These first two parts will highlight and introduce the features of these problems which are valuable for the integrated problem. Section 1.1.3. then reviews the current available information on the integrated scheduling problem. This information allows the reader to better understand the environment of the recovery problem.

1.1.1 Project scheduling problem

In project management, project scheduling is a widely discussed topic. According to Brucker, Drexl, Möhring, Neumann, and Pesch (1999) project scheduling is concerned with single-item or small batch production where scarce resources must be met when scheduling dependent activities over time. The purpose of project scheduling is to construct a timetable to provide a start and an end date for each project activity while trying to reach a certain scheduling objective. This is done taking activity relations, resource constraints, and other project characteristics into account. The generated schedule should help project leaders with a determination of the expected cost and time of the project as well as for each individual activity (Vanhoucke, 2013). In order to construct a feasible baseline schedule, the definition of the network must be done. Project scheduling is therefore split in first a definition phase, followed by a scheduling phase (Vanhoucke, 2013). In this definition phase, information on the resource characteristics, the scheduling objective, and the activity characteristics is given (Herroelen, Demeulemeester, & De Reyck, 1999). This phase will be highlighted in section 1.1.1.1. The information of the definition phase is then used as input

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for the construction of the schedule, i.e. the scheduling phase, afterwards. More information on the scheduling phase is found in section 1.1.1.2.

1.1.1.1 Definition of the network

Constructing the network by incorporating the logical sequences between activities present in the project, is a first important step in building a baseline schedule (Vanhoucke, 2013). A common way for constructing the network, is by seeing the network as a set of arcs and nodes. The network is then graphically represented by a graph G (N, A) where the set N is used for the set of nodes and the set A is used to denote the set of arcs. In literature, there are two popular ways for displaying the network. The first one, called activity-on-the-arc (AoA), uses the arcs to represent the activities and the nodes denote the start and/or finish of the set of activities, whereas the second one, called activity-on-the-node (AoN), uses the arcs to denote the precedence relations and the nodes express the different activities. In Figure 1.1, a representation of both these universally known network representations is given. These representations are also commonly used to present the integrated scheduling problem.

Figure 1.1: A) AoA representation of link between activities i & j; B) AoN representation of link between activities i & j

Aside from the graphical representation of the network, the resource characteristics, scheduling objectives, and activity characteristics should also be defined in the definition of the network. These topics are discussed next as they are relevant in this dissertation for describing the baseline schedules.

1. Resource characteristics

An important factor that influences the definition of a network is the presence of limited project resources. When there is a limited availability of resources in a project, the problem type turns in to the well-known RCPSP (resource-constrained project scheduling problem). This basic type of project scheduling covers the wide variety of problems scheduling project activities subject to precedence and resource constraints (Herroelen et al., 1998). The resources constraining the problem may possess a varying set of characteristics, leading to different optimization procedures. Nudtasomboon and Randhawa (1997) describe three kinds of resources available, i.e. renewable, non-renewable, and doubly-constrained. When resources are renewable, the resources are constrained over a specific time period. Machines, personnel, and power are frequently used examples of renewable resources. Non-renewable resources are constrained over the

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resource. Next to these renewable and non-renewable resources, there also exist doubly-constrained resources, which comprise characteristics of the previous two types. These resources are constrained both at each time period as well as over the complete project duration. An example of this last type of resource is a total project budget with an extra constraint on the maximum amount spent per time period (OR-AS, n.d.).

2. Scheduling objectives

Another relevant feature of the RCPSP is the scheduling objective the construction of the timetable is aiming for. The possible objectives, which are often referred to as performance measures, are numerous and complex. A common classification of these performance measures is a split up between regular and nonregular measures of performance (Herroelen et al., 1999). The regular performance measures involve penalty functions which are nondecreasing in activity completion times (Conway, Maxwell, & Miller, 1967). Examples of criteria used in these regular performance measures are the minimization of the project duration or the minimization of project tardiness or lateness. In addition to the regular scheduling objectives, there are the nonregular objectives. In case of using a nonregular measure of performance, the performance measure may improve when delaying a project activity (Vanhoucke, 2013). Practical applications of these nonregular performance measures often introduce financial aspects of project management. The maximization of the net present value of a project characterized by arbitrary cashflow is a known example of a nonregular scheduling objective (Herroelen et al., 1999).

However, this classification is not exclusive. It is possible that there are several relevant objectives included at the same time. Here, a distinction must be made between a multicriteria case and a multi-objective case. In the latter case, different objectives are weighed or combined whereas in the former case the different measures are to be ranked according to criteria in order to specify in which order they should be considered (Vanhoucke, 2013).

3. Activity characteristics

A third relevant factor in project scheduling are the activity characteristics. This aspect of project scheduling is quite elaborate and can be described along several sub-components (Herroelen et al.,1999). The relevant activity characteristics of extensive classification system by Herroelen et al. (1999) will be pinpointed in the next few sections.

A first relevant component indicates if activity splitting is allowed or not. This characteristic is also known as the preemption of project activities. Activity splitting often results in two conditions, i.e. preempt-resume or preempt-repeat (Herroelen et al., 1999). In the preempt-resume case, the project allows an activity to be interrupted and resumed at a later point in time. When the project activities can be interrupted but must be completely redone, the project allows preemptions of the preempt-repeat type. This characteristic is

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extremely important when rescheduling projects after being disrupted. Therefore, it will also be further elaborated in section 1.3 of this chapter, which deals with project recovery.

The precedence relations and constraints present in a project are the second sub-component of activity characteristics that needs to be elaborated on. The relations or links between various activities incorporate logical sequences and are called “technological precedence relations” (Vanhoucke, 2013). These precedence relations available can be described according to their relation type, their time-lag, and their time-lag requirement. The default precedence relation type is the one called “Finish-Start” or “𝐹𝑆𝑖𝑗”, where

an activity j can only start after the finish of activity i. These precedence relations impose hard constraints for the project scheduling problem that must always be satisfied.

The third relevant activity characteristic is the duration of activities. Activities might have integer durations or continuous durations (Herroelen et al., 1999). These durations indicate the estimation on how much time is needed after the activity start to complete the activity. Only after this activity duration, the successors of the activity can be started.

The nature of resource requirements of the network activities is a fourth component of the activity characteristics. There is a distinction between having a constant discrete amount of resources required, where there several resources for every time period, and a variable discrete amount of resources required, where several units varies over the period of activity execution (Herroelen et al., 1999). The authors also indicate that there is a possibility that the activity resource requirements are determined in function of the activity duration.

The financial implications of the activities are a last sub-component of activity characteristics. There are several ways that the cash flows in a project can be specified. In one way, the cash flows are known and associated with certain activities or events, while another project may assume that cash flows happen periodic and occur at a regular time. Moreover, in other projects the timing and the amount of the cash flows still must be determined (Herroelen et al, 1999).

An overview of the five relevant components considered in this problem accompanied with a brief description is given in Table 1.1.

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ACTIVITY CHARACTERISTIC DESCRIPTION

1. Activity splitting Describes whether activity preemption is allowed or not. 2. Precedence constraints Informs about the logical sequences present in the project. 3. Duration Expresses whether the durations are integer or

continuous.

4. Resource requirements Points out how the activities request their resources. 5. Financial implications Describes how cash flows are specified in the project.

Table 1.1. Relevant activity characteristics

An important to note here is the fact that there is always a default setting to all these subcomponents of the activity characteristics. This implies that when there is nothing specified for a certain sub-component, this component is either absent, has a value equal to zero, or must be determined later on. Furthermore, the previous sections only highlight few relevant features of the definition of RCPSP. For a more extensive and detailed overview on RCPSP, I would like to refer to Icmeli, Erenguc, and Zappe (1993), Elmaghraby (1995), Özdamar and Ulusoy (1995), Herroelen et al. (1999), Brucker et al. (1999) and Hartmann and Briskorn (2010).

1.1.1.2 The project scheduling phase

The defined network from the previous phase is used as input to build a baseline schedule for the project (Vanhoucke, 2013). The wide set of characteristics of the scheduling problem leads to a broad collection of methods and models used to solve these problems. As the scope of the dissertation concerns problems where the execution of activities requires resources, more specifically human resources, a restriction to the scheduling problems called the resource constrained project scheduling problem is in place.

The field of RCPSP still covers a wide variety of problem types. According to Herroelen et al. (1998) a general formulation for the RCPSP is as follows:

𝑀𝑖𝑛 𝑓𝑛 (1)

subject to

𝑓1 = 0 (2)

𝑓𝑗− 𝑑𝑗 ≥ 𝑓𝑖 , ∀(𝑖, 𝑗) ∈ 𝐻 (3)

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where n is the total number of activities and 𝑑𝑖 is the fixed duration of activity i (1 ≤ 𝑖 ≤ 𝑛). The start time

of activity i is denoted by 𝑠𝑖 (1 ≤ 𝑖 ≤ 𝑛) and its finish time by 𝑓𝑖 (1 ≤ 𝑖 ≤ 𝑛). There are K renewable

resource types and each activity i has a constant resource requirement 𝑟𝑖𝑘 (1 ≤ 𝑖 ≤ 𝑛, 1 ≤ 𝑘 ≤ 𝐾) of

resource type k. Each resource type k has a constant availability of 𝑎𝑘 . Moreover, H denotes the set of pairs

of activities indicating precedence constraints and 𝑆𝑡 denotes the set of activities in progress in the interval

]𝑡 − 1, 𝑡] ∶ 𝑆𝑡 = {𝑖|𝑓𝑖− 𝑑𝑖< 𝑡 ≤ 𝑓𝑖}. Equation (2) assigns a completion time of 0 to the dummy start

activity 1. The precedence constraints given by equation (3) indicate that activity j can only be started if al predecessor activities i are completed. Resource constraints (4) indicate that for each time period ]𝑡 − 1, 𝑡] and for each resource type k, the renewable amounts required by the activities in progress cannot exceed the resource availability. The objective function of minimizing the project duration is given by equation (1). This minimization of the project lead time is often the most important objective of the problem (Vanhoucke, 2013).

Even though the RCPSP model as given above is powerful, unfortunately it cannot cover all the applications relevant. Over the past decades, more general project scheduling problems, using the RCPSP as a starting point, have been developed (Hartmann & Briskorn, 2010). As the purpose of this dissertation does not focus solely on the project scheduling problem, I would like to refer the interested reader to Hartmann and Briskorn (2010) for a first-rate survey of these generalizations of the variants and extensions of this model available in modern literature.

For the actual solution methods available for the RCPSP, it must be noted that the RCPSP is recognized as a NP-hard problem in the strong sense (Blazewicz, Lenstra & Rinnooy Ka, 1983). This well-known problem has attracted numerous researchers who developed a solution procedure for the problem. The solution methods found in literature are divided into two categories, either (meta)heuristic solution techniques or exact solution techniques. For exact solution techniques, numerical implicit methods such as dynamic programming and the branch-and-bound method are frequently used. These exact solutions aim for finding an optimal solution to the problem but are less suitable for larger problems. Heuristic solution procedures of the RCPSP are more applicable to larger problems. They are aiming to find a good, although not optimal solution to the problem. According to Vásquez, Calvo, and Ordóñez (2013), the heuristics can be split up in four different categories: priority-rule-based heuristics, standard heuristics, non-standard meta-heuristics, and miscellaneous heuristics. Going more into detail on the solution techniques is out of the scope of this dissertation.

1.1.2 Personnel scheduling problem

Another important scheduling problem related to the integrated problem is the personnel scheduling problem. The general purpose of personnel scheduling, or rostering, is to construct a work timetable for the

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staff such that an organization can satisfy the demand for its goods and/or services (Ernst, Jiang, Krishnamoorthy, Owens, & Sier, 2004a). Like the project scheduling problem, the personnel scheduling problem has been broadly studied and analyzed in various contexts and industries. The problem gained a lot of attention due to economic reasons, as the labor cost is a major direct cost component for many companies and accounting for 30-50% of the total project cost (Adrian, 1987; Larson & Gray, 2011). In recent years, Van den Bergh et al. (2013) indicate also the growing importance of employee satisfaction on top of the personnel efficiency while rostering. An overview of the different problem types and the models to solve the personnel scheduling problem is presented in both Ernst et al. (2004a) and Van den Bergh et al. (2013).

When dealing with the personnel scheduling, a popular taxonomy considers the differentiation between strategic, tactical, and operational approaches. First of all, strategic, or long-term, approaches are also specified as the planning or staffing phase of personnel scheduling. Here, the organization needs to decide on a long-term sustainable plan and budget to address any staffing concerns (Gaines, 2018). Secondly, tactical, or mid-term, scheduling concerns with the construction of the baseline personnel schedule given the decisions made in the strategic phase. This phase is often referred to as the scheduling phase. Constructing a baseline schedule typically spans the horizon of one month. Finally, the operational approach deals with last-minute schedule changes within the short timeframe varying between several hours up to several days (Zeltyn et al., 2011). This third phase is also called the allocation phase of personnel scheduling (Ingels & Maenhout, 2017). In this operational allocation phase, accurate information on the state of the personnel schedule is needed to decide on the actual allocation of staff. As this section of the first chapter deals with the construction of the baseline schedule as well as deciding on the characteristics of the staffing plan, a combination of the details on the strategic and tactical approaches are discussed. The operational approaches are further elaborated in section 1.3 of this first chapter of the dissertation.

In this dissertation, personnel scheduling is reviewed in the context where a project needs to be staffed. According to the rostering classification of Ernst, Jiang, Krishnamoorthy, and Sier (2004b), the project personnel scheduling problem would be identified as a combination of task-based demand rostering and the days-off rostering problem. The personnel rostering is considered as task-based demand rostering, on the one hand, as the personnel requirements are obtained from a list of tasks (project activities), where these tasks are defined with a specific earliest start and finish time and a duration. Personnel rostering is also considered as days-off rostering, on the other hand, where the days-off of the project workers need to be determined over the project horizon. For the determination of these days-on and days-off for the project workers, the distinction between cyclical and non-cyclical scheduling is noteworthy. Cyclical scheduling is less flexible as regular workers are assigned to a fixed line of work that is repeated over time with different possible start times (Maenhout & Vanhoucke, 2017). Non-cyclical scheduling is more flexible as the lines-of-work performed by the regular workers are independent of each other. In non-cyclical scheduling in a

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project environment, lines-of-work are defined over the complete project horizon. The composition of these independent lines is defined by the time-related constraints such as the maximum number of assignments, maximum number of consecutive days-on/days-off, etc. which are further discussed in section 1.1.2.1.

Therefore, in the following paragraphs, firstly the valuable characteristics of the personnel scheduling problem in the context of project personnel scheduling are highlighted. The definition of these characteristics can be compared with the “definition phase” in the project scheduling problem. The information on these characteristics is found in section 1.1.2.1. Afterwards an introduction to the personnel scheduling techniques and solution methods for this complex problem is presented in section 1.1.2.2. Again, this may be considered as the actual “scheduling phase” of this problem type.

1.1.2.1 Characteristics

Comparable to the project scheduling problem, there is a wide set of options available which make the personnel scheduling problem very diverse. Conforming to Van den Bergh et al. (2013), there are four different classification fields of these problems; (1) the personnel characteristics, decision delineation and shifts definition, (2) constraints, performance measures and flexibility, (3) solution method and uncertainty incorporation and (4) application area and applicability of research. Of these four classification fields, only the personnel characteristics, the types of constraints, and performance measures are reviewed here as these are the aspects to be when both constructing the baseline schedules subject to schedule disruptions and recovering from schedule disruptions.

1. Personnel characteristics

The first relevant characteristic of the personnel scheduling problem is the classification of personnel members. A way to classify personnel members is to look at their labor contract. Personnel members can be regular workers or hired temporary workers. When dealing with regular workers, there is also the distinction between full-time and part-time workers (Van den Bergh et al., 2013). A second characteristic of the personnel is the heterogeneity of the personnel members. When scheduling a heterogeneous workforce, then each member possesses a set of specific skills. These skills, in return, are needed to perform certain tasks available in the project. A third characteristic of the personnel is the allowance of grouping the employees or not (Van den Bergh et al., 2013). Some problems require scheduling of a crew (or team) instead of considering each employee separately (Van den Bergh et al., 2013). These three ways of classifying personnel are crucial elements to be specified when defining the integrated problem and defining the acceptable recoveries.

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2. Constraints

A second classification field of the personnel scheduling problem are the constraints identified in the problem. The personnel scheduling problem covers a broad set of constraints, which are entailed in the next paragraph. All these constraints make this an over-constrained problem. In the set of constraints, there is the need for a distinction between hard and soft constraints. Blöchliger (2004) defines hard constraints as constraints that can never be violated. Soft constraints, on the other hand, can be violated and the solution may be still acceptable (Blöchliger, 2004). However, a range of acceptable values and an optimal value needs to be defined for a soft constraint (Blöchliger, 2004). A common way to manage these soft constraints in the personnel scheduling problem is to associate a penalty function with each soft constraint (Blöchliger, 2004). This penalty function increases with the degree of constraint violation.

In addition to the distinction between hard and soft constraints, the constraints in the personnel scheduling problem can also be classified according to their type. Van den Bergh et al. (2013) classify the constraints in three different categories. The categories introduced are coverage, time-related, and fairness and balance constraints. Under the coverage constraints, the problem specifies towards which degree understaffing and/or overstaffing is allowed. Moreover, constraints to ensure the presence of a certain skill are also included in the category of coverage constraints (Van den Bergh et al.,2013). Coverage constraints are vertical constraints and are often considered as hard constraints available in personnel rostering. Time-related constraints, as a second category, originates from Brucker, Burke, Curtois, Qu, and Berghe (2010). Popular time-related constraints used in literature are the maximum or minimum number of assignments allowed, the maximum number hours and overtime, the maximum or minimum of consecutive days off, the number of shifts/days on and off, and the time between assignments (Van den Bergh et al., 2013). In the third category of balance and fairness constraints, operators want to create fairness in the work environment by incorporating constraints to balance the dissimilarities of workers over the time-related constraints (Van den Bergh et al., 2013). Often personnel members are also allowed to indicated preferences according to working a specific day or a specific shift. The comparison of the deviation from the preferences can also be incorporated as a balance of fairness constraint.

All the constraints of either one of the three types, i.e. coverage, time-related, and fairness, can be considered and defined as a hard or a soft constraint. Variation along the different personnel rostering problems exist due to whether the different types of constraints or incorporated or not, and if they are either a hard or soft a personnel constraint.

3. Performance measures

The last classification field is the target of the personnel scheduling problem. This is defined as the objective or the performance measure of the problem. This objective is also specified as the performance measure of the scheduling problem. As there are multiple stakeholders involved, multiple objectives are available.

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Accordingly, the personnel scheduling problem might have several relevant categories of performance measures. A first category of rostering objectives is maximizing efficient and effective staffing. In this category, the scheduler might want to minimize the understaffing, minimize the overstaffing, level the understaffing deficits, and overstaffing surpluses or do a combination of them. The minimization of personnel cost or minimization of number of employees is also covered by this category. Another category of rostering objectives includes maximizing job satisfaction level of employees. In this case job preferences, fairness and healthy work patterns for the employees are optimized when scheduling these human resources. It is noteworthy that due to the variety of stakeholders, each with his own priorities, the case of a multi-objective model for the personnel scheduling problem is frequently appearing in literature (Van den Bergh et al., 2013).

An overview of the relevant personnel scheduling characteristics considered in this dissertation accompanied with a short description on their specifications is given in Table 1.2.

PERSONNEL SCHEDULING

CHARACTERISTICS DESCRIPTION

1. Characteristics of the member - Heterogenous vs. homogenous - Incorporation of skills

- Personal or crew scheduling

2. Typical constraints - Coverage constraints

- Time-related constraints - Balance and fairness constraints

3. Objective - Maximization of the schedule efficiency vs.

maximization of the job satisfaction vs. multi-objectives

Table 1.2: Personnel scheduling characteristics

1.1.2.2 The personnel scheduling techniques

Once the characteristics of the personnel scheduling problem are clear, the personnel members need to be scheduled given the prespecified set of hard and soft constraints in order to optimize the given performance measure of the problem. As the set of different rostering problem types is very diverse, solution techniques are varying and tailored to the different problem types and context of the problem.

According to Van den Bergh et al. (2013), the solution approaches to the rostering problem are classified in six categories. Mathematical programming is the first category. In this category, all methods including either linear programming, goal programming, integer programming, mixed integer programming, column

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generation, branch-and-price, dynamic programming, or Lagrange relaxation are classified. The second category of solution methods are the metaheuristics. Metaheuristics are useful when the problem type becomes too complex which makes exact methods often inefficient or ineffective. Popular metaheuristics to solve the rostering problem are tabu search algorithms, genetic algorithms, and simulating annealing algorithms. Next to these categories, simulation is another frequently returning solution technique. These methods help researchers in validating their deterministic approaches or identifying the labor demand. Monte Carlo simulation is a popular simulation method used. However, practitioners prefer the use of discrete event simulation over Monte Carlo for rostering. The fourth category are solution methods based on constraint programming. Because the large set of constraints available in the problem, constraint programming is a useful solution technique. Queuing methods are the next category in Van den Bergh et al. (2013). Usually when applied, these approaches estimate the staffing demands and are combined with IP models to identify the actual staffing plan afterwards. The last category in Van den Bergh et al. (2013) is identified as “other”. Like the combination of queuing and mathematical programming, other combinations of different categories are possible to offer the most desirable solution to the problem.

Further elaborating on how these techniques work in practice is however out of scope for this dissertation. I refer the interested reader to Van den Bergh et al. (2013) for an overview of the research according to the different techniques applied to the personnel scheduling problem.

1.1.3 Integrated scheduling problem

Defining these two scheduling problems separately, ignores that these two problems are often related and need to be scheduled around the same pool of human resources. When both the project and personnel scheduling problems occur in a project, it is quite common to do this sequentially to decompose the complexity of the problem. First of all, the project schedule is constructed. The scheduled activity start dates and their durations determine the daily labor-demand profile. This serves as an input for the personnel scheduling that is done in a second phase. However, as mentioned in the introduction, Alfares and Bailey (1997) indicate that this traditional two-step approach leads to sub-optimal performance. Integration of the two problems could increase the overall performance of the system. An overview of the existing literature on this integration is therefore given in the following sections. This overview helps the reader to understand the baseline problems’ environment that is subject to project disruption better. However, as both the project and the personnel scheduling problem consist of a lot of constraints to be respected, integration has several forms depending on the constraints integrated. Hence, it is important that, in order to solve this integrated scheduling problem, first the characteristics of both problems need to be defined. Both the activity and project characteristics as well as personnel staffing characteristics are required.

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The articles that contribute to the definition and solution of the integrated scheduling problem will be reviewed hereafter. In this dissertation, the articles that both schedule the project activities and construct an employee roster integrated are more relevant as these include the characteristics that also define the environment of the problem subject to uncertainty in this research. These articles will be reviewed more thoroughly in section 1.1.3.1. In section 1.1.3.2. a short overview of the literature on the dealing with project scheduling and staff assignment is given as is a related problem.

1.1.3.1 Integrated project and staff scheduling

Alfares and Bailey (1997) pioneered by trying to solve both project and personnel scheduling in one phase. In the problem formulation, the authors include several constraints to ensure that each project activity needs to be started and can only start after the finish of all its immediate predecessors. Next, the coverage constraint of the personnel scheduling problem is also present, and overstaffing is allowed as long as the total size of the workforce in any given week does not exceed a predefined limit. In their paper, an integer linear programming optimization procedure for solving the integration of these two scheduling problems is presented. However, their ILP optimization procedure for the integrated problem becomes large and complex when looking at more realistic problems. This resulted in the introduction of a heuristic approach based on dynamic programming. Both the ILP and the heuristic approach aim for minimizing the project duration and personnel staffing costs. In their integrated problem, they schedule a homogenous workforce, without a specific skill set, to a feasible fixed days-off tour. Hence, personnel scheduling is done cyclical. In a next research paper, Alfares, Bailey, and Lin (1999) extended this problem formulation, by including the personnel characteristic of skill. The workforce is heterogenous as project activities may require several labour skills for its executions. They present an ILP model for the integrated multiple-resource scheduling (IMRS) problem (Alfares et al.,1999). This is a similar problem but with multiple types of workers needed to execute the project.

Integration of the two scheduling problems in a project environment is extended by Maenhout and Vanhoucke (2016). In their problem formulation, both staffing and scheduling of the activities of a single project is integrated. Compared to Alfares and Bailey (1997), Maenhout and Vanhoucke (2016) allow for more personnel flexibility as the personnel roster is constructed in a non-cyclical way. Moreover, they allow for scheduling regular personnel time units, overtime units, and temporal personnel time units. Similar to Alfares and Bailey (1997), the objective is to minimize both the project duration as well as the fixed and variable costs of personnel resources. The problem under study is solved to optimality using an integer programming column generation procedure, i.e. branch-and-price. In Maenhout and Vanhoucke (2017), the effect on the personnel cost of incorporation of the non-cyclical way of personnel scheduling as well as allowing for flexible personnel resources is proven to be beneficial.

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In Van Den Eeckhout, Maenhout, and Vanhoucke (2019), the integration is further extended by improving the resource demand flexibility of the project activities. The authors integrate the discrete resource/time trade-off in their problem formulation by allowing the project activities to be performed in multiple modes (Van Den Eeckhout et al., 2019). These alternative execution modes of the project activities increase project scheduling flexibility to decrease the overall staffing budget. Similar to the problem type of Maenhout and Vanhoucke (2016), both regular personnel units and temporary personnel units are available. The objective of their formulation is to minimize the total personnel cost needed to carry out the project as the problem under study is a budgeting problem (Van Den Eeckhout et al., 2019). To solve this integrated multi-mode project and personnel staffing problem, a heuristic solution procedure is proposed. In Van Den Eeckhout, Vanhoucke, and Maenhout (2020), this defined problem is further investigated. An exact procedure, i.e. a decomposed branch-and-price procedure that outperforms the existing approaches to solve this problem type, is formulated.

The models and approaches highlighted above incorporate time-related calendar constraints on the personnel side as well as schedule the activity start times. This type of integration is relevant in this dissertation and will be used to conduct further research. However, when discussing and analyzing the integration of project scheduling and personnel scheduling, there are several related problems.

1.1.3.2 Integrated project scheduling and staff assignment

Another popular form of integration of the two problems is where the availabilities of the human resources are known. Here, integration is specified as scheduling a project combined with the assignment of resources to the project activities. Vairaktarakis (2003) define this problem as ‘the resource-constrained job assignment problem (RCJAP)’. This problem has been extended several times. Wu and Sun (2006) define in their problem formulation also the presence of learning effects, where efficiency of staff will improve by doing more tasks. Bellenguez-Morineau and Néron (2007) include a multi-skilled labor force, where the project activities to be scheduled need different skills and the personnel resources have more than one skill. Therefore, skill demand of project activities must be matched with skill availabilities. In Drezet and Billaut (2008), the resource requirements of the activities are time dependent. Moreover, they enhance the problem as the legal constraint of a maximum number of employee assignments is imposed. Valls, Pérez, and Quintanilla (2009) design also a modified version of the job assignment problem; ‘the Skilled Workforce Project Scheduling Problem’. This problem includes extensions such as variable activity duration depending on the assigned worker, as well as activity critically levels and maximum dates. In their problem, a heterogenous workforce is also assumed. Tiwari, Patterson, and Mabert (2009) incorporate also the heterogeneity of the workforce but enlarges the problem with the incorporation of the quality aspect of project activities. Moreover, the job assignment needs to be done for multiple projects scheduled around the same pool of resources. Walter and Zimmermann (2010) discuss the project in the context where employees of a company need to be assigned to projects, apart from their operational work. The authors try

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to minimize the individual project assignment of the employees again in a multi-project environment, where the set of projects to be executed is already defined. Heimerl and Kolisch (2010) also contribute to this problem by proposing a mixed integer problem formulation for the assignment problem of a multi-skilled internal workforce as well as considering the availability of external workforce resources. In the different versions of the problem type, the optimization procedures used vary from meta-heuristics to exact procedures to solve the different problems. A last paper is this short summation, is the one of Fernandez-Viagas and Framinan (2014). First, the authors properly sum the relevant articles dealing with this integrated assignment problem. Afterwards, they contribute to the problem by inclusion of controllable processing times where there exists a piece-wise linear relationship between the processing times of the activities and the amount of resources allocated.

A short introduction on the related integrated problem of RCJAP has been drawn in this section. The job assignment problem is not further discussed here as it deviates from the dissertations’ focus. Nevertheless, this does not imply this problem is generally irrelevant and that the type of integration described in section 1.1.3.1. is the only type of integration discussed in literature.

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1.2 Uncertainty

In the previous section, the goal was to construct a precedence feasible project plan where project activity start times as well as the personnel roster needed to be defined. This initial scheduling phase relies on the assumption that all estimated parameters are correct and known in advance. However, this assumption is unrealistic given the fact that forecasts are always wrong. During the execution, the project and personnel schedule are subject to a considerable amount of uncertainty (Herroelen & Leus, 2005). The quote starting this second section (Retrieved from Badiru , 2014, p.97) of the first chapter indicates that the original planned and forecasted project and personnel parameter rarely hold. Perminova, Gustafsson, and Wikström (2008) define a general understanding of what project and personnel uncertainty exactly is. They define project uncertainty as: “an event or a situation, which was not expected to happen, regardless of whether it could have been possible to consider it in advance”. Atkinson et al. (2006) indicate that the presence of project uncertainty is frequently recognized as a central issue. Moreover, they highlight that the sources of project variability are wide-ranging and project uncertainty can take various forms. Recognizing this full range of variability sources is beneficial for the project manager (Atkinson et al., 2006).

This section will follow the categorization of Van den Bergh et al. (2013), who classified uncertainty along three sources of operational variability i.e. uncertainty of arrival, uncertainty of capacity and uncertainty of demand. These are further explained below to allow the reader to become more familiar with the different possible disruption scenarios that could occur in a project with human resources. Moreover, the goal of this dissertation, i.e. identifying the efficiency of the different recovery strategies, will also be analyzed according to these three sources of operational variability. Therefore, the remainder of this second section of the first chapter will elaborate on the different sources of uncertainty.

1.2.1 Uncertainty of arrival

The first source of operational variability is the uncertainty of arrival. Van den Bergh et al. (2013) define uncertainty of arrival as the unpredictable arrival pattern of the workload. When this type of uncertainty is translated to a project and personnel scheduling environment, uncertainty of arrival always stems from the project side of the problem. Generally, the uncertainty of arrival impacts the duration, the start time and/or the finish time of the project activities. For example, when more detailed information on the project is available, the actual duration of the activities might not be accurate. Activity duration might increase, or

“No major project is ever installed on time, within budget, with the same staff

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the activity might finish earlier on. Another frequently used example of the uncertainty of arrival is where the number of project activities to be performed differs.

1.2.2 Uncertainty of capacity

Uncertainty of capacity is a second source of operational variability. Uncertainty of capacity is defined as “the deviations between the planned and the actual manpower” in Van den Bergh et al. (2013). Sources such as sick leave, absenteeism, or holidays contribute to this variability of the supply of resources. The uncertainty of capacity thus stems from the personnel side of the problem. The unavailability of scheduled resources results in a disruption of both the personnel schedule and the project schedule. The project schedule disrupts as the activity demanding the unavailable resource is now unable to be started or to be further executed. The unexpected change in resources availabilities has been cited by various authors as one of the most practical relevant disruptions in project management (Lambrechts, Demeulemeester & Herroelen, 2011).

1.2.3 Uncertainty of demand

The last source of operational variability is the uncertainty of demand. “The unpredictable workload” is the definition of this last source (Van den Bergh et al., 2013). This type of uncertainty indicates that the actual staffing scheduled on a specific day or shift differ from the required demand for the resource. An increase or decrease in the activity demand for this human resource is a clear example of this uncertainty. Maenhout and Vanhoucke (2018) indicate two different scenarios that might disrupt a baseline schedule. First, the resulting demand might be smaller than expected due to the removal of subtasks needed for a certain project activity. In the second scenario, the resulting demand exceeds the expected demand. The resulting demand can exceed the expected demand due to, on the one hand, a project activity might imply more subtasks than originally determined and, on the other hand, the project activity might need more personnel resources to execute the original set of tasks.

The practical details on how these three sources of operational variability are translated into specific disruptions of the baseline schedules are given in the research methodology and test design section of this dissertation. Next, in section 1.3 of this first chapter, an elaborate overview on how to deal and recover from these disruptions is given.

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1.3 Recovery strategies

As projects are executed in dynamic environments, baseline schedules are subject to a considerable amount of uncertainty. As mentioned in section 1.2, this uncertainty might lead to different possible disrupted situations. An appropriate and general definition of such a disrupted situation can be found in Clausen, Larsen, Larsen, and Hansen (2001). Clausen et al. (2001) define a disrupted situation or a disruption as “the state during the execution of the current operation, where the deviation from the original schedule is sufficiently large that the schedule must be changed”. As the quote by Publilius Syrus (n.d.) illustrates, having a recovery action at hand to deal with this uncertainty is necessary. This third section of the first chapter will deal with how your schedule can be changed and repaired once disrupted.

Handling these disruptions by repairing the project schedule might show similarities with the original problem of constructing a baseline schedule but there are also significant differences (Zhu, Bard & Yu, 2005). First, in the rescheduling problem, there is the important tradeoff between making proper decisions and speeding up the recovery process to avoid further difficulties (Zhu et al., 2005). Being able to react quickly in a cost-effective manner is a first objective of project rescheduling. Another additional aspect to consider when repairing your schedule, is that you might want to stay as close as possible to the original baseline schedule. Too large deviations might lead to failure of the project when full account is made of the deviation costs (Zhu et al., 2005). Moreover, these deviations often come along with undesirable side-effects such as having to change agreements with subcontractors, dealing with malcontent employees, etc. (Deblaere, Demeulemeester & Herroelen, 2011). As a result, the rescheduling problem becomes a multi-objective problem.

Generally, there exists a broad set of approaches on how to deal with this multi-objective problem. The reactive scheduling methods relevant in this dissertation are only the subset of these approaches. Therefore, to gain some understanding on the different ways of how project rescheduling is addressed in literature, the classification framework of Vieira et al. (2003) is presented first in section 1.3.1. After the general overview of project rescheduling methods, strategies, and policies, more details on the specific rescheduling methods to repair the disrupted schedule are given. Section 1.3.2 thoroughly reviews the recovery mechanisms that deal with the project rescheduling methods, whereas section 1.3.3 lists the personnel recovery mechanisms. This gives insights in all the possible recovery options available and allows to better understand the recovery methods analyzed in this dissertation.

“It’s a bad plan that admits of no modification.” - Publilius Syrus

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1.3.1 Rescheduling framework

Vieira et al. (2003) and Aytug et al. (2005) were the first to provide a classification of the rescheduling strategies, methods, and policies. As these reviews are somewhat similar and the visual framework of Vieira et al. (2003) is easy to follow, this framework will be used to structure this section. Relevant differences between these classifications will be mentioned where necessary.

The rescheduling framework of Vieira et al. (2003) includes three key elements to describe a rescheduling approach, i.e. the rescheduling environment, the rescheduling strategy, and the rescheduling methods. Section 1.3.1.1. elaborates on the first element, the rescheduling environment of the framework. Section 1.3.1.2. entails the rescheduling strategy and in section 1.3.1.3. the scheduling methods are discussed. A quick description, according to this framework, on how rescheduling approached in this dissertation is presented afterwards in section 1.3.1.4.

1.3.1.1 Rescheduling environments

The first element in the framework is the rescheduling environment, where the distinction is made between static and dynamic rescheduling environments. In a static environment, only one specific moment in time is considered for scheduling. Vieira et al. (2003) compare this to a project environment where the project horizon is fixed and as such, the number of activities or jobs to be scheduled is also known. A dynamic environment on the other hand sets no time constraint on the project horizon and project tasks continue to arrive during this infinite horizon. Therefore, in a dynamic project environment, there is an infinite set of jobs to be scheduled and specification details on variability of job arrival need to be estimated too. As this dissertation handles with the disruption of projects with a fixed horizon, only static rescheduling environments are relevant. Nevertheless, according to Vieira et al. (2003), a static project environment can be further specified by distinguishing between deterministic and stochastic static environments. As a deterministic environment assumes no uncertainty about the future, it is clear a stochastic static environment is a more appropriate description of the environment of the projects in this dissertation.

1.3.1.2 Rescheduling strategy

The second element present in the framework are the rescheduling strategies. According to Vieira et al. (2003), a rescheduling strategy identifies if schedules are generated before schedule execution or not. In the framework the distinction between two basic types of rescheduling strategies is made i.e. dynamic scheduling and predictive-reactive scheduling. Dynamic scheduling does not create schedules but dispatches jobs using the information currently available such that a complete schedule is never generated. Therefore, in a dynamic rescheduling strategy, there is the need for dispatching rules or other selection