Robust and reactive project scheduling: a review and classification of procedures

1
Robust and reactive project scheduling a review
and classification of procedures

• By W. Herroelen and R. Leus
• Presented by Safa Onur Bingöl

2
Agenda

• Introduction
• Deterministic baseline scheduling
• Generating predictive and reactive project
  Schedules
• Different approaches to multi-project scheduling
  problem
• Conclusion

3
Introduction

• Research in project scheduling has concentrated
  on the generation of a workable baseline schedule
  (pre-schedule, predictive schedule) assuming a
  deterministic environment and complete
  information
• Activities are scheduled subject to precedence
  constraints and resource constraints
• Under regular objectives or non-regular objectives

4
Introduction

• Baseline schedule serves very important
  functions
• 1. Allocate resources to different activities to
  optimize some measure of performance
• 2. Basis for planning external activities
• 3. Vital for cash flow projections and provides
  a yardstick to measure the management and
  personnel performance
• Reliable baseline schedules enable organizations
  to estimate project completion times and take
  corrective action when needed

5
Introduction

• Visibility of future actions is of crucial
  importance within the inbound and outbound supply
  chain
• In multi-project environments, a schedule needs
  to be sought before the start of the project with
  all involved parties
• May be necessary to agree on a time window for
  work to be done by subcontractors
• Organize production resources to best support
  smooth schedule execution

6
Introduction

• During execution, project is subject to
  considerable uncertainty such as
• Activities may take more or less time than
  estimated
• Unavailable Resources
• Late material supplies
• Modified due dates
• New activities may have to be incorporated
• Existing activities may have to be abandoned
• Recognition of uncertainty induce a number of new
  research efforts

7
Introduction

• A proactive baseline schedule that is protected
  as well as possible against anticipated schedule
  disruptions
• Reactive scheduling revises or re-optimizes the
  baseline schedule when unexpected events occur
• Predictive-reactive scheduling denote the case of
  a predictive baseline schedule that is developed
  prior to the start of the project and may be
  updated during the execution phase
• This paper aims to review the procedures for
  proactive and reactive project scheduling

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Deterministic Baseline Scheduling

• Focuses on the development of a workable schedule
  that defines the scheduled start times of the
  project activities, satisfies both the precedence
  constraints and the resource constraints and
  optimizes the scheduling objective

9
Deterministic Baseline Scheduling

• Objective is to minimize the project duration
  subject to the precedence constraints and the
  resource constraints for the single-renewable
  resource with availability of 10 units
• Minimum Duration Schedule

10
Deterministic Baseline Scheduling

• A critical sequence is a sequence of precedence
  and / or resource related activities that
  determines the duration of the corresponding
  schedule
• Minimum duration schedule shows a quite a number
  of critical sequences such as lt1,5,3,6,2,10gt,
  lt1,5,3,6,9,10gt, lt1,4,7,8,9,10gt etc.

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Deterministic Baseline Scheduling

• Minimum duration schedule may be optimal for a
  deterministic project setting, but it is
  vulnerable to uncertainty
• This schedule has insufficient flexibility for
  dealing with unexpected events in other words it
  is not robust
• Lack of robustness reveals itself as both a lack
  of stability and of quality

12
Deterministic Baseline Scheduling

• Stability or solution robustness refers to the
  insensitivity of activity start times to changes
  in the input data
• Quality robustness refers to the insensitivity of
  schedule performance in terms of objective value
• Robustness is closely related to flexibility
• A schedule is called flexible if it can be easily
  repaired, i.e. changed into a new high quality
  schedule

13
Generating Predictive and Reactive Project
Schedules

• Table 1 lists various methodologies for baseline
  schedule generation and reactive scheduling

14
Generating Predictive and Reactive Project
Schedules

• Dynamic scheduling using scheduling policies
• When no baseline schedule is generated
• Full dynamic scheduling procedure is used during
  project execution to decide which activity to
  start as time evolves
• Stochastic project scheduling views the problem
  of scheduling projects as a multi-stage decision
  process
• Scheduling decisions are made dynamically at
  stochastic decision points based on the observed
  data and a priori knowledge about activity
  processing time distributions

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Generating Predictive and Reactive Project
Schedules

• Common objective is to create a policy that
  minimizes the expected project duration over a
  class of policies (Igelmund and Radermacher 1983
  a, b)
• Fernandez (1995), Fernandez et al. (1996) show
  how to write the corresponding optimization
  problem in its general form as a multi-stage
  stochastic programming problem
• Branch and bound algorithms to compute optimal
  policies have been developed by Stork (2001)
• Heuristic procedures for solving the stochastic
  resource constrained project scheduling problem
  has been developed by Pet-Edwards (1996)

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Generating Predictive and Reactive Project
Schedules

• Generation of a baseline schedule
• No anticipation of variability
• Common practice in project scheduling is that
  generation of a baseline schedule before the
  start of the project
• Deterministic project scheduling procedure can be
  used without any anticipation of variability
• Single point estimates are used to produce
  deterministic values for parameters such as
  activity duration
• The objective is directly related to
  deterministic project performance
• This is the field of deterministic
  resource-constrained project scheduling

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Generating Predictive and Reactive Project
Schedules

• Proactive (robust) baseline scheduling
• Development of a baseline schedule that
  incorporates a degree of variability during
  project execution
• Basic idea is to build protection into
  pre-schedule

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Generating Predictive and Reactive Project
Schedules

• Critical chain scheduling / buffer management
  (CC/BM)
• The direct application of theory of constraints
  (TOC) to project management (Goldratt 1997)

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Generating Predictive and Reactive Project
Schedules

• CC/BM builds a baseline schedule using aggressive
  median or average activity duration estimates
• To minimize WIP, a precedence feasible schedule
  is constructed by scheduling activities at their
  latest start times based on critical path
  calculations
• If resource conflicts occur, activities are moved
  earlier in time
• If there is more than one critical chain,
  arbitrary choice is made

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Generating Predictive and Reactive Project
Schedules

• The safety in the durations of the critical chain
  activities is shifted to the end of the critical
  chain in the form of a project buffer (PB)
• Project buffer protects the project due date from
  variability in critical chain activities
• Feeding buffers (FB) are inserted whenever a
  non-critical activity joins the critical chain
• Feeding buffers protect the critical chain from
  disruptions on the activities feeding it and to
  allow critical chain activities to start early

21
Generating Predictive and Reactive Project
Schedules

• Default procedure is to use the 50 buffer sizing
  rule
• Use a project buffer of half of the project
  duration
• Use a feeding buffer of half of the duration of
  longest non-critical path leading into it
• Resource buffers (RB) are placed whenever a
  resource has to perform an activity on the
  critical chain and the previous critical chain
  activity is done by a different resource

22
Generating Predictive and Reactive Project
Schedules
23
Generating Predictive and Reactive Project
Schedules

• CC/BM approach does not rely on the buffered
  schedule but on so called projected schedule
• Projected schedule is precedence and resource
  feasible, contains no buffers
• Gating tasks (activities with dummy predecessors)
  start at their scheduled time in the buffered
  schedule
• Other tasks are started as soon as possible

24
Generating Predictive and Reactive Project
Schedules
25
Generating Predictive and Reactive Project
Schedules

• Projected schedule is recomputed when distortions
  occur
• This schedule is not a stable schedule
• Herroelen and Leus (2001) validated the working
  principles of CC/BM through a computational
  experiment and they reach the conclusion that
• (a) Updating the baseline schedule and the
  critical chain at each decision point yields the
  smallest project duration
• (b) Using a clever project scheduling mechanism
  such as branch and bound has a beneficial effect
  on the final makespan

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Generating Predictive and Reactive Project
Schedules

• (c) Using the 50 rule for buffer sizing may
  lead to a serious overestimation of the project
  buffer size
• (d) Beneficial effect of computing the buffer
  sizes using the root-square-error method
  increases with problem size
• (e) Keeping the critical chain activities in
  series is harmful to the final project makespan
• (f) Recomputing the baseline schedule at each
  decision point has a strong beneficial impact on
  the final project duration

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Generating Predictive and Reactive Project
Schedules

• In a multi-project environment, CC/BM relies on
  the common steps of TOC, applied as follows
• Prioritize the organizations projects
• Plan the individual projects according to the
  CC/BM fundamentals
• Stagger the projects
• Insert drum buffers
• Measure and report the buffers
• Manage the buffers

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Generating Predictive and Reactive Project
Schedules

• Robust precedence feasible schedules
• 1. Solution robust schedules in the absence of
  resource constraints
• Herroelen and Leus (2003b) develop mathematical
  programming models for the generation of stable
  baseline schedules under the assumption that
  proper amount of resources can be acquired if
  booked in advance and that a single activity
  disruption may occur during the schedule execution

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Generating Predictive and Reactive Project
Schedules

• They use expected weighted deviation of the start
  times as a stability measure
• They derive a LP model, dual of which corresponds
  to a minimum cost network flow problem, which can
  be solved efficiently
• The procedure can be applied to the project
  network in the paper assuming following
  parameters
• Project deadline of 14 periods (set equal to
  CC/BM project length)
• Equal disruption probabilities for the activities
• There is a 50 chance of both its duration is
  increased by 1 period or 2 periods

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Generating Predictive and Reactive Project
Schedules

• Resulting proactive reactive schedule is solution
  robust to the described disruption setting

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Generating Predictive and Reactive Project
Schedules

• A stable schedule attempts to spread out
  activities across the scheduling horizon such
  that small disruptions in activity durations are
  smoothed out and do not propagate through the
  network
• Objective function value of CC/BM based projected
  schedule will be at least twice of robust
  baseline schedule

32
Generating Predictive and Reactive Project
Schedules
33
Generating Predictive and Reactive Project
Schedules
Trade-off between makespan and stability!!!
34
Generating Predictive and Reactive Project
Schedules

• Tavares et al. (1998) study the risk of a project
  as a function of the duration uncertainty and the
  cost of each activity and the adopted schedule
• They increase the earliest activity start times
  by the product of the total float of the activity
  and a float factor ,
• They prove that adapted start times yield a
  feasible schedule
• Herroelen and Leus (2003b) allow float factor to
  vary among project activities to pursue stability
  in the schedule

35
Generating Predictive and Reactive Project
Schedules

• Other types of stability measures
• Number of distorted activities
• Number of times that an activity is re-planned
  etc.

36
Generating Predictive and Reactive Project
Schedules

• 2. Quality robust schedules
• Aims to maximize quality robustness
• Insensitivity of the schedule to disruptions that
  affect the value of performance metrics used to
  evaluate the quality of the schedule
• Metrics may relate to average quality robustness
  (expected difference between optimal makespan and
  the makespan realized by the application of
  proactive and reactive scheduling algorithm)

37
Generating Predictive and Reactive Project
Schedules

• Expected quality robustness does not guarantee
  the schedule performance (e.g. makespan) for each
  schedule realization
• Worst case quality robustness is an absolute
  guarantee that a schedule performance will be
  obtained
• May relate to the deviation between a negotiated
  performance value and the performance obtained by
  the proactive and scheduling algorithms
• Without resource constraints, optimizing the
  expected makespan and the worst case makespan
  performance is easy

38
Generating Predictive and Reactive Project
Schedules

• Solution and quality robust schedules in the
  presence of resource constraints
• - Resource feasible, protected baseline schedule
  is formed with resource availability of 10 units
  and project deadline of 14 units

39
Generating Predictive and Reactive Project
Schedules

• Precise resource allocation among different
  activities is crucial
• Leus and Herroelen (2003) study the problem of
  generating a robust resource allocation when a
  feasible baseline schedule exists and some
  advance knowledge about probability distribution
  of activity durations is available
• It is assumed that resource allocation is not
  changed during project execution
• Checking the feasibility of resource allocation
  solution can be done using maximal flow
  computations in the precedence network
• They develop a branch and bound procedure
  enhanced with constraint propagation that solves
  the robust resource allocation problem

40
Generating Predictive and Reactive Project
Schedules

• If activity 4 is deemed less risky than activity
  5, it should pass three of its six allocated
  resource units to activity 3 and the remaining
  three resource units to activity 7, activity 7
  receives the remaining four units from activity 5

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Generating Predictive and Reactive Project
Schedules

• Reactive Scheduling
• Refers to the scheduling modifications that may
  have to be made during project execution
• Use of reactive scheduling procedures in
  combination with a baseline schedule referred as
  predictive-reactive scheduling
• If there is no baseline schedule used, it is
  referred as completely reactive scheduling which
  dispatches activities on line or real time

42
Generating Predictive and Reactive Project
Schedules

• Reactive scheduling has two types
• Schedule repair Aims quick schedule consistency
  restoration
• Rescheduling Involves a full scheduling of the
  part of the project that remains to be executed
  at the time the reaction is initiated

43
Generating Predictive and Reactive Project
Schedules

• Schedule repair
• Involves simple control rules such as right-shift
  rule
• Can lead to poor results since it does not
  re-sequence activities

44
Generating Predictive and Reactive Project
Schedules

• Rescheduling
• May use any deterministic performance measure
  such as the new project makespan (complete
  regeneration)
• Schedule repair can be viewed as a heuristic
  rescheduling pass
• Artigues and Roubellat (2000) study a
  multi-project, multi-mode setting with ready
  times and due dates, it is desired to insert a
  new unexpected activity into a given baseline
  schedule such that the resulting impact on
  maximum lateness is minimized
• They restrict the solution to those schedules in
  which the resource allocation remains unchanged

45
Generating Predictive and Reactive Project
Schedules

• Using a resource network flow representation,
  they develop a stepwise procedure for generating
  a set of dominant insertion cuts for the network
• From each insertion cut, they derive the best
  execution mode and valid insertion arc subset
• In terms of computational burden, insertion
  algorithm outperforms complete rescheduling
• The mean makespan increase is below the activity
  duration of the inserted activity
• The mean makespan increase is smaller for the
  insertion algorithm

46
Generating Predictive and Reactive Project
Schedules

• Frequent rescheduling can result in instability
  and lack of continuity in detailed plans,
  resulting in increased costs and increased
  nervousness
• Rescheduling aims to generate a new schedule that
  deviates from the original schedule as little as
  possible
• Such a minimum perturbation strategy relies on
  the use of exact or suboptimal algorithms using
  as objective the minimization of the differences
  between activity start times in the new schedule
  and the original schedule (El Sakkout and Wallace
  2000)

47
Generating Predictive and Reactive Project
Schedules

• Calhoun et al. (2002) make a distinction between
  re-planning (fixing the schedule before the start
  of the work period) and re-scheduling
  (re-assigning tasks and resources during the work
  period)
• Formulate the problem as a goal programming model
• Use a heuristic to provide an initial solution
  that is subsequently improved using a tabu search
  procedure
• Adding the minimum number of changed activities
  as an extra goal they offer a tabu search
  procedure for re-planning and for re-scheduling
  the activities that are not locked in time

48
Generating Predictive and Reactive Project
Schedules

• In pursuit of rescheduling stability, algorithms
  that use a match-up point is proposed (Akturk and
  Gorgulu 1999, Bean et al. 1991)
• Idea is to follow the pre-schedule if no
  disruption occurs
• Goal is to match up with the pre-schedule at a
  certain time in the future whenever a deviation
  from the initial parameter values arise

49
Generating Predictive and Reactive Project
Schedules

• Contingent scheduling
• Management may make manual changes to the
  schedule during project execution
• Billaut and Roubellat (1996a) suggest generating
  for every resource so-called group sequence, i.e.
  a totally or partially ordered set of groups of
  operations and to consider all the schedules
  obtained by an arbitrary choice of the ordering
  of operations inside each group
• Decision-maker will have several feasible
  schedules
• During execution it becomes possible to switch
  from one solution to another when a disruption
  occurs

50
Generating Predictive and Reactive Project
Schedules

• Activity crashing
• During project execution, corrective actions may
  be taken by crashing some activity durations
• Sensitivity analysis
• What are the limits to the change of a parameter
  such that the solution remains optimal?
• Given a specific change of a parameter, what is
  the new optimal cost?
• Given a specific change of a parameter, what is a
  new optimal solution?

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Generating Predictive and Reactive Project
Schedules

• Posing similar questions in a project scheduling
  environment is an interesting area of future
  research
• Penz et al. (2001) determine the sensitivity
  guarantee of off-line single and parallel machine
  algorithms
• For a minimization objective function f, the
  sensitivity guarantee of an offline algorithm
  ALG for problem instance I is a function
  , such that for any perturbation , is is
  the smallest value satisfying
  where and
  . and are
  objective values of algorithm ALG and optimal
  objective value.

52
Different approaches to multi-project scheduling
problem

• No single method for managing a multi-project
  organization exists
• Best way to coordinate, schedule resources and
  control schedule performance depends on the
  project environment
• Dependency versus variability
• Variability factor involves a joint impression of
  the uncertainty, variability associated with the
  size of the project parameters, uncertainty about
  basis of estimates, uncertainty about the
  process, uncertainty about the objectives,
  uncertainty about fundamental relationships
  between the parties involved

53
Different approaches to multi-project scheduling
problem

• Projects are said to be dependent if they
  coordinate with non-project parties whether they
  are internal or external to the organization
• Refers to both shared resources as well as
  dependence on outside contractors
• Hendricks et al. refer to the degree of shared
  resources as the project scatter factor it
  measures to what extent projects consist of
  full-time members
• Resource dedication profile influences project
  scatter factor
• Tight due dates and unreliable suppliers increase
  dependence
• Drum activities are referred as all activities
  that are dependent

54
Different approaches to multi-project scheduling
problem

• 1. Low variability, totally independent project
• Fully dedicated resources without outside
  restrictions
• A deterministic baseline schedule can be used
• Minor disruptions
• 2. High variability, totally independent project
• High uncertainty during project execution
• Dispatching or a predictive-reactive approach can
  be used
• When uncertainty is very high, dispatching is
  preferable or vice versa

55
Different approaches to multi-project scheduling
problem

• 3. Low variability, rather independent project
• Drum plan is generated
• Drum activities are scheduled for efficiency and
  solution quality
• Remaining (independent) tasks are then planned
  around this drum plan
• 4. High variability, rather independent project
• Drum plan should now be generated for robustness
• Remaining activities are either dispatched or
  predictive-reactive approach is used

56
Different approaches to multi-project scheduling
problem

• 5. Low variability, rather dependent project
• Large number of resources are shared or a large
  number of activities have a constrained time
  window
• Robust plan should be set up to prevent
  propagation of small disruptions
• Remainder should be planned in as efficiently as
  possible
• 6. High variability, rather dependent project
• Not overly detailed robust drum plan should be
  set up
• Bottleneck resources will probably have a queue
  of jobs
• Independent activities are dependent on execution
  times of the drum activities

57
Different approaches to multi-project scheduling
problem

• 7. Low variability, totally dependent project
• Generation of an aggregate plan seems to be
  sufficient
• Goal of resource allocation is to obtain a
  feasible plan with minimal conflicts
• Small amount of slack should integrated into the
  plan to smooth out small disruptions
• 8. High variability, totally dependent project
• Best dealt with process management viewpoint
• Resources are often workstations that are visited
  by work packages
• Priorities can be set for the resources in
  choosing the next work package to consider

58
Different approaches to multi-project scheduling
problem
59
Different approaches to multi-project scheduling
problem

• The role of CC/BM
• For a single project environment, the methodology
  seems practical and well thought-out
• But it imposes extra constraints on project
  execution
• For single projects, the unconditional focus on a
  critical chain seems useless since it enforces a
  rigid focus on what was critical at the start of
  the project but may not be critical after a
  certain amount of time
• Activity durations are based on the behaviour of
  human resources, so one should not rely on
  statistical techniques for modelling them

60
Different approaches to multi-project scheduling
problem

• Rescheduling is disapproved by CC/BM because it
  is said to be harmful to stability
• It follows from an investigation of CC/BM that
  projected schedule is unavoidable which needs to
  be rescheduled anyway
• Stability within separate projects is far from
  guaranteed given that CC/BM boils down to
  dispatching based on a constantly rescheduled
  projected schedule
• Although CC/BM seems to be based on dispatching,
  it is not adapted to environments with high
  uncertainty such as new product development

61
Different approaches to multi-project scheduling
problem

• Critical chain approach falls short of covering
  the scheduling needs of every multi-project
  organization
• Staggering the projects around the constraining
  resource may result in low throughput if there
  are several constraining resources each leading
  to a different schedule
• Especially in low variability environments,
  multi-tasking without overloading the system may
  result in beneficial results

62
Conclusion

• Objective of this paper is to review the
  methodologies for proactive and reactive project
  scheduling
• To present some hints to identify a proper
  scheduling methodology for different scheduling
  environments
• Research efforts aim at generating solution and
  quality robust schedules together with effective
  reactive scheduling mechanism
• Critical chain methodology suffers from
  oversimplification of the issues and is not
  universally applicable

63

• DISCUSSION