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

8. 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 <1,5,3,6,2,10>, <1,5,3,6,9,10>, <1,4,7,8,9,10> etc.

11. 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

15. 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)

16. 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

17. 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

18. 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)

19. 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

20. 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

26. 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

27. 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 organization’s 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

28. 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

29. 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

30. Generating Predictive and Reactive Project Schedules Resulting proactive reactive schedule is solution robust to the described disruption setting

31. 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

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

41. 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?

51. 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