Robust and Reactive Project Scheduling: A review and classification of procedures Willy Herroelen Roel Leus

Robust and Reactive Project Scheduling:

A review and classification of proceduresWilly Herroelen

Roel Leus

OUTLINE• Introduction• Deterministic Baseline Scheduling• Generating Predictive and Reactive Schedules• Different approaches to multi-project scheduling• Conclusions

IntroductionProcedures that yields workable BASELINE SCHEDULES

Deterministic Environment

Complete Information

IntroductionProcedures that yields workable BASELINE SCHEDULES

Min/Max Regular/Nonregular Objectives

Subject to Precedence Constraints

Resource Constraints

Introduction

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• Identifies peak & low capacity requirement periods

• Baseline Schedules serves very important functions

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IntroductionMaterial

ProcurementPreventive

MaintenanceCommittment to

due dates

Basis for planning External Activities

Introduction• Enables – visibility of future– agreement among all parties• producer• clients• suppliers • subcontractors and etc.

Introduction

Supplier A

Supplier B

Producer

Supplier C

Production Schedules

• Enables Just In Time material delivery

Introduction• Baseline Schedule– Vital for cash flow projections–Measures the perfomance • Managers,• Shop floor personel

IntroductionMore or Less execution times

Unavailable resources

Late arrival of materials

Modified Release and due dates

New Activities

• During execution, project is subject to considerable uncertainty

P R O J E C T

Introduction• Recognition of uncertainty – Proactive baseline schedule• Protected against disruptions• Minimize the total weighted instability

– Reactive scheduling• Doesn’t directly consider the uncertainty during the generation of the initial schedule• Revises or re-optimizes the schedule when unexpected events or disruptions occur

– Predictive – Reactive scheduling • Generation of a predictive schedule • Re-optimize by rescheduling policies

Deterministic Baseline Scheduling• Development of a workable schedule – Defines the scheduled start times– Satisfies;• Precedence contstraints• Resource constraints

– Optimizes the scheduling objective; • most often project duration

Deterministic Baseline Scheduling

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Minimum Duration Schedule with constant resource level


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Critical Path<1, 4, 7, 8, 9, 10>


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Critical Path<1, 4, 7, 8, 9, 10><1, 5, 3, 6, 2, 10><1, 4, 3, 6, 9, 10>…16


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- Optimal for deterministic setting


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- Optimal for deterministic setting- Extremely vulnerable to uncertainty

3’


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- Optimal for deterministic setting- Extremely vulnerable to uncertainty- True optimality can only be ascertained in real world


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- Optimal for deterministic setting- Extremely vulnerable to uncertainty- True optimality can only be ascertained in real world - Has insufficient built-in slack or flexibilityNot ROBUST


Lack of RobustnessLack of Stability

Lack of Quality

: Not Solution Robust

: Not Quality RobustFlexibility

Generating Predictive and Reactive Project Schedules• Dynamic Scheduling –No baseline schedule– Decide which activity to start as time evolves– Stochastic Project Scheduling• Precedence and resource constraints• Multi stage decision process• Scheduling strategies

–Minimize the expected project duration? ? ? ? ? ?

Generation of a Baseline Schedule• No anticipation of variability• Proactive (robust) baseline scheduling– CC/BM– Robust precednce feasible schedules

• Solution robust• Quality robust

– S&Q Robust with resource constraints• Reactive Scheduling– Schedule Reapir– Rescheduling– Contingent scheduling– Activity Crashing– Sensitivity Analysis

Generation of a Baseline Schedule• No anticipation of variability• Proactive (robust) baseline scheduling– CC/BM– Robust precedence feasible schedules









Critical Chain Scheduling/Buffer Management• CC/BM – Direct application of the theory of constraints to project management

IdentifyExploitSubordinateElevateRepeat

Critical Chain Scheduling/Buffer Management• Builds a baseline schedule– Aggressive median or Average activity duration estimates– Activity due dates are eliminated–Multi tasking is avoided

Aggressive Median

Critical Chain Scheduling/Buffer Management• Create a precendence feasible schedule– Consider the precedence constraints– Schedule the activities at their latest start times– Resolve the resource conflicts by moving activities earlier in time

• Indentify the critical chain– Determines the overall duration of the project

Critical Chain Scheduling/Buffer Management

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Precedence Feasible Schedule Activity Precedence Duration2 - 43 - 24 - 25 - 26 3 37 4 28 7, 5 39 6, 8 4


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Critical Chain Scheduling/Buffer Management• During Execution in CC/BM –Do not rely on buffered schedule ,–but on projected schedule• Precedence and Resource feasible• Contains no buffers• Executed by roadrunner mentality


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Buffered Schedule


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Projected Schedule

Critical Chain Scheduling/Buffer Management• Conclusion after 110 Patterson test problem;–Updating the baseline schedule and critical chain at each decision point

• Best estimate of final project duration• Yields smallest project duration

–%50 buffer sizing, seriously overestimates –Using root-square-error method for buffer sizing is more beneficial as the problem size increases– Do not keep the critical chain activities in series– Recompute the baseline schedule at each decision point

Critical Chain Scheduling/Buffer Management• In a multi-project environment1. Prioritize the organization’s projects

• Avoid multi tasking2. Plan the individual projects according to CC/BM• Identify the bottleneck resource3. Stagger the projects4. Insert drum buffers5. Measure and report the buffers6. Manage the buffers




Robust Precedence Feasible Schedules• Solution Robust Schedules– Activity start times are insensitive to disruptions– Stable

• Quality Robust Schedules– Overall project duration is insensitive to disruptions– Robustnes in the objective function value

Solution Robust SchedulesMathematical Programming Model

Stable Baseline SchedulesAssumptions• Resource can be booked in advanvence • Single activity disruption𝑴𝒊𝒏 𝑬 [ h𝑊𝑒𝑖𝑔 𝑡𝑒𝑑𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑜𝑓

𝐴𝑐𝑡𝑖𝑣𝑖𝑡𝑦 𝑆𝑡𝑎𝑟𝑡 𝑇𝑖𝑚𝑒𝑠 ]

Herroelen & Leus (2003)

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• Deadline = 14• Equal disruption probability• P(duration of disruption=1) = 0,5• P(duration of disruption=2) = 0,5

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Solution Robust Schedules

• Solution Robust• Weighted Expected Deviation is minimized

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Solution Robust Schedules• Stable Schedules, spread out the activities

Solution Robust Schedules0,04

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Solution RobustCC/BM (proj)Density Function of the Makespan• Resource Constraints are disregarded

• Activity durations are stochastic (triangular)• Min =10, Max =22• STABLE has HIGHER MAKESPAN

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Solution Robust Schedules• Other types of schedule disruptions– less execution times– change in the execution mode• planned / unplanned pre-emption

– delay in the starting times–modification of the structure of the project• new activities• changed precedence

• Other metrics for stability measure–# of disrupted activities–# of re-planned activities

Quality Robust Schedules• Maximizes the quality robustness• Metrics used for quality robustness– Average quality robustness– Expected quality robustness–Worst case quality robustness




Solution and Quality Robust Schedules

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Precedence and Resource feasible

Solution and Quality Robust SchedulesCC/BM Projected Schedule Solution and Quality Robust Schedule

Solution and Quality Robust Schedules

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Resource Allocation is the cruical issue that remains to be solved




Reactive Scheduling• Schedule modifications, made during execution• May be based on various underlying strategies– Very simple techniques (schedule repair)– Full scheduling







Rescheduling• Yang (1996)– New makespan minimization

• Artigues and Roubelat (2000)– Multi-project, Multi-mode– Ready times and due dates– Insert a new unexpected activity – Minimize the maximum lateness– They used a polynomial algorithm and tested in on 110 Patterson test problems against complete rescheduling– Insertion method outperforms complete recheduling– Mean increase of makespan ≤ inserted activity duration

Rescheduling• Frequent Rescheduling– Instability and lack of continuity– Increased costs– Increased shop floor nervousness

• Minimum perturbation strategy–Minimize the start time differences–Minimize the number of activites that will be performed with different resources

• Using Match-up point–Match up with the pre-schedule at a certain time in future




Contingent Scheduling• Manual changes during execution• Billaut and Roubelat (1996a,b)– Generate for every resoure a group sequence– Consider arbitrary ordering of operation inside each group.– If disruption occurs, switch from one solution to another

• Several other extensions are studied




Sensitivity Analysis• Hall and Posner (2000a, b)

– Limits of parameters in which solution remains optimal– New optimal cost and solution after a parameter change

Sensitivity Analysis• Penz et al.(2001) Sensitivity guarantee of scheduling algorithms – For problem instance , min. objective , algortihm ,– Performance guarantee of scheduling algorithm where – With variability / perturbation vector , the effective performance ratio is , – Then the sensitivity guarantee of an algorithm

𝜺≥‖�⃗�‖

Multi-project Scheduling Problem• No single best method• Best way for– Coordination and Scheduling of resources– Control of schedule, depends on the project environment

• Two key determinants 1. Variability2. Independence

Multi-project Scheduling Problem

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when how

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quality

timecontent

Uncertainty&

Variability

Objectives

PrioritiesFundamental Relationships

whom

Trade off

Multi-project Scheduling Problem• Ward and Chapman (2002)– Explore and Understand the origins of the uncertainties– Before managing them


• Hendricks et al.(2002)– Project Scatter Factor : degree of shared resources– Dependence ~ degree of free dispatching or scheduling– Intermediate milestones increases dependence– Uncertain or tight ready days increases dependence– All activities = Drum Activities + Remainder

Project

Non-Project PartiesINTERNAL EXTERNAL


TOTALLY DEPENDENT

variability

LOW

HIGH

RATHERDEPENDENTRATHERINDEPENDENTTOTALLY INDEPENDENT

1 3 5 72 4 6 8


TOTALLY DEPENDENT

variability

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• No outside restrictions• Deterministic schedule• Minor Disruptions

• Uncertainty during execution• Dispatching rules or predictive reactive scheduling • Feasible schedule for drum activities

• Remainder activities are planned around them

• Drum Plan must be Robust• Dispatching / predictive-reactive for remainder

• Shared resources• Constrained activities• Robust plan

• Aggregate plan• Resource allocation with minimal conflicts• Slacks if possible

• Robust Drum Plan• Sufficient oppurtunity for uncertain events

• Resources are often workstations • Rough ballpark plan for intermediate milestones


TOTALLY DEPENDENT

variability

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HIGH


Deterministic plans


TOTALLY DEPENDENT

variability

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Fire fighting mode beacuse of intermediate milestones


TOTALLY DEPENDENT

variability

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Lack of CoordinationInsufficient Stability

Multi-project Scheduling Problem• The role of CC/BM– Integrated methodology for project planning and execution– Needs to be credited for

• duration estimation problem• Parkinson’s law and Student syndrome• Multi tasking

– Suitable for single projects

Summary and Conclusions• Objective of the paper– Review the methodologies for proactive and reactive project scheduling– Proper scheduling methodology for different environments

• Generating S&Q robust with effective reactive scheduling mechanism are still burn-in• CC/BM– Attracted a lot of attention– Suffers from

• Over simplification• Not universally applicable

Thank you.Questions ?

Documents

Robust and Reactive Project Scheduling: A review and classification of procedures Willy Herroelen Roel Leus