M1

M2

M3

M4

1 2 3

1 2

1 2

1

3

3t

Applications of Dynamic

Re-scheduling Methodologies

Gerry Kelleher and Abdennour el-Rhalibi

Introduction

Preparing predictive schedule is not enough. • there are many events that require the revision of the

predictive schedule.• a frequent comment in many scheduling contexts is that

scheduling is not a problem but rescheduling is

Terminology

• Rescheduling, process of updating an existing production schedule in response to disruptions

• Disruptions (Rescheduling Factors)

• Machine Failure• Urgent Job Arrival• Job cancellation• Due date change• Operator Absenteeism

• Change in Job Priority • Delay in Arrival• Rework or Quality

Problems• Over or under estimation

of processing times

Terminology

• Scheduling, creating production schedules and

• Rescheduling framework, consists of rescheduling environment, rescheduling strategies, rescheduling policy and rescheduling methods

Triggering Events

• The current schedule has become infeasible

• The current schedule is likely to fail based on some performance measures

• Detection of opportunities to improve the schedule while the current schedule is still acceptable

• Rescheduling is done with fixed frequency

Rescheduling Framework

Rescheduling Strategies (any environment with variability)

Dynamic (no schedule)Dispatching rules Control-theoretic

Predictive-reactive (generate and update)

Periodic HybridEvent-drivenRescheduling Policies)

Rescheduling Methods (for predictive-reactive)

Schedule GenerationNominal Schedules

Schedule RepairRight-shift

ReschedulingComplete

RegenerationPartial

ReschedulingRobust

Schedules

Rescheduling Strategies

Dynamic Scheduling• do not use scheduling policies, uses

current information to dispatch the jobs (eg FIFO, EDD, SPT…)

• tradeoff utility, measure of improvement, against stability, measure of nervousness

• three types of actions upon information arrival: no move, repair and reschedule.

Dynamic Scheduling

• Utility, a measure of improvement such as, decrease in total completion time

• Utility & Stability vs. time of arrival information and/or change in the current system

• Decide on repair or reschedule

n

iiiiii DCCtt

1

}|),'||'(|min{

• Stability, a measure of nervousness, such as, total change in start times and completion times

Predictive-Reactive Scheduling

• Evaluation step, generate a robust schedule, evaluating the impact that a disruption causes

• Solution step, determine rescheduling solutions enhancing the current performance

• Revision step, update the existing schedule or generate a new one

Rescheduling Methods

Right shift rescheduling, postpones each remaining operations

Partial rescheduling, schedules only operations affected by the disruption

1. Matchup scheduling, reschedule all the jobs before a matchup point

2. If point too large, use integer programming or dispatching rulesRegeneration, reschedule the entire jobs before the rescheduling point

P I S C E S(Pipeline Intermodal System to Support Control Expedition and Scheduling)(Pipeline Intermodal System to Support Control Expedition and Scheduling)

IN-96-SC.1204

Partners: Fraser Williams Logistics Ltd.

Van Ommeren Agencies Rotterdam BV

Liverpool John Moores University

PROJECT FUNDED BY THE EUROPEAN COMMISSION UNDER THE TRANSPORT RTD PROGRAMME OF THE

4TH FRAMEWORK PROGRAMME

PISCES and Logistics Evolution

Demand Forecasting Purchasing

Requirements Planning

Manufacturing Inventory

Materials Handling

Distribution Planning

Production Planning

Warehousing

Industrial Packaging

Inventory

Order ProcessingTransportation

Customer Service

Materials Management

LogisticsPhysical

Distribution

Fragmentation

1960s

Evolving Integration

1980s

Total Integration

2000s

Warehousing

Transportation

PISCES

PO

PPipeline ipeline IIntermodal System to ntermodal System to SSupport upport CControl ontrol EExpedition and xpedition and SSchedulingcheduling

PISCESDatabase

Freight Forwarder

Global carrier

Manufacturer

Wholesaler/Retailer

Transportation

Distribution Centre

Bookings Cargo receipts Packing

lists Shipping advice

Cargo Manifests Shipment Status

Pre advice of container contents

Customsclearance

Accept shipmentsinto inventory

Check commodityavailability/location

Delivery Details

Cus

tom

s do

cum

enta

tion

PPipeline ipeline IIntermodal System to ntermodal System to SSupport upport CControl ontrol EExpedition and xpedition and SSchedulingcheduling

SERVICES/

EVENTS

EQUIPMENT

INFORMATION

•Speed of information transfer related to need•Neutral database to maintain relationships•No need to publicise actual parties or cargo details•Integrate info/services/equipment to flex critical path•Provide adaptive algorithms for scheduling/optimisation •Focus on ‘operational’ milestones•Easy access via Internet

VELOCITY CRITICAL PATH

Throughput levels Employment levels Distribution routes

Vehicle scheduling Order tracking Inventory replenishment

Support to Logistics Management Decisions

STRATEGIC

TACTICAL

OPERATIONAL

Location Choice Transport Mode Selection Vendor Choice

Uncertainty

Scope

Time frame

 

Figure 1: The Vehicle Routing Problem

: Client

: Depot

CUSTOMER

PORT

DEPOT

CUSTOMER

DEPOT

CUSTOMER

ContainerTransport

Collection Positioning

Delivery

Empty Empty RunningRunning Delivery

Delivery

Positioning

Delivery

Collection

Collection

Delivery

CUSTOMER

PORT

DEPOT

CUSTOMER

DEPOT

CUSTOMER

ContainerTransport

Collection Positioning

Delivery

Empty Empty RunningRunning Delivery

Delivery

Positioning

Delivery

Delivery

EmptyCollection

Collection

Collection

1

2

34

56

Transport Scheduling

Rotterdam

Antwerp

Dortmund

Basel

Munich

Amsterdam

Hannover

Cologne

Duisberg

Stuttgart

Metz

Strasbourg

Bonn

Trier

Rotterdam

Antwerp

Dortmund

Basel

Munich

Amsterdam

Hannover

Cologne

Duisberg

Stuttgart

Metz

Strasbourg

Bonn

Trier

Transport Scheduling

CONTAINERS CONTAINERS

TRANSPORTTRANSPORT

TRIANGULATION:TRIANGULATION:

CONSTRAINTSCONSTRAINTS

Multiple Types of Vehicles

Transport Scheduling

Pickup andDelivery

Time Window

Capacited Vehicles

Multiple Ports/Depots

Intermodality

Constraints on Length/Duration

of Tour

DynamicChanges

Containers/GoodsCompatibility

SCHEDULINGSCHEDULING

OptimisationOptimisationCriteriaCriteria

RESCHEDULINGRESCHEDULING

Transport Scheduling

Empty Running

Maximise Use of Intermodal Alternative:Barge/Train

Cost

Total Traveled Distance

Minimise Changes from the Initial

Routing

Maximise Length of

Triangulated Legs

Minimise Introduction of New Resources

Minimise Delays

Design of a Software Package to Produce Routing Scheduler

• Application to the Triangulation Problem, for the Transport of Containers.

• Application to Classical Vehicle Routing Problems.

We take advantage of two techniques by using an hybrid approach:

1 a CSP program to compute feasible solutions on a subspace of the search space.

2 a GA to explore the space formed by the solutions provided by the CSP, and perform the optimisation

Routing SchedulerRouting SchedulerC

SP

Gen

erat

or

Var

iab

les

Dom

ain

s C

onst

rain

ts CSP Solver

Forward Checking/Orderings

Selection

Replacement

Recom

bin

ationM

utation

Constraint Satisfaction and Genetic Algorithm

Offspring

ParentFeasible solutions

Repaired solutions

Infeasible solutions

CONSIGNMENT

MANAGEMENT PROGRAMSDATABASE

Population

Reasoning Module

Optimisation Module

Performance on Van Ommeren’s Problems

Triangulated

Transport

Requests

CurrentTotal

Distance

Distancewith

Triangulation

CurrentEmpty

Running

EmptyRunning

withTriangul

ation

Improved Level

ofEmpty

Running

Improved

Distanceperform

ance

R1-R40 20 20 10 10 50.00% 0.00%R3-R43 1332 1104 666 438 39.67% -17.11%R4-R88 1248 778 624 154 19.79% -37.66%R5-R90 612 319 306 13 4.07% -47.87%R7-R64 656 529 328 201 37.9% -19.35%

R10-R62 358 352 179 173 49.14% -9.21%R14-R47 854 700 427 273 39.00% -18.03%R15-R74 696 400 348 52 13.00% -42.52%R16-R26 228 210 112 96 45.71% -7.89%R17-R54 704 693 352 341 49.20% -1.56%R19-R58 178 132 132 54 40.09% -25.84%R21-R81 206 140 140 74 67% -

52%-24.73%

R25-R37 770 522 385 137 26.24% -32.20%R27-R63 500 314 250 64 20.38% -37.20%R32-R46 482 374 241 133 35.35% -22.40%R34-R71 708 458 354 104 22.70% -35.31%R35-R70 1162 1061 581 480 45.24% -8.69%R36-R38 520 398 260 138 34.67% -23.46%R42-R72 184 156 92 64 41.02% -15.21%R44-R69 28 14 14 0 0.00% -50.00%R50-R79 1404 1276 702 574 44.9% -9.11%R52-R86 460 446 230 216 48.43% -3.04%R80-R93 148 148 74 74 50.00% 0.00%

Total 13438 10544 6807 3863 36.66% -21.53%

Trian

gulation

of Con

tainers T

ransp

ort

Tyre Manufacturing (Pirelli)

• Problem - add rescheduling capability to an existing system - BIS (Banbury Information System

• Scheduling of the Banbury Area is a job-shop scheduling task input to the system is a production plan containing customers and production orders (denoted requirements – typically ~50 per day).

• Scheduling horizon varies with the due-date of the orders, ( typically ~2 days).

Scheduling difficult, complex in itself but also requires reaction in real-time to change:

•small revisions because of short stops of machines. •major revisions because of breakdown •customer order changes•feedback from quality control on finished tyres •breakdowns in semi-manufacturing, building and curing areas.

The objectives to be optimised include:

1. Minimise the tardiness of the requirements2. Keep stock-levels within a defined minimum/maximum3. Optimise the standing times of compounds4. Maximise machine utilisation5. Minimise set-up-time for the machines6. Use prioritised machines

   

 Table 1 Causes of Rescheduling

Cause Typical frequency

(times/week)

Typical Duration (hours)

Banbury breakdown 1 - 2 2 - 8

Banbury stoppages < 1 1 - 24

Rework ~ 3  

Lack of raw-material sometimes  

Change in requirements seldom  

 System Architecture Schematic

•HCI

DB HCI

ExplanationGenerator

ScheduleEvalutor

ManualReviser

Reason Maintenance

Scheduler and Re-scheduler

Manufacturing EnvironmentCommunication

System DB

RMS DB

Zone 1 Zone 3Zone 2

Zone 4

Shift3

Shift2Shift1 Shift3

Shift2

Shift1

DAY 1 DAY 2

Rescheduling Time

Reaction Time

Dosage Time

Dosage Horizon

Time Zones for Rescheduling

Zone 1 Zone 3Zone 2

Zone 4

max

Disruption Weight

time

Disruption Function Weighting

Evaluation criteria BIS TRISprototype

TRISfinal prototype

Number of real time changes to schedule

2-3 per day 1-2 per day < 1 per day

Number of re-scheduling Not available

Not available

1-2 per week

“Out of stock” (per day) < 1 per day < 1 per day < 1 per day

Stock levels (total batches) 1300 -1450 1200 -1300 < 1000

Lateness 3-4 per day 1-2 per day < 1 per day

Use of highest priority machine 93 % 93 % 94-95 %

Machine saturation 90 % 94 % 93-97 %Lead time factor 80 % 90 % > 90 %WIP ~ 100 ~ 100 ~ 100Standing time 1-4 hours 1-4 hours 1-4 hours

Average set-up ~ 5 mins ~ 5 mins ~ 3-4 mins

Preparation of data 2-3 hours 30-40 mins 30-40 mins

Manual revision of the schedule 2 hours 2 hours 30 mins

Build Original Schedule

Build Minimal Constraint Model

Add on Rescheduling

Need for Rescheduling

Build New Working Context(input solution creating dependency model)

Manual Rescheduling (HCI based dependency analysyis)

Autonomous Rescheduling (automatic dependency analysyis)

Legacy System

Notes and Conclusion

• Cost of rescheduling policies depends on frequency of rescheduling

• Implementation of rescheduling policy depends on information acquisition

• More research on the interaction of rescheduling policies with other production planning decisions is needed

04/18/23 Rescheduling 36

 

 

Size of Disruption This refers to the duration for which the schedule is subject to disruptions, such as machine breakdown. This expressed as a percentage of the initial’s schedule makespan.

Incidence of the disruption This refers to the time of occurrence of the disruption, which can occur either early or late in the schedule.

Size of the Schedule This refers to the size of the scheduling problem, and is expressed as the number of job operations present in the initial schedule.

Schedule Structure This refers to the tightness of the schedule, as it shows in the Gantt chart. We can also estimate it by considering the difference of values the utility function (e.g. makespan) of the worst and best solution found by CSP/GA

Disruption Dimension Problem Category (PC1)

1

Problem Category (PC2) 2

Size of disruption

Machine Breakdown

Small1-5% of Makespan

Large 6-10% of Makespan

Process time Change

Small1-5% of Makespan

Large 6-10% of Makespan

Urgent Job Process Time about1-5% of Makespan

Process Time about1-5% of Makespan

Incidence of disruptions Early5-55% of Makespan

Late60%-90% of Makespan

Schedule size Small <200 operations(about 10 jobs)

Large200-300 operations(about 20 jobs)

Schedule structure Tight (<100) / Loose(>100)

Tight (<100) / Loose(>100)

Problem Instancename

Size of Problems Size of Schedule Incidence of Disruptions Size of Disruptions

orb1 10x10 PC1 Early (5-55%) Small (1%-5%)

orb2 10x10 PC1 Late (60%-90) Large(6%-10%)

orb3 10x10 PC1 Early (5-55%) Large(6%-10%)

orb4 10x10 PC1 Late (60%-90) Small(1%-5%)

orb5 10x10 PC1 Early (5-55%) Small(1%-5%)

abz5 10x10 PC1 Late (60%-90) Large(6%-10%)

abz6 10x10 PC1 Early (5-55%) Large(6%-10%)

abz7 20x15 PC2 Late (60%-90) Small(1%-5%)

ab8 20x15 PC2 Early (5-55%) Small(1%-5%)

abz9 20x15 PC2 Late (60%-90) Large(6%-10%)

la19 10x10 PC1 Early (5-55%) Large(6%-10%)

la20 10x10 PC1 Late (60%-90) Small(1%-5%)

la21 15x10 PC1 Early (5-55%) Small(1%-5%)

la24 15x10 PC1 Late (60%-90) Large(6%-10%)

la25 20x10 PC2 Early (5-55%) Large(6%-10%)

la27 20x10 PC2 Late (60%-90) Small(1%-5%)

la29 20x10 PC2 Early (5-55%) Small (1%-5%)

la36 15x15 PC2 Late (60%-90) Large(6%-10%)

la38 15x15 PC2 Early (5-55%) Large(6%-10%)

la39 15x15 PC2 Late (60%-90) Small (1%-5%)

la40 15x15 PC2 Early (5-55%) Small (1%-5%)

Efficiency defined as the percentage change in makespan of the repaired schedule compared to the preschedule

100*}1{0

0

MMM new

where, = EfficiencyMnew = Makespan of the rescheduled schedule

Mo = Makespan of the preschedule

Stability is the absolute sum of difference in starting times of the job operations between the initial and the rescheduled schedules. It is then normalized as a ratio of total number of operations in the schedule. A schedule will be stable if it deviates minimally from the preschedule.

k

jj

k

j

p

ijiji

P

SSj

1

1 1

*

where, = Normalized deviation.pj = number of operations of job j.k = number of jobs.Sji* = Starting time of ith operation of job j in repaired schedule.

Sji = Starting time of ith operation of job j in original schedule.

Problem Description RSREfficiency%

AOR Efficiency%

CSP/GAEfficiency%

RSRStability%

AORStability% 

CSP/GAStability% 

orb1-10x10

PC1/ Early /Small/tight

96-97% 97-100 91-98% 8-11% 1-3% 1-4%

orb2-10x10

PC1/Late /Large/loose

88-94% 95-96% 94-99% 4-9% 1-2% 1%

orb3-10x10

PC1/Early/Large/tight

84-89% 92-97% 97-98% 11-17% 4-9% 10-13%

orb4-10x10

PC1/Late /Small/tight

95% 95-100% 98-99% 2-3% 1-2% 2%

Orb5-10x10

PC1/Early /Small/tight

94-99% 100% 97-98% 7-9% 3 4-6%

abz5-10x10

PC1/Late /Large/loose

92-93% 96-97% 93% 33-38% 17-25% 11-29%

Abz6-10x10

PC1/Early /Large/loose

59-70% 72-79% 81-82% 43-68% 12-19% 26%

abz7-20x15

PC2/Late/ Small/tight

94% 99% 96-97% 3-6% 1-2% 4%

ab8-20x15

PC2/Early Small/tight

91-93% 93-98% 91% 18-19% 9-13% 14%

Abz9-20x15

PC2/Late /Large/tight

83-92% 91-94% 87-98% 43-45% 21% 17-23%

Problem Description RSREfficiency%

AOR Efficiency%

CSP/GAEfficiency%

RSRStability%

AORStability% 

CSP/GAStability%

la19-10x10

PC1/Early Large/loose

82-87% 86-93% 84-85% 71-75% 34-35% 24-37%

la20-10x10

PC1/Late /Small/tight

92-97% 92-98% 93% 5-7% 2-3% 2-4%

la21-15x10

PC1/Early /Small/tight

83-90% 96-98% 94-97% 10-14% 2-7% 5-9%

la24-15x10

PC1/Late /Large/tight

88-89% 91-96% 95% 14-17% 9-13% 11%

la25-20x10

PC2/Early /Large/tight

78-84% 80% 82-87% 37-48% 17-38% 45-47%

la27-20x10

PC2/Late/Small/tight

92-97% 94-98% 92% 9-15% 3-6% 11%

la29-20x10

PC2/Early /Small/tight

73-74% 80-88% 79-83% 25-29% 19-23% 26-27%

la36-15x15

PC2/Late /Large/loose

63-89% 75-89% 84-86% 31-45% 13-27% 22-29%

la38-15x15

PC2/Early /Large/tight

56-63% 68-75% 77% 67-71% 19-24% 32%

la39-15x15

PC2/Late /Small /tight

69-70% 79-83% 77-80% 33-38% 9-14% 19-26%

la40-15x15

PC2/Early /Small/tight

67-71% 80-85% 87% 28-36% 11-17% 9%

importance

Time/number of actions

optimisation criteria

t0Disruption incidents(s)