DECISION SUPPORT SYSTEMS FOR PLANNING AND

SCHEDULING IN PRACTICE

Michael PinedoStern School of Business

New York University

DECISION SUPPORT SYSTEMS FOR PLANNING AND

SCHEDULING IN PRACTICE

I. Application Areas, Infrastructures,General Architectural Issues

II. System Requirements

III. Planning and Scheduling Techniques

IV. System Implementations Commercial Packages

Part I.

Application Areas, Infrastructures, General

Architectural Issues

• Application Areas– Planning and Scheduling in

Manufacturing and Services

• Infrastructures– In Manufacturing– In Supply Chain Management– In Services

• General Issues regarding– Systems Architecture– For Production Scheduling– For Workforce Scheduling

APPLICATION AREAS OF PLANNING AND SCHEDULING

• Manufacturing– Process– Discrete– Automotive– Food and Snacks

• Services:– Crew Scheduling (Airlines)– Workforce Scheduling (Call Centers)– Reservation Systems and Yield

Management

INFORMATION SYSTEM INFRASTRUCTURE IN

MANUFACTURING ENVIRONMENTS

• Interfaces with Forecasting, Medium Term, and Long Term Planning

• Interfaces with Product Design and Facility Layout

•Workforce Scheduling in–Cell Centers–Hospitals

•Reservation Systems in –Airlines–Hotels–Car Rentals

INFORMATION SYSTEM INFRASTRUCTURE IN

SERVICE ENVIRONMENTS

Part II.

Important Issues in Design of Decision Support Systems

IMPORTANT ISSUES IN DESIGN OF DECISION SUPPORT

SYSTEMS•Module Design and Interfacing•GUI Design•Design of Link Between GUI and Algorithm Library•Internal Reoptimization•External Reoptimization

MODULAR (OBJECT-ORIENTED) DESIGN

Standardization of Data Transfers Between Modules.Data Concerning:

– Jobs (Operations)– Work Centers (Machines)– Schedules

Have to be Properly Organized in order to make Transfer of Data Easy.

EXAMPLE: Plugging in New Algorithm in Existing System should be Easy.

GUI’SSHOULD ALLOW:

• Interactive Optimization– Freezing Jobs and Reoptimize– Creating New Schedules by Combining

Different Parts from Different Schedules

• Cascading and Propagation EffectsAfter a Change or Mutation by the User, the

System– does Feasibility Analysis– takes care of Cascading and Propagation

Effects,– does Internal Reoptimization

GRAPHICS USER INTERFACES FOR SCHEDULING

PRODUCTION PROCESSES

•Gantt Chart Interface•Dispatch List Interface•Time Buckets•Throughput Diagrams

IMPORTANT OBJECTIVES TO BE DISPLAYED

• Due Date Related– Number of Late Jobs– Maximum Lateness– Average Lateness

• Productivity and Inventory Related– Total Setup Time– Total Machine Idle Time– Average Time Jobs Remain in

System

SEQUENCE DEPENDENTSETUP TIMES

Sijk = The Time it Takes to Setup for Job k at the Completion of Job j on Machine i.

•One way to Retrieve These Data is Through a Table Look-up

•Another way is Through a FormulaJob j Carries a Number of Parameters in its Data String

aij, bij, cij (color, sizes, etc.)

Sijk = fi (aij, aik) + gi (bij, bik) + hi (cij, cik)

or

Sijk = MAX (fI (aij, aik), gi (bij, bik), hi (cij, cik))

INTERNAL RE OPTIMIZATION AFTER A CHANGE BY THE USER

Internal Reoptimization Should Satisfy Certain Conditions:

C.U. = Change by the UserI. R. = Internal Reoptimization

Internal Reoptimizaton Should be ReversibleC. U. I. R. Reverse C. U. I. R.

Original ScheduleInternal Reoptimization Should be CommutativeC. U. 1 I. R. C. U. 2 I. R.

Same ScheduleC. U. 2 I. R. C. U. 1 I. R.

Part III.

Planning and Scheduling Optimization Techniques

PLANNING AND SCHEDULING OPTIMIZATION TECHNIQUES

• Dispatching Rules• Composite Dispatching

Rules• Dynamic Programming• Integer Programming• Column Generation• Branch and Bound• Beam Search

• Local Search• Decomposition Techniques

– Temporal– Machine (Shifting Bottleneck)

• Drum-Buffer-Rope• Hybrid Methods

PLANNING AND SCHEDULING OPTIMIZATION TECHNIQUES

(continued)

IMPORTANT CHARACTERISTICS OF OPTIMIZATION TECHNIQUES

• Quality of Solutions Obtained(How Close to Optimal?)

• Amount of CPU-Time Needed(Real-Time on a PC?)

• Ease of Development and Implementation(How much time needed to code, test, adjust and modify)

Local Search

ValueObjectiv

eFunctio

n

Dispatching

Rules

Beam Search Branch and

BoundCPU - Time

COMPOSITE PRIORITY RULE THAT IS MIXTURE OF

THREE BASIC PRIORITY RULES:

• Weighted Shortest Processing Time First

• Earliest Due Date First• Shortest Setup Time First

DYNAMIC PROGRAMMINGCharacterizing Equations:

(i) Initial Conditions(ii) Recursive Relation(iii) Optimal Value FunctionExample: Consider a Single Machine and

Objective Function

Let J Denote a Subset of the n Jobs. Assume J is Processed First.Let V(J) = hj (Cj)

Initial Conditions:V({j}) = hj (pj) j = 1, …, n

Recursive Relation:

V(J) = min (V(J- {j}) +

hj( pk)) j J

Optimal Value Function:V({1,…., n})

INTEGER PROGRAMMING FORMULATIONS

•Hard Problems can often be Formulated as I.P.s.

•These I.P.s are often Solved via Branch and Bound

•Many Applications of I.P. Formulations in– Workforce scheduling– Crew Scheduling

I.P. FORMULATION OF WORKFORCE SCHEDULING

PROBLEM•Predetermined Cycle of m Periods

•During Period i presence of bi needed

•n Different Shift Patterns•Shift Pattern j a1j 0

a2j 1. 1. 1. 0amj 0

•cj is Cost of Assigning one Person to Shift j

•xj is Integer Decision Variable Representing Number Assigned to Shift j

MINIMIZEc1 x1 + c2 x2 + …. + cn xn

SUBJECT TO:a11 x1 + a12 x2 + … + a1n xn > b1

a12 x1 + a22 x2

. .

. .

. .

am1 x1 + am2 x2 + … + amn xn > bm

xj Integer

I.P. FORMULATION OF CREW SCHEDULING PROBLEM

• m Jobs (Flight Legs)• n Feasible Combinations of Jobs one Crew can

Handle (Round Trips)

• cj Cost of Round Trip j

INTEGER PROGRAM

• min c1 x1 + x2 x2 + …. + cn xn

• S.T. a11 x1 + a12 x2+ …. + ain xn > 1

am1 x1 + am2 x2+ ….+ amn xn > 1

xj {0, 1}

• Each Column is a Round Trip• Each Row is a Job that must be Covered

SET PARTITIONING PROBLEM

DISJUNCTIVE PROGRAMMING FORMULATIONS

•Hard Problems can often be Formulated as Disjunctive Programs

•These Programs are often Solved via Branch and Bound

•Many Applications of Disjunctive Programs in Job Shop Scheduling

MINIMIZING THE MAKESPANIN A JOB SHOP

pij = processing time of job j on machine i

yij = starting time of job j on machine i

DISJUNCTIVE PROGRAMMinimize Cmax

Subject toykj - yij > pij For All (i, j) (k, j)

Cmax - yij > pij For All (i, j)

yij - yiℓ > pi ℓ or yiℓ - yij > pij For All (i, ℓ) ( i, j)

yij > 0 For All (i,j)

There are Disjunctive Programs for Job Shopswith other Objectives

LOCAL (NEIGHBORHOOD) SEARCH METHODS

•Simulated Annealing(Probabilistic

Method)•Tabu-Search

(Deterministic Method)

•Genetic Algorithms

IMPORTANT CHARACTERISTICS OF LOCAL SEARCH PROCEDURES

•Schedule Representation Needed for Procedure

•The Neighborhood Design•The Search Process within

the Neighborhood•The Acceptance-Rejection

Criterion

DECOMPOSITION TECHNIQUES•Machine Decomposition

(Shifting Bottleneck Techniques)•Temporal Decomposition

IMPORTANT CHARACTERISTICS OF DECOMPOSITION TECHNIQUES

•Select as the next Subproblem to Solve always the one that Appears the Hardest

(“Follow the Path of the Most Resistance”)•After the Completion of Each Step, Reoptimize

all the Steps that were Done Before

HYBRID METHODS• Scheduling techniques can be

Combined in Series•E.G., FIRST USE A DISPATCHING RULE,

THEN FOLLOW UP WITH A LOCAL SEARCH

• Scheduling Techniques can be Combined in an Integrated Manner

•E.G., A DISPATCHING RULE CAN BE USED WITHIN A BRANCH AND BOUND TO OBTAIN UPPER BOUNDS.

•DYNAMIC PROGRAMMING ROUTINE CAN BE USED FOR A SINGLE MACHINE SUBPROBLEM WITHIN A MACHINE DECOMPOSITION TECHNIQUE

Part IV.

System Implementation Issues

Commercial Packages

ERP-SYSTEMSSAP, Baan, JD Edwards, People Soft

GENERAL OPTIMIZATIONIlog, Dash

GENERAL SCHEDULING(Often in Framework of Supply Chain

Management)I2, Cybertec, AutoSimulation, IDS Professor

ScheerSCHEDULING OIL AND PROCESS INDUSTRIES

Haverly Systems, Chesapeake, FinitySCHEDULING CONSUMER PRODUCTS

Manugistics, NumetrixSCHEDULING WORKFORCE IN CALL CENTERS

AIX, TCS, Siebel

ROBUSTNESS

• Unexpected (Random) Events• Inaccuracy of Data

CAUSES OF PERTURBATIONS:

ValueObjective

Solution Space

MEASURES OF ROBUSTNESS• δ - Perturbation; Amount of Time

Completion of a Task is Postponed

•Z - Value of the Objective UnderOriginal Schedule

•Z1 - Value of the Objective Under New Situation (without rescheduling)

Z1 - Zδ

= L (δ) L (δ)

δ

OPTION: Reschedule After Perturbation

•Local Rescheduling•Global Rescheduling

PRACTICAL CONSIDERATION:•New Schedule Should be Similar to Old Schedule(Distance Measure)

RULES TO FOLLOW IN ORDER TO GENERATE ROBUST SCHEDULES

• Insert Idle times(Especially Where Perturbationsare to be Expected)

• Less Flexible Job FirstMore Flexible Jobs Later

• Do NOT Postpone Processing when Possible(NOTE: This Would Go Against JIT Principles)

LEARNING MECHANISMS

• Rote Learning(When Solution Space is Relatively

Small)• Classifier Systems

(Often Based on Genetic Algorithms)

• Case Based Reasoning(Parameter Adjustment Methods)

• Induction Methods and Neural Nets

PARAMETER ADJUSTMENTATCS - RuleIj (t, ℓ ) =wj exp (- (dj-pj-t)+) exp (- sℓ j)pj k1p k2 s

k1 and k2 are hard to determine

k1 and k2 Functions of–Due Date tightness τ–Due Date Range R–Setup Time Severity η

ON-LINE LEARNING

Every Time the Problem is Solved, the Problem is also Solved for k1 + δ, k1 - δ, k2 +

δ, k2 - δ

Dependent Upon the Outcome the Parameters are Adjusted for the Next Time.

NEURAL NETApplication:

•m Resources in Parallel•Different Speeds•Setups

INPUT UNIT

OUTPUT UNIT

HIDDEN UNITS• Jobs Arrive at Different Times• Jobs Have Due Dates

Machines have Attributes• Increase in Total Weighted Completion Time• Increase in Number of Late Jobs•Current Number of Jobs on Machine

OFF-LINE TRAINING BY AN EXPERT

Expert Plus LearningAlgorithm (Back Propagation)Determine the Connection Weights

MULTIPLE OBJECTIVESEXAMPLE:

•m Resources in Parallel•n Jobs•Due Dates•Sequence Dependent Setups

OBJECTIVES:•Minimize Sum of Setup Times•Minimize Penalties Due to Late Delivery

Weights of the Two Objectives Vary over Time and Depend on Status Quo.

GENERAL FRAMEWORK:

• Mixing of Priority Rules• Switching Over Between Rules

Scaling Parameters and Switch-Over Times Depend on the Data Set

Framework Above can be Combined with Local Search Heuristic.

DESIGN ISSUES WITH REGARD TO DECISION SUPPORT SYSTEMS

FOR PLANNING AND SCHEDULING

•Robustness•Multiple Objectives•Learning mechanisms

Michael PinedoStern School of BusinessNew York University

DECISION SUPPORT SYSTEMS

•Forecasting•Facility Location•Supply Chain

Management•Routing and Distribution

PLANNING AND SCHEDULING

•Characteristics:–Engines Often Based on

Combinatorial Algorithms

–Systems Often have to Operate in Real Time

IMPORTANCE OF PLANNING AND SCHEDULING SYSTEMS

• 150 Software Companies– I2– Manugistics– Bender-Synquest– IDS - Scheer– SAP– Bran

PLANNING AND SCHEDULING FRAMEWORK

• Resources (Machines)• Tasks (Jobs)• Due Dates• Objectives

GOAL:

• Determine a Schedule (solution)That Minimizes the Objective(s)