decision support systems for planning and scheduling in practice
TRANSCRIPT
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 PRACTICEI. 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 Effects
After 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)
orSijk = 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 ReoptimizationInternal 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 andObjective 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 iyij = 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 Shops
with 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
IssuesCommercial 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 Under
Original 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 determinek1 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 UNITOUTPUT
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 SetFramework 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)