Modeling Scheduling Problems
Agenda
 Overview of Models
 Notation
 Objectives
 Machine Configurations
 Processing Characteristics
 Constraints
6/28/2016
45-865 Sequencing and Scheduling
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Overview of models
 Project Scheduling
precedence constraints
minimize makespan
critical tasks can be identified
 Job Shop Scheduling
Jobs
Machine Sequence
1
1, 2, 3
2
2, 1, 4, 3
3
1, 2, 4
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Overview of models
 Job Shop Scheduling
minimize makespan or no of tardy jobs
Mostly for make-to-order manufacturing systems
Also in services
 Flexible Manufacturing Systems
An automated material handling system controls
the movement of jobs
Mostly for mass production systems
Maximize throughput
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Overview of models
 Lot Scheduling
Switching between products incurs a setup cost
Minimize total inventory and setup costs
Process industries, e.g. oil refinery, paper mill
 Reservation Systems
Job start and complete times are fixed
Decide to process the job or not
Maximize no of jobs processed or utilization
Services, e.g. hotels, car rental agencies.
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Overview of models
 Timetabling
Certain jobs use the same equipment and cannot be
processed at the same time
Minimize makespan
Examples: repair shops, classroom scheduling
 Workforce Scheduling
Assign personnel to shifts
Constraints due to equipment requirements and
work rules
Minimize no of employees or total cost
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Notation
Input Data
Processing time (pij )
Output Data
Completion time (Cij or Cj)
Release time (rj )
Due date (dj )
Model representation:
Machine Configuration | Constraints | Objectives
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Notation- Completion time
Resources
1
1
2
4
3
3
4
2
1
2
4
3
1
Time
C4
3
2
C1
C2, C3
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Objectives
 Flowtime
Time job j spends in the system
Flow time: Fj = Cj - rj
1) Minimize average flowtime
2) Minimize maximum flowtime
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Objectives
 Throughput
Flow shop models or continuous processes
Bottleneck machines determine output rate
1) Maximize utilization of the bottleneck
2) Minimize sum of sequence-dependent setups
 Makespan
Determined by the last completed job
Cmax = max(C1, C2, …, Cn )
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Objectives
 Due Date Related Objectives
1) Minimize maximum lateness
Lateness of job j:
Maximum lateness:
2) Minimize number of tardy jobs
Tardiness of job j:
Objective function:
3) Minimize total weighted tardiness:
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Objectives-due date related
Lj
Tj
dj
Lateness of a job
Cj
dj
Cj
Tardiness of a job
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Objectives
 Minimizing Total Cost
1) Setup Costs
2) WIP Inventory Costs
min WIP  min throughput time  min mean flowtime
3) Finished Goods Inventory Costs
4) Personnel Costs
 Minimizing Total Earliness (JIT)
 Maximizing Robustness
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Machine Configurations
Single-Machine
Parallel-Machine
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Machine Configurations
Flow Shop
Job Shop
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Processing Characteristics
 Sequence-Dependent Setup Times and Costs
Length of setup depends on jobs
 sijk : setup time for processing job k after job j on
machine i
Costs: waste of material, labor
 Preemptions
Interrupt the processing of a job to process another
one with higher priority
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Constraints
 Precedence Constraints
Precedence-constraints graph contains no cycles
 Routing Constraints
Specifies a sequence of operations for each job and
the machines at which these operations must be
processed
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Constraints
 Material Handling Constraints
Completion
time




Start time
Storage Space Constraints
Machine Eligibility Jobs
Tooling and Resource
Personnel
Buffer Space
Machines
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