Modeling Scheduling Problems Agenda Overview of Models Notation

Modeling Scheduling Problems Agenda · Overview of Models · Notation · Objectives · Machine Configurations · Processing Characteristics · Constraints 12/15/2021 45 -865 Sequencing and Scheduling 1

Overview of models · Project Scheduling ¨ precedence constraints ¨ minimize makespan ¨ critical tasks can be identified · Job Shop Scheduling 2

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 3

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. 4

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 5

Notation Model representation: Machine Configuration | Constraints | Objectives 6

Notation- Completion time Resources 1 1 2 4 3 3 4 2 1 2 4 3 1 Time C 4 3 2 C 1 C 2, C 3 7

Objectives · Flowtime ¨ Time job j spends in the system ¨ Flow time: Fj = Cj - rj 1) Minimize average flowtime 2) Minimize maximum flowtime 8

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(C 1, C 2, …, Cn ) 9

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: 10

Objectives-due date related Lj Tj dj Lateness of a job Cj dj Cj Tardiness of a job 11

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 12

Machine Configurations Single-Machine Parallel-Machine 13

Machine Configurations Flow Shop Job Shop 14

Processing Characteristics · Sequence-Dependent Setup Times and Costs ¨ Length of setup depends on jobs ¨ : 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 15

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 16

Constraints · Material Handling Constraints Completion time · · Start time Storage Space Constraints Machine Eligibility Jobs Tooling and Resource Personnel Buffer Space Machines 17