Download - CURRENT TRENDS IN DETERMINISTIC SCHEDULING 1- Scheduling Theory 2- Search Algorithms 3- Scheduling Practice 1- Scheduling Theory 2- Search Algorithms 3-

CURRENT TRENDS IN DETERMINISTIC SCHEDULING

1- Scheduling Theory2- Search Algorithms3- Scheduling Practice


Recent Developments in;

Recent Developments in Scheduling Theory:

Classical Scheduling : Machine

Job1-job-on-1-machine

0< r 1Jobs

r positive integer

1-job-on-r-machine :

Job


EXAMPLES

Berth allocation problem :• A large vessel may occupy several berths for loading/unloading (r is a positive integer)• Several vessels may share one berth (0 < r 1)

Parallel computing systems :• In order to detect faults , a job may need to be processed by several processors. (r positive integer)


r positive integer

Each job may require a fixed number of machines, yet the machines required are not specified. nonfix

The set of machines for particularjobs are specifically fixed fix

Most problems in the 1-job-on-r-machine pattern are NP-hardexcept for some special cases!


Machine Scheduling with availability constraints :

• Most studies assume that machines are always available.

• In real industry settings this assumption may not be true.

Reasons for machines not being available all the time: • Machine breakdown (stochastic)• Preventive maintenance during the scheduling period (deterministic).


Deterministic Case

• Machine i is unavailable from sik until tik (0 sik tik ) 0 k ni ni : the number of unavailability periods during the planning horizon.

...Machine i

ni= 2

0 tSi1 ti1 Si2 ti2End of

planning horizon


In most manufacturing cases ni 1, because it is unlikely to have more than one preventive maintenance during the planning horizon.

Two cases for these problems :

i- Resumable: If a job cannot be finished before the next down period of a machine and the job can continue after the machine has become available again

ii- Nonresumable: If the job has to restart rather than continue.

Recent Developments in Search Algorithms:

• Many scheduling problems are so complex

• Cannot be formulated easily as mathematical problems

Two types of search techniques :

i- Neighbourhood search techniquesii- Constraint-guided heuristic search techniques


Neighbourhood search techniques: Based on local improvement

Global minLocal min

• Fairly modest programming effort is required• Structural knowledge needed with regard to the problem is significantly less than the knowledge required for a mathematical programming approach.


Design criteria to compare various neighbourhoodsearch techniques:

i- The mapping of the data in a format suitable for the algorithm: The description of a schedule should be both concise and unambiguous

ii- The neighbourhood design: Specifies the set of all the neighbours of a given solution. e.g. in a single machine scheduling problem, the neighbourhood of any given schedule can consist of all schedules that can be obtained through a pairwise swap.


iii- The search process within the neighbourhood: A search has to be conducted that leads to the next schedule in the search process. A simple way is to select schedules in the neighbourhood at random, evaluate these schedules and decide which one to accept.

iv- The acceptance-rejection criterion: Whenever a schedule within the neighbourhood is selected, a decision has to be made whether or not to accept.

Design criteria to compare various neighbourhoodsearch techniques:


Three main techniques of neighbourhood search:i- Simulated annealingii- Tabu search (Applied most often to scheduling problems)iii- Genetic algorithms


Simulated Annealing and Tabu Search:Have many characteristics in common

The difference between them lies in the acceptance-rejection criterion

Simulated annealing : (Probabilistic)Iteration k: Sk S S is accepted with probability:

( ) ( )( , ) exp k

kk

G S G SS S

P

And rejected with 1-P(Sk,S), The parameters are referred to as cooling parameters.Tabu Search : (Deterministic)Keeps track mutations made to go from a schedule to a neighbouring one in tabu list consisting of a fixed number of entries (5-15).

Cycling!


Simulated annealingJob shop scheduling problems withmakespan objective

Tabu search

Single machine, parallel machine, flow shop, flexible flow shop, job shop with objectives that include makespan, total weighted completion time, total weighted tardiness.


Genetic Algorithms :

subchromosomes

generations

chromosomes

Least fittest individual

...

mutationCross-over


• Genetic algorithms are more powerful than simulated annealing and tabu search since they are special cases of genetic algorithms with the number of individuals in each generation is equal to one but at the same time slower than them since genetic algorithms keep track of multiple solutions at each iteration.

• Recently being applied to scheduling problems in particular to the job shop scheduling problems with makespan objective.


Constraint-guided heuristic techniques :

• Completely different from neighbourhood search techniques.

• Do not attempt to find optimal schedules; merely seek to find a good feasible schedule

• The problem is formulated through a list of rules or constraints that the schedule has to satisfy

• Focuses on partial solutions and attempt to extend these partial solutions until a complete solution is obtained that is feasible.

• Most stringent constraints are tried to satisfy first and less stringent constraints are left for the final part of the search process.


Many of the research on this field are gathered around:

• Constraint relaxation techniques: Hard vs. soft constraints

• Constraint Propagation: Implied constraints

• Conflict Resolution: Consistency checking

Recent Developments in Scheduling Practice:

Some emerging new applications of scheduling :

• Flexible resource scheduling

• Scheduling variable speed machines

• Scheduling with finite capacity input and output machines

• Scheduling of machine and material handling operations

• Integrating scheduling with batching and lot-sizing


Scheduling of machine and material handling operations

• Differs from classical scheduling in the sense that two types of resources are involved: machines and material handling devices.

• Material handling can take a significant portion of the total cost, at times 80%.


Scheduling of machine and material handling operations

In these problems following issues must be addressed simultaneously:

• Sequencing that specifies the order in which jobs are processed at machining centers

• Scheduling that makes time-phased routing and dispatching of transporters for job pick-up and delivery

• Facility layout and flowpath design that makes efficient operations possible

Due to combinatorial nature of the problems, finding an optimal solution that addresses all these issues at the same time is very difficult.


…

...

n jobs

m machining centers

Input buffer

Output buffer

K identical transporters

Transporters andmachines can hold1 job at a time

Flowpath


Recent work can be divided into:

i- Robotic cell scheduling

ii- Scheduling of Automated Guided Vehicles (AGVs)

iii- Cyclic scheduling of hoists subject to time-window constraints

Differ mainly in the structure of their constraints:Robotic cell scheduling problem has the fewest constraints while cyclic scheduling of hoists with time windows is the most restrictive


Robotic Cell Scheduling Problem :

...

Main concern is to find the job input sequence and therobot move sequence with respect to a certain objective.


Among the three problems robotic cell scheduling is the one for which most analytical results are available.

Can be analysed in following categories:i- The no-buffer case (most research considers this case)ii- The finite-buffer case

Also many variations of the problem exists such as multiple parts or identical parts to be scheduled, number of machines in the cell etc.


Scheduling of AGVs :

Deals with automated job shop with non-zero buffers at machining centers and multiple AGVs travelling on a shared network.

Main concern is how to schedule the moves of AGVs in a traffic network so that traffic collusions are eliminated and the risk of machine blocking is minimized.


Flowpaths :

i- Unidirectional( )

ii- Bidirectional( ): Higher control and implementation cost, greaterpotential to improve productivity, fewer AGVs, reduced travel time

Network Configurations :i- Single-loop : All machines accessible via the loop, avoiding AGVcollusions easy

ii- Multi-loop : AGV collusion and machine blocking are the majorconcerns in scheduling.

Many results developed for the robotic cell scheduling problemscan be applied to the cases with single loop and zero buffer.


Analytical approaches that guarantee optimal objective functionvalues are limited to special cases.

AGV dispatching rules can be classified into:

i- Work center-initiated rules : Work center selects an AGV whenever it finishes an operationii- Vehicle-initiated rules : AGV selects a pick up when it becomes idle

a-Pull-based policy: Work center with the highest need of job replenishment is selected, then a job that can be sent to this work center is selected among the candidatesb-Push-based policy: First a job is selected and then a work center to which the job should be sent.


The Hoist Scheduling Problem

• Most distinct feature is that the job processing time at each machine is strictly limited by a lower and an upper bound.

• Hoist schedule that causes a hoist not to pick up a job within the time window is infeasible.

• Also the traffic collusions must be eliminated.

• Single hoist scheduling problem with numerical processing times can be viewed as a special case of robotic cell scheduling problem

• Multiple hoist problem can be considered as a special class of AGV scheduling problems.