Lecture No 22

Held on: October 16, Monday

Notes Prepared by: Vivek Gupta

 

SCHEDULING AND SEQUENCING

It deals with:-

• At what time the job be processed?
• How to schedule job?
• How to allocate employees?

Definition:-

• Sequencing: Arranging in order.
• Scheduling: Also includes the time when a process has to be done.

It includes:-

    1) Allocate scarce resources to activities over time.

• Orders in which jobs are completed on a machine.
• Order in which loan application process a bank.
• Order in which sequencing computer service requests at CPU.
• Plane landing:-( Not dependent on first come first serve basis-It may depend on size of the aircraft.)
• How to serve the patient sitting outside the doctor's room.

    Here we are going to use deterministic model i.e. the processing time will be assumed. We use deterministic model as a simplification as actual time is not always constant but varies slightly. e.g. 10+-.05. Here we take time as 10 min and neglect +-0.5.

    2) Scheduling on a single process. e.g. Doctor's clinic.

•  Many times whole plant may be thought of a single process. e.g. . shop is making cars, trucks and the problem is of scheduling that which product has to be made.
• Typically, a single bottleneck exists where optimal scheduling is critical means if there is a bottleneck then the problem reduces to single process.
• Serves as a building block to understand more complex scheduling issue.

        Optimization on a single machine may not give optimal solution for whole system in all cases.
 

Simplifying Assumptions:-

1. All jobs for processing are available at time t=0.
2. Set up times are independent of job sequences thus they are included in processing time.

           This is useful when some all the machines are not used in the sequencing.

1. No break downs occur in processing facility.

Notations:-
        Pi    :    Processing times for job i ( includes setup time).
        Di    :    Due date for job i.
        Ri    :    Arrival time for job i. ( Here Ri=0)
        Wi    :    Waiting time for job i.
        Ci    :    Completion time for job i.
        Fi    :    Flow time for job i.
                        Fi = Ci - Ri    Here Fi = Ci.
                             = Wi + Pi.
        Ti    :    Tardiness for the job i. --> It measures how late you are.
                        If ( Ci - Di) > 0 then Ti = Ci - Di.
                        It means that if you are early no reward is awarded but if late penalty is imposed.

 

Some Criteria for assessing scheduling policy:

·        Minimize average tardiness   i.e.  1/nSTi.

·        Minimize average flow time i.e.   1/nSFi à ( min work in process)                                                    

The reason of minimizing average flow time are:

·       Cost is proportional to it.

·       It may be satisfactory to customer.

·       Minimize maximum tardiness

Tmax = max Ti

·       Minimize number of tardy jobs.

It may help in number of order you loose.

 

Example of Scheduling Procedures:

        SPT (Shortest Processing Time Procedure)

Product	Production Time	Due Date
1	4	6
2	7	9
3	2	19
4	8	17

Here SPT is <3, 1, 2, 4> depending on increasing production time.

Flow time (Fi) for i th process = SP( for 1 to i-1)+Pi

Average Flow Time = (F1+F2+F3+F4)/4

                                = (6 + 13 + 2 + 21)/4 = 10.5

                 i-1                        P_i   P _i+1

If we are not using SPT then there is atleast one pair such that P_i>P _i+1

If we have SPT then P1<=P2<=P3<=P4……<=Pn

Before interchanging, let the flow time of i and i+1 process be c+Pi and c+P_i+P _i+1 .

After interchanging i th process by i +1 th

        The time becames 2c+2P_i+P _i+1  and 2c+P_i+2P _i+1

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