Question

Chapter 10: Currently a company that designs Web sites has five customers in its backlog. The time since the order​ arrived, processing​ time, and promised due dates are given in the following table.

Job	Time Since Order Arrived (days ago)	Processing Time (days)	Due Date (days from now)
A	6	18	66
B	3	24	58
C	2	32	80
D	10	22	26
E	8	12	50

1. Create a schedule using the first-come first-serve (FCFS) rule, calculating the average flow time and average days past due.
2. Create a schedule using the earliest due date (EDD) rule, calculating the average flow time and average days past due.
3. Comment on the performance of the FCFS and EDD rules relative to average flow time and average days past due.

Answer 1

a.

Schedule using first-come first-serve (FCFS) rule :

Arrange jobs in their arrival order chronologically ,

which would be D, E, A, B, C as per time since order arrived in days ago, in the table given

Now the table below provides the Schedule using FCFS :

Job	Time Since Order Arrived (days ago)	Start time	Processing Time (days)	End Time (= Start Time + Processing Time)	Flow TIme (= TIme Since order Arrived +End Time)	Due Date (days from now)	Days Past Due (= End Time - Due Date ; when End Time > Due Date else 0 )
D	10	0	22	22	32	26	0
E	8	22	12	34	42	50	0
A	6	34	18	52	58	66	0
B	3	52	24	76	79	58	22
C	2	76	32	108	110	80	28

All the bold lettered columns in above table are taken directly from the given table and the rest columns values are calculated as per equation given which is self explanatory.

Average Flow time = (32 + 42 + 58 + 79 +110 ) / 5 = 321 / 5 = 62.5

Average Days Past Due = ( 0 + 0 + 0 +22 + 28) / 5 = 50 / 5 = 10

b.

Schedule using earliest due date (EDD) rule :

Arrange jobs in their earliest due date chronologically ,

which is D, E, B, A, C as per due date, in the table given

Now the table below provides the Schedule using EDD :

Job	Time Since Order Arrived (days ago)	Start time	Processing Time (days)	End Time (= Start Time + Processing Time)	Flow TIme (= TIme Since order Arrived + End Time)	Due Date (days from now)	Days Past Due (= End Time - Due Date ; when End Time > Due Date else 0 )
D	10	0	22	22	32	26	0
E	8	22	12	34	42	50	0
B	3	34	24	58	61	58	0
A	6	58	18	76	82	66	10
C	2	76	32	108	110	80	28

All the bold lettered columns in above table are taken directly from the given table and the rest column values are calculated as per equation given which is self explanatory.

Average Flow Time = (32 + 42 + 61 + 81 + 110) / 5 = 326 / 5 = 65.2

Average Days Past Due = ( 0 + 0 + 0 + 10 + 28 ) / 5 = 38 / 5 = 7.6

c.

We can see

Average Flow Time in FCFS = 62.5 is lesser than in EDD = 65.2

This makes sense , as in FCFS schedule, one prioritises to finish the tasks arrived earlier which in turn improves the Total Flow Time, and hence we find better Average Flow Time.

Average Days Past Due in EDD = 7.6 is lesser than in FCFS = 10

This makes sense , as in EDD schedule, one prioritises to finish the tasks which have earlier due dates, which in turn improves the Total Days Past Due, and hence we find better Average Days Past Due.