A Method for Resolving a Schedule

1. How can the widgets have different priorities in different processes? I'd have thought priorities would be assigned by widget.

2. Can a given process run simultaneously on several widgets?

Is one to assume that each process is linear (one after the other) and not parallel (each process is only being done on one widget at a time)? Also, can one assume that the order of the processes will be different for each widget?

One thing seems obvious to me, unless I am missing something, that there is a lot of wasted time waiting for a process to begin if all widgets started at the same time.

The process for the first process is going to set the priorities for the other processes by default...first come first served. Otherwise there is a lot of wasted waiting time.

Widget #3 takes 12.5 days to complete without waiting time and would logically start first on the first process. If it had to wait for widgets 1 and 2 to finish process 1 it would be waiting 2.2 days just to get started. Widget 4 would have to wait 3.9 days to get started and couldn't possibly finish on time. Widget 3 would have to start first and not waste any time just to finish on time.

The starting times have to be staggered so that at some point all processes are being carried out simultaneously thereby eliminating a lot of waiting time.

So does this look like a good result?

Row\Col	H	I	J	L	M	N
2	Widget	Process	Minutes	Start	End
3	Widget 3	Process 1	600	0	600
4	Widget 1	Process 1	300	600	900
5	Widget 2	Process 1	500	900	1400
6	Widget 4	Process 1	400	1400	1800
7	Widget 3	Process 2	900	600	1500
8	Widget 2	Process 2	600	1500	2100
9	Widget 1	Process 2	750	2100	2850
10	Widget 4	Process 2	600	2850	3450
11	Widget 1	Process 3	1200	2850	4050
12	Widget 4	Process 3	1400	4050	5450
13	Widget 3	Process 4	1500	1500	3000	Done
14	Widget 2	Process 4	1350	3000	4350	Done
15	Widget 1	Process 5	1200	4050	5250	Done
16	Widget 4	Process 5	200	5450	5650	Done

The priority column in my sheet is the order that the processes must take place. So on process 1 for example, widget 1 has to be started first because it is priority one, and then widget 2 must be made and so on.

That certainly doable, but it does not optimize total processing time.

I'm out unless you choose to clarify that this is a real problem, and why the arbitrary constraints are applied.

My thought process was almost identical to that of shg.

You wanted to know why widget 3 had to be started first. I have explained that in msg #3. Priorities as far as my own experience is concerned is to maximize the use of resources to minimize wasted time in order to efficiently meet deadlines. That does not seem to be the case here.

I'm out.

Ditto .

@ndm:

A BUAGC* of the process flows shown in the prior post:

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*Butt-Ugly ASCII Gantt Chart

Row\Col	B	C	D	E	F	G	H	I	J
2	Widget	Process	Time	Pri	Start	End
3	Widget 1	Process 1	6	1	0	6			F3: =MAX(IFERROR(LOOKUP(2, 1/(B$2:B2=B3), G$2:G2), 0), IFERROR(LOOKUP(2, 1/(C$2:C2=C3), G$2:G2), 0))
4	Widget 2	Process 1	10	2	6	16			G3: =F3+D3
5	Widget 3	Process 1	12	3	16	28			H3: =IF(COUNTIF(B3:B$16, B3) = 1, "Done", "")
6	Widget 4	Process 1	8	4	28	36
7	Widget 3	Process 2	18	1	28	46
8	Widget 2	Process 2	12	2	46	58
9	Widget 1	Process 2	15	3	58	73
10	Widget 4	Process 2	12	4	73	85
11	Widget 1	Process 3	24	1	73	97
12	Widget 4	Process 3	28	2	97	125
13	Widget 3	Process 4	30	1	46	76	Done
14	Widget 2	Process 4	27	2	76	103	Done
15	Widget 4	Process 5	4	1	125	129	Done
16	Widget 1	Process 5	24	2	129	153	Done

I divided all the times by their greatest common denominator (50). Multiply it back and you have your original numbers.

Divide the end time (153 in the last post) by the number of processing minutes in a day, and add it to the start date to get finish date.

@shg

Your Gantt chart reminds me of the method I had before I had a computer and scheduling software. I would use graph paper and cut strips to length to represent processes and their time requirements....worked great. I could shuffle the strips around until I found the most efficient setup.

Probably gave you a deeper understanding of the complexities to consider algorithms later.

@shg
For sure it certainly helped in the development of the methodology to solve later problems.