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RE: [Help-glpk] GLPK shift coverage example
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From: |
D'Agostino, Larry - TX |
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Subject: |
RE: [Help-glpk] GLPK shift coverage example |
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Date: |
Thu, 26 Mar 2009 09:55:40 -0500 |
Sorry about the formatting. This should work.
/* File: shiftcover.mod */
/* WORKFORCE SHIFT COVERAGE assignment problem */
/* Written by Larry D'Agostino <larrydag -at- sbcglobal -dot- com>
Maximize Productivity with Industrial Engineer and Operations Research
Tools
http://industrialengineertools.blogspot.com
/* The WORKFORCE SHIFT COVERAGE is an assigment problem that determines
the schedule of crew given available time and shifts.
The objective is to cover the available time given hourly demand with the
minimum
number of crew members.
This is a set covering problem that is very common among finding crew
and shift allocations. Notice in the data section the workforce shift
allocation
per day of the week.*/
/* ----- Model PARAMTERS and SETS -----*/
param numhrs;
/* number of hours of operations in a given day */
param dys;
/* number of days in a week */
set S;
/* set of crew shifts */
set H := 1..numhrs;
/* set of hours of a day*/
set D;
/* set of days of a week*/
param dmnd{h in H, d in D};
/* demand for crew members given h hour and d day */
param shifts{d in D, h in H, s in S};
/* shifts to assign to crew members given d day, h hour, and s shift schedule
/*----- Model VARIABLES -----*/
var crew{s in S}, integer, >=0;
/* number of crew assigned to shift S */
/*----- Model CONSTRAINTS -----*/
s.t. Coverage{h in H, d in D}: sum{s in S} crew[s]*shifts[d,h,s] >= dmnd[h,d];
/* number of crew to cover with a shift given hourly demand and day */
/*----- Model OBJECTIVE -----*/
minimize obj: sum{s in S} crew[s];
/* minimize number of crew to cover demand*/
solve;
display crew;
printf "\n";
printf "Total Crew: %3d\n\n", sum{s in S} crew[s];
printf "\n\n";
printf "Weekly Crew Schedule\n\n";
printf "Hour ";
printf{d in D} " %s ", d;
printf "\n";
for {h in H} {
printf " %2s ",h;
printf{d in D} " %3d ", sum{s in S} crew[s]*shifts[d,h,s];
printf "\n";
}
printf"\n";
data;
param numhrs := 16;
set D := SUN, MON, TUE, WED, THU, FRI, SAT;
set S := Sh1, Sh2, Sh3, Sh4, Sh5, Sh6, Sh7, Sh8, Sh9;
param dmnd : SUN MON TUE WED THU FRI SAT :=
1 0 3 3 4 3 2 0
2 0 14 14 16 14 12 12
3 0 24 24 27 24 20 15
4 0 28 28 32 28 23 15
5 0 33 33 37 33 24 16
6 0 34 34 38 34 24 15
7 0 35 35 39 35 25 11
8 0 35 35 40 35 27 0
9 0 34 34 39 34 25 0
10 0 31 31 35 31 24 0
11 2 24 24 27 24 25 0
12 3 19 19 21 19 21 0
13 2 24 24 27 24 13 0
14 2 16 16 18 16 0 0
15 0 7 7 7 7 0 0
16 0 5 5 5 5 0 0;
param shifts :=
['SUN',*,*]:
Sh1 Sh2 Sh3 Sh4 Sh5 Sh6 Sh7 Sh8 Sh9 :=
1 0 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0 0
3 0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0 0
5 0 0 0 0 0 0 0 0 0
6 0 0 0 0 0 0 0 0 0
7 0 0 0 0 0 0 0 0 0
8 0 0 0 0 0 0 0 0 0
9 0 0 0 0 0 0 0 0 0
10 0 0 0 0 0 0 0 0 0
11 0 0 0 0 0 0 0 0 1
12 0 0 0 0 0 0 0 0 1
13 0 0 0 0 0 0 0 0 1
14 0 0 0 0 0 0 0 0 1
15 0 0 0 0 0 0 0 0 0
16 0 0 0 0 0 0 0 0 0
['MON',*,*]:
Sh1 Sh2 Sh3 Sh4 Sh5 Sh6 Sh7 Sh8 Sh9 :=
1 1 0 0 0 0 0 0 0 0
2 1 1 0 0 0 0 0 0 0
3 1 1 1 0 0 0 0 0 0
4 1 1 1 1 0 0 0 0 0
5 0 1 1 1 1 0 0 0 0
6 1 0 1 1 1 1 0 0 1
7 1 1 0 1 1 1 1 0 1
8 1 1 1 0 1 1 1 1 1
9 1 1 1 1 0 1 1 1 1
10 0 1 1 1 1 0 1 1 1
11 0 0 1 1 1 1 0 1 0
12 0 0 0 1 1 1 1 0 1
13 0 0 0 0 1 1 1 1 1
14 0 0 0 0 0 1 1 1 1
15 0 0 0 0 0 0 1 1 1
16 0 0 0 0 0 0 0 1 1
['TUE',*,*]:
Sh1 Sh2 Sh3 Sh4 Sh5 Sh6 Sh7 Sh8 Sh9 :=
1 1 0 0 0 0 0 0 0 0
2 1 1 0 0 0 0 0 0 0
3 1 1 1 0 0 0 0 0 0
4 1 1 1 1 0 0 0 0 0
5 0 1 1 1 1 0 0 0 0
6 1 0 1 1 1 1 0 0 1
7 1 1 0 1 1 1 1 0 1
8 1 1 1 0 1 1 1 1 1
9 1 1 1 1 0 1 1 1 1
10 0 1 1 1 1 0 1 1 1
11 0 0 1 1 1 1 0 1 0
12 0 0 0 1 1 1 1 0 1
13 0 0 0 0 1 1 1 1 1
14 0 0 0 0 0 1 1 1 1
15 0 0 0 0 0 0 1 1 1
16 0 0 0 0 0 0 0 1 1
['WED',*,*]:
Sh1 Sh2 Sh3 Sh4 Sh5 Sh6 Sh7 Sh8 Sh9 :=
1 1 0 0 0 0 0 0 0 0
2 1 1 0 0 0 0 0 0 0
3 1 1 1 0 0 0 0 0 0
4 1 1 1 1 0 0 0 0 0
5 0 1 1 1 1 0 0 0 0
6 1 0 1 1 1 1 0 0 1
7 1 1 0 1 1 1 1 0 1
8 1 1 1 0 1 1 1 1 1
9 1 1 1 1 0 1 1 1 1
10 0 1 1 1 1 0 1 1 1
11 0 0 1 1 1 1 0 1 0
12 0 0 0 1 1 1 1 0 1
13 0 0 0 0 1 1 1 1 1
14 0 0 0 0 0 1 1 1 1
15 0 0 0 0 0 0 1 1 1
16 0 0 0 0 0 0 0 1 1
['THU',*,*]:
Sh1 Sh2 Sh3 Sh4 Sh5 Sh6 Sh7 Sh8 Sh9 :=
1 1 0 0 0 0 0 0 0 0
2 1 1 0 0 0 0 0 0 0
3 1 1 1 0 0 0 0 0 0
4 1 1 1 1 0 0 0 0 0
5 0 1 1 1 1 0 0 0 0
6 1 0 1 1 1 1 0 0 0
7 1 1 0 1 1 1 1 0 0
8 1 1 1 0 1 1 1 1 0
9 1 1 1 1 0 1 1 1 0
10 0 1 1 1 1 0 1 1 0
11 0 0 1 1 1 1 0 1 0
12 0 0 0 1 1 1 1 0 0
13 0 0 0 0 1 1 1 1 0
14 0 0 0 0 0 1 1 1 0
15 0 0 0 0 0 0 1 1 0
16 0 0 0 0 0 0 0 1 0
['FRI',*,*]:
Sh1 Sh2 Sh3 Sh4 Sh5 Sh6 Sh7 Sh8 Sh9 :=
1 1 0 0 0 0 0 0 0 0
2 1 1 0 0 0 0 0 0 0
3 1 1 1 0 0 0 0 0 0
4 1 1 1 1 0 0 0 0 0
5 0 1 1 1 1 0 0 0 0
6 1 0 1 1 1 1 0 0 0
7 1 1 0 1 1 1 1 0 0
8 1 1 1 0 1 1 1 1 0
9 1 1 1 1 0 1 1 1 0
10 0 1 1 1 1 0 1 1 0
11 0 0 1 1 1 1 0 1 0
12 0 0 0 1 1 1 1 0 0
13 0 0 0 0 1 1 1 1 0
14 0 0 0 0 0 1 1 1 0
15 0 0 0 0 0 0 1 1 0
16 0 0 0 0 0 0 0 1 0
['SAT',*,*]:
Sh1 Sh2 Sh3 Sh4 Sh5 Sh6 Sh7 Sh8 Sh9 :=
1 0 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0 1
3 0 0 0 0 0 0 0 0 1
4 0 0 0 0 0 0 0 0 1
5 0 0 0 0 0 0 0 0 1
6 0 0 0 0 0 0 0 0 1
7 0 0 0 0 0 0 0 0 1
8 0 0 0 0 0 0 0 0 0
9 0 0 0 0 0 0 0 0 0
10 0 0 0 0 0 0 0 0 0
11 0 0 0 0 0 0 0 0 0
12 0 0 0 0 0 0 0 0 0
13 0 0 0 0 0 0 0 0 0
14 0 0 0 0 0 0 0 0 0
15 0 0 0 0 0 0 0 0 0
16 0 0 0 0 0 0 0 0 0;
-----Original Message-----
From: Andrew Makhorin [mailto:address@hidden
Sent: Thursday, March 26, 2009 9:37 AM
To: D'Agostino, Larry - TX
Cc: 'address@hidden'
Subject: Re: [Help-glpk] GLPK shift coverage example
Hi Larry,
> I #8217;ve been working on a workforce shift coverage model recently.
> The purpose is to find an optimal shift schedule given various shift
> schedule proposals. The example below is just one proposal. This is a
> very common problem among assigning crew members to a given shift
> allotment to cover demand. I think this type of problem makes for a
> great example.
Thank you very much for your example model.
> Andrew, feel free to use this model as an example in GLPK
> (if you feel it has not been used already). I #8217;m sure your going to
> have to modify the formatting as I copied it over from GUSEK. And as
> always I would welcome critiques and (better yet) improvements.
>
> File: shiftcover.mod
Could you please re-post your model as a plain text attachment?
There is a formatting problem. Thanks.
Andrew Makhorin