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alpar@1
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/* File: shiftcover.mod */
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alpar@1
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alpar@1
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/* WORKFORCE SHIFT COVERAGE assignment problem */
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alpar@1
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alpar@1
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/* Written by Larry D'Agostino <larrydag -at- sbcglobal -dot- com>
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Maximize Productivity with Industrial Engineer and Operations Research Tools
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http://industrialengineertools.blogspot.com
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alpar@1
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/* The WORKFORCE SHIFT COVERAGE is an assigment problem that determines
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the schedule of crew given available time and shifts.
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The objective is to cover the available time given hourly demand with the minimum
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number of crew members.
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This is a set covering problem that is very common among finding crew
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and shift allocations. Notice in the data section the workforce shift allocation
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per day of the week.*/
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alpar@1
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alpar@1
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alpar@1
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/* ----- Model PARAMTERS and SETS -----*/
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param numhrs;
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/* number of hours of operations in a given day */
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alpar@1
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param dys;
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/* number of days in a week */
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alpar@1
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set S;
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/* set of crew shifts */
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set H := 1..numhrs;
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/* set of hours of a day*/
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alpar@1
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set D;
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/* set of days of a week*/
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param dmnd{h in H, d in D};
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/* demand for crew members given h hour and d day */
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param shifts{d in D, h in H, s in S};
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/* shifts to assign to crew members given d day, h hour, and s shift schedule
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/*----- Model VARIABLES -----*/
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var crew{s in S}, integer, >=0;
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/* number of crew assigned to shift S */
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/*----- Model CONSTRAINTS -----*/
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s.t. Coverage{h in H, d in D}: sum{s in S} crew[s]*shifts[d,h,s] >= dmnd[h,d];
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/* number of crew to cover with a shift given hourly demand and day */
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/*----- Model OBJECTIVE -----*/
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minimize obj: sum{s in S} crew[s];
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/* minimize number of crew to cover demand*/
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solve;
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display crew;
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printf "\n";
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printf "Total Crew: %3d\n\n", sum{s in S} crew[s];
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printf "\n\n";
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printf "Weekly Crew Schedule\n\n";
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printf "Hour ";
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printf{d in D} " %s ", d;
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printf "\n";
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for {h in H} {
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printf " %2s ",h;
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printf{d in D} " %3d ", sum{s in S} crew[s]*shifts[d,h,s];
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printf "\n";
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}
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printf"\n";
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data;
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param numhrs := 16;
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set D := SUN, MON, TUE, WED, THU, FRI, SAT;
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alpar@1
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set S := Sh1, Sh2, Sh3, Sh4, Sh5, Sh6, Sh7, Sh8, Sh9;
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param dmnd : SUN MON TUE WED THU FRI SAT :=
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1 0 3 3 4 3 2 0
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alpar@1
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2 0 14 14 16 14 12 12
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alpar@1
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3 0 24 24 27 24 20 15
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alpar@1
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4 0 28 28 32 28 23 15
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alpar@1
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5 0 33 33 37 33 24 16
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alpar@1
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6 0 34 34 38 34 24 15
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alpar@1
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7 0 35 35 39 35 25 11
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alpar@1
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8 0 35 35 40 35 27 0
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alpar@1
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9 0 34 34 39 34 25 0
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alpar@1
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10 0 31 31 35 31 24 0
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alpar@1
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11 2 24 24 27 24 25 0
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alpar@1
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12 3 19 19 21 19 21 0
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alpar@1
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13 2 24 24 27 24 13 0
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alpar@1
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14 2 16 16 18 16 0 0
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alpar@1
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15 0 7 7 7 7 0 0
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alpar@1
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16 0 5 5 5 5 0 0;
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alpar@1
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param shifts :=
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['SUN',*,*]:
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Sh1 Sh2 Sh3 Sh4 Sh5 Sh6 Sh7 Sh8 Sh9 :=
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alpar@1
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1 0 0 0 0 0 0 0 0 0
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alpar@1
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2 0 0 0 0 0 0 0 0 0
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alpar@1
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3 0 0 0 0 0 0 0 0 0
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alpar@1
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4 0 0 0 0 0 0 0 0 0
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alpar@1
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5 0 0 0 0 0 0 0 0 0
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alpar@1
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6 0 0 0 0 0 0 0 0 0
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alpar@1
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7 0 0 0 0 0 0 0 0 0
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alpar@1
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8 0 0 0 0 0 0 0 0 0
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alpar@1
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9 0 0 0 0 0 0 0 0 0
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alpar@1
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10 0 0 0 0 0 0 0 0 0
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alpar@1
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11 0 0 0 0 0 0 0 0 1
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alpar@1
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12 0 0 0 0 0 0 0 0 1
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alpar@1
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13 0 0 0 0 0 0 0 0 1
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alpar@1
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14 0 0 0 0 0 0 0 0 1
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alpar@1
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15 0 0 0 0 0 0 0 0 0
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alpar@1
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16 0 0 0 0 0 0 0 0 0
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alpar@1
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alpar@1
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alpar@1
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['MON',*,*]:
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Sh1 Sh2 Sh3 Sh4 Sh5 Sh6 Sh7 Sh8 Sh9 :=
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alpar@1
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1 1 0 0 0 0 0 0 0 0
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alpar@1
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2 1 1 0 0 0 0 0 0 0
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alpar@1
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3 1 1 1 0 0 0 0 0 0
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alpar@1
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4 1 1 1 1 0 0 0 0 0
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alpar@1
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5 0 1 1 1 1 0 0 0 0
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alpar@1
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6 1 0 1 1 1 1 0 0 1
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alpar@1
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7 1 1 0 1 1 1 1 0 1
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alpar@1
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8 1 1 1 0 1 1 1 1 1
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alpar@1
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9 1 1 1 1 0 1 1 1 1
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alpar@1
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10 0 1 1 1 1 0 1 1 1
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alpar@1
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11 0 0 1 1 1 1 0 1 0
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alpar@1
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12 0 0 0 1 1 1 1 0 1
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alpar@1
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13 0 0 0 0 1 1 1 1 1
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alpar@1
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14 0 0 0 0 0 1 1 1 1
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alpar@1
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15 0 0 0 0 0 0 1 1 1
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alpar@1
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16 0 0 0 0 0 0 0 1 1
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alpar@1
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alpar@1
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['TUE',*,*]:
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Sh1 Sh2 Sh3 Sh4 Sh5 Sh6 Sh7 Sh8 Sh9 :=
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alpar@1
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1 1 0 0 0 0 0 0 0 0
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alpar@1
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2 1 1 0 0 0 0 0 0 0
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alpar@1
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3 1 1 1 0 0 0 0 0 0
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alpar@1
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4 1 1 1 1 0 0 0 0 0
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alpar@1
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5 0 1 1 1 1 0 0 0 0
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alpar@1
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6 1 0 1 1 1 1 0 0 1
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alpar@1
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7 1 1 0 1 1 1 1 0 1
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alpar@1
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8 1 1 1 0 1 1 1 1 1
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alpar@1
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9 1 1 1 1 0 1 1 1 1
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alpar@1
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10 0 1 1 1 1 0 1 1 1
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alpar@1
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11 0 0 1 1 1 1 0 1 0
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alpar@1
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12 0 0 0 1 1 1 1 0 1
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alpar@1
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13 0 0 0 0 1 1 1 1 1
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alpar@1
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14 0 0 0 0 0 1 1 1 1
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alpar@1
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15 0 0 0 0 0 0 1 1 1
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alpar@1
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16 0 0 0 0 0 0 0 1 1
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alpar@1
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alpar@1
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['WED',*,*]:
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alpar@1
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Sh1 Sh2 Sh3 Sh4 Sh5 Sh6 Sh7 Sh8 Sh9 :=
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alpar@1
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1 1 0 0 0 0 0 0 0 0
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alpar@1
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2 1 1 0 0 0 0 0 0 0
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alpar@1
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3 1 1 1 0 0 0 0 0 0
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alpar@1
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4 1 1 1 1 0 0 0 0 0
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alpar@1
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5 0 1 1 1 1 0 0 0 0
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alpar@1
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6 1 0 1 1 1 1 0 0 1
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alpar@1
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7 1 1 0 1 1 1 1 0 1
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alpar@1
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8 1 1 1 0 1 1 1 1 1
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alpar@1
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9 1 1 1 1 0 1 1 1 1
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alpar@1
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10 0 1 1 1 1 0 1 1 1
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alpar@1
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11 0 0 1 1 1 1 0 1 0
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alpar@1
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12 0 0 0 1 1 1 1 0 1
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alpar@1
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13 0 0 0 0 1 1 1 1 1
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alpar@1
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14 0 0 0 0 0 1 1 1 1
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alpar@1
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15 0 0 0 0 0 0 1 1 1
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alpar@1
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16 0 0 0 0 0 0 0 1 1
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alpar@1
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alpar@1
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['THU',*,*]:
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alpar@1
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Sh1 Sh2 Sh3 Sh4 Sh5 Sh6 Sh7 Sh8 Sh9 :=
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alpar@1
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1 1 0 0 0 0 0 0 0 0
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alpar@1
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2 1 1 0 0 0 0 0 0 0
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alpar@1
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3 1 1 1 0 0 0 0 0 0
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alpar@1
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4 1 1 1 1 0 0 0 0 0
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alpar@1
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5 0 1 1 1 1 0 0 0 0
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alpar@1
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6 1 0 1 1 1 1 0 0 0
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alpar@1
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7 1 1 0 1 1 1 1 0 0
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alpar@1
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8 1 1 1 0 1 1 1 1 0
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alpar@1
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9 1 1 1 1 0 1 1 1 0
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alpar@1
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10 0 1 1 1 1 0 1 1 0
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alpar@1
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11 0 0 1 1 1 1 0 1 0
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alpar@1
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12 0 0 0 1 1 1 1 0 0
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alpar@1
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13 0 0 0 0 1 1 1 1 0
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alpar@1
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14 0 0 0 0 0 1 1 1 0
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alpar@1
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15 0 0 0 0 0 0 1 1 0
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alpar@1
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16 0 0 0 0 0 0 0 1 0
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alpar@1
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alpar@1
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['FRI',*,*]:
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alpar@1
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Sh1 Sh2 Sh3 Sh4 Sh5 Sh6 Sh7 Sh8 Sh9 :=
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alpar@1
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1 1 0 0 0 0 0 0 0 0
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alpar@1
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2 1 1 0 0 0 0 0 0 0
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alpar@1
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3 1 1 1 0 0 0 0 0 0
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alpar@1
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4 1 1 1 1 0 0 0 0 0
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alpar@1
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5 0 1 1 1 1 0 0 0 0
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alpar@1
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6 1 0 1 1 1 1 0 0 0
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alpar@1
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7 1 1 0 1 1 1 1 0 0
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alpar@1
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8 1 1 1 0 1 1 1 1 0
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alpar@1
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9 1 1 1 1 0 1 1 1 0
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alpar@1
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10 0 1 1 1 1 0 1 1 0
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alpar@1
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11 0 0 1 1 1 1 0 1 0
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alpar@1
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12 0 0 0 1 1 1 1 0 0
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alpar@1
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13 0 0 0 0 1 1 1 1 0
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alpar@1
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223 |
14 0 0 0 0 0 1 1 1 0
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alpar@1
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224 |
15 0 0 0 0 0 0 1 1 0
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alpar@1
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16 0 0 0 0 0 0 0 1 0
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alpar@1
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226 |
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alpar@1
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['SAT',*,*]:
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alpar@1
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228 |
Sh1 Sh2 Sh3 Sh4 Sh5 Sh6 Sh7 Sh8 Sh9 :=
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alpar@1
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229 |
1 0 0 0 0 0 0 0 0 0
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alpar@1
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230 |
2 0 0 0 0 0 0 0 0 1
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alpar@1
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231 |
3 0 0 0 0 0 0 0 0 1
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alpar@1
|
232 |
4 0 0 0 0 0 0 0 0 1
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alpar@1
|
233 |
5 0 0 0 0 0 0 0 0 1
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alpar@1
|
234 |
6 0 0 0 0 0 0 0 0 1
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alpar@1
|
235 |
7 0 0 0 0 0 0 0 0 1
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alpar@1
|
236 |
8 0 0 0 0 0 0 0 0 0
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alpar@1
|
237 |
9 0 0 0 0 0 0 0 0 0
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alpar@1
|
238 |
10 0 0 0 0 0 0 0 0 0
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alpar@1
|
239 |
11 0 0 0 0 0 0 0 0 0
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alpar@1
|
240 |
12 0 0 0 0 0 0 0 0 0
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alpar@1
|
241 |
13 0 0 0 0 0 0 0 0 0
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alpar@1
|
242 |
14 0 0 0 0 0 0 0 0 0
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alpar@1
|
243 |
15 0 0 0 0 0 0 0 0 0
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alpar@1
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244 |
16 0 0 0 0 0 0 0 0 0;
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