| author | Alpar Juttner <alpar@cs.elte.hu> |
| Mon, 06 Dec 2010 13:09:21 +0100 | |
| changeset 1 | c445c931472f |
| permissions | -rw-r--r-- |
1 /* File: shiftcover.mod */
3 /* WORKFORCE SHIFT COVERAGE assignment problem */
5 /* Written by Larry D'Agostino <larrydag -at- sbcglobal -dot- com>
7 Maximize Productivity with Industrial Engineer and Operations Research Tools
8 http://industrialengineertools.blogspot.com
11 /* The WORKFORCE SHIFT COVERAGE is an assigment problem that determines
12 the schedule of crew given available time and shifts.
14 The objective is to cover the available time given hourly demand with the minimum
15 number of crew members.
17 This is a set covering problem that is very common among finding crew
18 and shift allocations. Notice in the data section the workforce shift allocation
19 per day of the week.*/
22 /* ----- Model PARAMTERS and SETS -----*/
24 param numhrs;
25 /* number of hours of operations in a given day */
27 param dys;
28 /* number of days in a week */
30 set S;
31 /* set of crew shifts */
33 set H := 1..numhrs;
34 /* set of hours of a day*/
36 set D;
37 /* set of days of a week*/
39 param dmnd{h in H, d in D};
40 /* demand for crew members given h hour and d day */
42 param shifts{d in D, h in H, s in S};
43 /* shifts to assign to crew members given d day, h hour, and s shift schedule
45 /*----- Model VARIABLES -----*/
47 var crew{s in S}, integer, >=0;
48 /* number of crew assigned to shift S */
51 /*----- Model CONSTRAINTS -----*/
53 s.t. Coverage{h in H, d in D}: sum{s in S} crew[s]*shifts[d,h,s] >= dmnd[h,d];
54 /* number of crew to cover with a shift given hourly demand and day */
57 /*----- Model OBJECTIVE -----*/
59 minimize obj: sum{s in S} crew[s];
60 /* minimize number of crew to cover demand*/
62 solve;
63 display crew;
65 printf "\n";
66 printf "Total Crew: %3d\n\n", sum{s in S} crew[s];
70 printf "\n\n";
71 printf "Weekly Crew Schedule\n\n";
72 printf "Hour ";
73 printf{d in D} " %s ", d;
74 printf "\n";
75 for {h in H} {
76 printf " %2s ",h;
77 printf{d in D} " %3d ", sum{s in S} crew[s]*shifts[d,h,s];
78 printf "\n";
79 }
80 printf"\n";
84 data;
86 param numhrs := 16;
88 set D := SUN, MON, TUE, WED, THU, FRI, SAT;
90 set S := Sh1, Sh2, Sh3, Sh4, Sh5, Sh6, Sh7, Sh8, Sh9;
92 param dmnd : SUN MON TUE WED THU FRI SAT :=
93 1 0 3 3 4 3 2 0
94 2 0 14 14 16 14 12 12
95 3 0 24 24 27 24 20 15
96 4 0 28 28 32 28 23 15
97 5 0 33 33 37 33 24 16
98 6 0 34 34 38 34 24 15
99 7 0 35 35 39 35 25 11
100 8 0 35 35 40 35 27 0
101 9 0 34 34 39 34 25 0
102 10 0 31 31 35 31 24 0
103 11 2 24 24 27 24 25 0
104 12 3 19 19 21 19 21 0
105 13 2 24 24 27 24 13 0
106 14 2 16 16 18 16 0 0
107 15 0 7 7 7 7 0 0
108 16 0 5 5 5 5 0 0;
111 param shifts :=
112 ['SUN',*,*]:
113 Sh1 Sh2 Sh3 Sh4 Sh5 Sh6 Sh7 Sh8 Sh9 :=
114 1 0 0 0 0 0 0 0 0 0
115 2 0 0 0 0 0 0 0 0 0
116 3 0 0 0 0 0 0 0 0 0
117 4 0 0 0 0 0 0 0 0 0
118 5 0 0 0 0 0 0 0 0 0
119 6 0 0 0 0 0 0 0 0 0
120 7 0 0 0 0 0 0 0 0 0
121 8 0 0 0 0 0 0 0 0 0
122 9 0 0 0 0 0 0 0 0 0
123 10 0 0 0 0 0 0 0 0 0
124 11 0 0 0 0 0 0 0 0 1
125 12 0 0 0 0 0 0 0 0 1
126 13 0 0 0 0 0 0 0 0 1
127 14 0 0 0 0 0 0 0 0 1
128 15 0 0 0 0 0 0 0 0 0
129 16 0 0 0 0 0 0 0 0 0
132 ['MON',*,*]:
133 Sh1 Sh2 Sh3 Sh4 Sh5 Sh6 Sh7 Sh8 Sh9 :=
134 1 1 0 0 0 0 0 0 0 0
135 2 1 1 0 0 0 0 0 0 0
136 3 1 1 1 0 0 0 0 0 0
137 4 1 1 1 1 0 0 0 0 0
138 5 0 1 1 1 1 0 0 0 0
139 6 1 0 1 1 1 1 0 0 1
140 7 1 1 0 1 1 1 1 0 1
141 8 1 1 1 0 1 1 1 1 1
142 9 1 1 1 1 0 1 1 1 1
143 10 0 1 1 1 1 0 1 1 1
144 11 0 0 1 1 1 1 0 1 0
145 12 0 0 0 1 1 1 1 0 1
146 13 0 0 0 0 1 1 1 1 1
147 14 0 0 0 0 0 1 1 1 1
148 15 0 0 0 0 0 0 1 1 1
149 16 0 0 0 0 0 0 0 1 1
151 ['TUE',*,*]:
152 Sh1 Sh2 Sh3 Sh4 Sh5 Sh6 Sh7 Sh8 Sh9 :=
153 1 1 0 0 0 0 0 0 0 0
154 2 1 1 0 0 0 0 0 0 0
155 3 1 1 1 0 0 0 0 0 0
156 4 1 1 1 1 0 0 0 0 0
157 5 0 1 1 1 1 0 0 0 0
158 6 1 0 1 1 1 1 0 0 1
159 7 1 1 0 1 1 1 1 0 1
160 8 1 1 1 0 1 1 1 1 1
161 9 1 1 1 1 0 1 1 1 1
162 10 0 1 1 1 1 0 1 1 1
163 11 0 0 1 1 1 1 0 1 0
164 12 0 0 0 1 1 1 1 0 1
165 13 0 0 0 0 1 1 1 1 1
166 14 0 0 0 0 0 1 1 1 1
167 15 0 0 0 0 0 0 1 1 1
168 16 0 0 0 0 0 0 0 1 1
170 ['WED',*,*]:
171 Sh1 Sh2 Sh3 Sh4 Sh5 Sh6 Sh7 Sh8 Sh9 :=
172 1 1 0 0 0 0 0 0 0 0
173 2 1 1 0 0 0 0 0 0 0
174 3 1 1 1 0 0 0 0 0 0
175 4 1 1 1 1 0 0 0 0 0
176 5 0 1 1 1 1 0 0 0 0
177 6 1 0 1 1 1 1 0 0 1
178 7 1 1 0 1 1 1 1 0 1
179 8 1 1 1 0 1 1 1 1 1
180 9 1 1 1 1 0 1 1 1 1
181 10 0 1 1 1 1 0 1 1 1
182 11 0 0 1 1 1 1 0 1 0
183 12 0 0 0 1 1 1 1 0 1
184 13 0 0 0 0 1 1 1 1 1
185 14 0 0 0 0 0 1 1 1 1
186 15 0 0 0 0 0 0 1 1 1
187 16 0 0 0 0 0 0 0 1 1
189 ['THU',*,*]:
190 Sh1 Sh2 Sh3 Sh4 Sh5 Sh6 Sh7 Sh8 Sh9 :=
191 1 1 0 0 0 0 0 0 0 0
192 2 1 1 0 0 0 0 0 0 0
193 3 1 1 1 0 0 0 0 0 0
194 4 1 1 1 1 0 0 0 0 0
195 5 0 1 1 1 1 0 0 0 0
196 6 1 0 1 1 1 1 0 0 0
197 7 1 1 0 1 1 1 1 0 0
198 8 1 1 1 0 1 1 1 1 0
199 9 1 1 1 1 0 1 1 1 0
200 10 0 1 1 1 1 0 1 1 0
201 11 0 0 1 1 1 1 0 1 0
202 12 0 0 0 1 1 1 1 0 0
203 13 0 0 0 0 1 1 1 1 0
204 14 0 0 0 0 0 1 1 1 0
205 15 0 0 0 0 0 0 1 1 0
206 16 0 0 0 0 0 0 0 1 0
208 ['FRI',*,*]:
209 Sh1 Sh2 Sh3 Sh4 Sh5 Sh6 Sh7 Sh8 Sh9 :=
210 1 1 0 0 0 0 0 0 0 0
211 2 1 1 0 0 0 0 0 0 0
212 3 1 1 1 0 0 0 0 0 0
213 4 1 1 1 1 0 0 0 0 0
214 5 0 1 1 1 1 0 0 0 0
215 6 1 0 1 1 1 1 0 0 0
216 7 1 1 0 1 1 1 1 0 0
217 8 1 1 1 0 1 1 1 1 0
218 9 1 1 1 1 0 1 1 1 0
219 10 0 1 1 1 1 0 1 1 0
220 11 0 0 1 1 1 1 0 1 0
221 12 0 0 0 1 1 1 1 0 0
222 13 0 0 0 0 1 1 1 1 0
223 14 0 0 0 0 0 1 1 1 0
224 15 0 0 0 0 0 0 1 1 0
225 16 0 0 0 0 0 0 0 1 0
227 ['SAT',*,*]:
228 Sh1 Sh2 Sh3 Sh4 Sh5 Sh6 Sh7 Sh8 Sh9 :=
229 1 0 0 0 0 0 0 0 0 0
230 2 0 0 0 0 0 0 0 0 1
231 3 0 0 0 0 0 0 0 0 1
232 4 0 0 0 0 0 0 0 0 1
233 5 0 0 0 0 0 0 0 0 1
234 6 0 0 0 0 0 0 0 0 1
235 7 0 0 0 0 0 0 0 0 1
236 8 0 0 0 0 0 0 0 0 0
237 9 0 0 0 0 0 0 0 0 0
238 10 0 0 0 0 0 0 0 0 0
239 11 0 0 0 0 0 0 0 0 0
240 12 0 0 0 0 0 0 0 0 0
241 13 0 0 0 0 0 0 0 0 0
242 14 0 0 0 0 0 0 0 0 0
243 15 0 0 0 0 0 0 0 0 0
244 16 0 0 0 0 0 0 0 0 0;