在以下情况下，我一直在研究AMPL中的护士调度问题：
总数没有。护士= 20
总数没有。 shits = 3＃morning，day，night
规划地平线7天：让我们说M T W R F Sa Su
伴随以下限制：
成本方案：
Morning shift: $12
Day shift: $13
Night shift : $15
目标函数是根据护士偏好最小化操作成本。
有谁能让我知道如何制定这个问题？
答案 0 :(得分：0)
首先，在您的问题定义中有一些不寻常的事情：
我在Mathprog中构建了问题，但代码应该或多或少等于AMPL。我开始为护士，日和轮班设置三套。
set shifts := {1,2,3};
set days := {1,2,3,4,5,6,7};
set nurses := {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20};
shedule被定义为一组二进制变量：
var schedule{nurses, days, shifts}, binary;
简单目标包含本周所有护士/班次与相关价格的总和：
minimize cost: sum{i in nurses, j in days}(schedule[i,j,1]*c_morning+schedule[i,j,2]*c_day+schedule[i,j,3]*c_night);
对于您的第一个约束，可以将每位护士的所有班次总和限制为5，因为每天只有一个班次：
s.t. working_days{n in nurses}:
sum{i in days, j in shifts}(schedule[n,i,j]) <= 5;
休息日是问题中最困难的部分。为了简单起见，我创建了另一套只包含日子的套装，护士可以连续四个班次。您还可以使用原始天数制定约束，并排除前四天。
set nigth_days := {5,6,7};
s.t. rest{n in nurses,i in nigth_days}:
(schedule[n,i-4,3]+schedule[n,i-3,3]+schedule[n,i-2,3]+schedule[n,i-1,3]+sum{j in shifts}(schedule[n,i,j])) <= 4;
由于夜班后没有早班，我使用了与休息日相同的尝试。第七天被排除在外，因为没有第八天我们可以寻找早班。
set yester_days := {1,2,3,4,5,6};
s.t. night_morning{i in yester_days, n in nurses}:
(schedule[n,i,3]+schedule[n,i+1,1]) <= 1;
应该满足每班四名护士的需求（由于5班制限制，我已经减少了4名以上的护士是不可行的）
s.t. demand_shift{i in days, j in shifts}:
sum{n in nurses}(schedule[n,i,j]) = 4;
第五个限制是将每天的班次限制为最多一次。
s.t. one_shift{n in nurses, i in days}:
sum{ j in shifts}(schedule[n,i,j]) <= 1;
答案 1 :(得分：0)
set nurse; #no. of full time employees working in the facility
set days; #planning horizon
set shift; #no. of shift in a day
set S; #shift correseponding to the outsourced nurses
set D;#day corresponding to the outsourced nurses
set N;#
# ith nurse working on day j
# j starts from Monday (j=1), Tuesday( j=2), Wednesday (j=3), Thursday(j=4), Friday(j=5), Saturday(j=6), Sunday(j=7)
#s be the shift as morning, day and night
param availability{i in nurse, j in days};
param costpershift{i in nurse, j in days, s in shift};
param outcost{n in N, l in D, m in S};
var nurseavailability{i in nurse,j in days,s in shift} binary; # = 1 if nurse i is available on jth day working on sth shift, 0 otherwise
var outsourced{n in N, l in D, m in S} integer;
#Objective function
minimize Cost: sum{i in nurse, j in days, s in shift} costpershift[i,j,s]*nurseavailability[i,j,s]+ sum{ n in N, l in D, m in S}outcost[n,l,m]*outsourced[n,l,m];
#constraints
#maximum no. of shifts per day
subject to maximum_shifts_perday {i in nurse,j in days}:
sum{s in shift} nurseavailability[i,j,s]*availability[i,j] <= 1;
#maximum no. of working says a week
subject to maximum_days_of_work {i in nurse}:
sum{j in days,s in shift} availability[i,j]*nurseavailability[i,j,s]<=5; #maximum working days irrespective of shifts
# rest days after night shifts
subject to rest_days_after_night_shift{i in nurse}:
sum{j in days} availability[i,j]*nurseavailability[i,j,3]<=4;
#demand per shift
subject to supply{j in days, s in shift, l in D, m in S}:
sum{i in nurse} availability[i,j]*nurseavailability[i,j,s] + sum{n in N} outsourced[n,l,m]=7;
#outsourcing only works well when there is more variability in supply.
#increasing the staff no. would be effective for reducing the cost variability in demand.
#considering a budget of $16,000 per week
#outsourcing constraints: a maximum of 20 nurses can be outsourced per shift
# no. of fulltime employees=30
#demand is 7 nurses per shift
#the average variability
#all nurses are paid equally @ $12 per hour.
#cost of an outsourced shift is $144.
#cost of morning shift is $96.
#cost of day shift is $104.
#cost of night shift is $120.
data;
#set nurse ordered:= nurse1 nurse2 nurse3 nurse4 nurse5 nurse6 nurse7 nurse8
#nurse9 nurse10 nurse11 nurse12 nurse13 nurse14 nurse15 nurse16 nurse17
#nurse18 nurse19 nurse20;
set nurse:= 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30;
#set days ordered:= Monday Tuesday Wednesday Thursday Friday Saturday Sunday;
set days:= 1 2 3 4 5 6 7;
#set shift ordered:= Morning Day Night;
set shift:= 1 2 3;
set D:= 1 2 3 4 5 6 7; #outsourced days
set S:=1 2 3; #outshit
set N := 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20;
param outcost
[*,*,1]:
1 2 3 4 5 6 7:=
1 144 144 144 144 144 144 144
2 144 144 144 144 144 144 144
3 144 144 144 144 144 144 144
4 144 144 144 144 144 144 144
5 144 144 144 144 144 144 144
6 144 144 144 144 144 144 144
7 144 144 144 144 144 144 144
8 144 144 144 144 144 144 144
9 144 144 144 144 144 144 144
10 144 144 144 144 144 144 144
11 144 144 144 144 144 144 144
12 144 144 144 144 144 144 144
13 144 144 144 144 144 144 144
14 144 144 144 144 144 144 144
15 144 144 144 144 144 144 144
16 144 144 144 144 144 144 144
17 144 144 144 144 144 144 144
18 144 144 144 144 144 144 144
19 144 144 144 144 144 144 144
20 144 144 144 144 144 144 144
[*,*,2]:
1 2 3 4 5 6 7:=
1 144 144 144 144 144 144 144
2 144 144 144 144 144 144 144
3 144 144 144 144 144 144 144
4 144 144 144 144 144 144 144
5 144 144 144 144 144 144 144
6 144 144 144 144 144 144 144
7 144 144 144 144 144 144 144
8 144 144 144 144 144 144 144
9 144 144 144 144 144 144 144
10 144 144 144 144 144 144 144
11 144 144 144 144 144 144 144
12 144 144 144 144 144 144 144
13 144 144 144 144 144 144 144
14 144 144 144 144 144 144 144
15 144 144 144 144 144 144 144
16 144 144 144 144 144 144 144
17 144 144 144 144 144 144 144
18 144 144 144 144 144 144 144
19 144 144 144 144 144 144 144
20 144 144 144 144 144 144 144
[*,*,3]:
1 2 3 4 5 6 7:=
1 144 144 144 144 144 144 144
2 144 144 144 144 144 144 144
3 144 144 144 144 144 144 144
4 144 144 144 144 144 144 144
5 144 144 144 144 144 144 144
6 144 144 144 144 144 144 144
7 144 144 144 144 144 144 144
8 144 144 144 144 144 144 144
9 144 144 144 144 144 144 144
10 144 144 144 144 144 144 144
11 144 144 144 144 144 144 144
12 144 144 144 144 144 144 144
13 144 144 144 144 144 144 144
14 144 144 144 144 144 144 144
15 144 144 144 144 144 144 144
16 144 144 144 144 144 144 144
17 144 144 144 144 144 144 144
18 144 144 144 144 144 144 144
19 144 144 144 144 144 144 144
20 144 144 144 144 144 144 144;
param availability:
1 2 3 4 5 6 7 :=
1 0 0 0 0 0 0 0
2 1 1 1 1 1 1 1
3 1 1 1 1 1 1 1
4 1 1 1 1 1 1 1
5 1 1 1 1 1 1 1
6 1 1 1 1 1 1 1
7 1 0 1 1 1 1 1
8 1 1 1 1 1 1 1
9 1 1 1 1 1 1 1
10 1 1 1 1 1 1 1
11 1 1 1 1 1 1 1
12 1 1 1 1 1 1 1
13 1 1 1 1 1 1 1
14 1 1 1 1 1 1 1
15 1 1 1 1 1 1 1
16 1 1 1 1 1 1 1
17 0 1 1 1 1 1 1
18 1 1 1 1 1 1 1
19 1 1 1 1 1 1 1
20 1 1 1 1 1 1 1
21 1 1 1 1 1 1 1
22 1 1 1 1 1 1 1
23 1 1 1 1 1 1 1
24 1 1 1 1 1 1 1
25 1 1 1 1 1 1 1
26 1 1 1 1 1 1 1
27 1 1 1 1 1 1 1
28 1 1 1 1 1 1 1
29 1 1 1 1 1 1 1
30 1 1 1 1 1 1 1;
param costpershift:=
[*,*,1]: 1 2 3 4 5 6 7 :=
1 96 96 96 96 96 96 96
2 96 96 96 96 96 96 96
3 96 96 96 96 96 96 96
4 96 96 96 96 96 96 96
5 96 96 96 96 96 96 96
6 96 96 96 96 96 96 96
7 96 96 96 96 96 96 96
8 96 96 96 96 96 96 96
9 96 96 96 96 96 96 96
10 96 96 96 96 96 96 96
11 96 96 96 96 96 96 96
12 96 96 96 96 96 96 96
13 96 96 96 96 96 96 96
14 96 96 96 96 96 96 96
15 96 96 96 96 96 96 96
16 96 96 96 96 96 96 96
17 96 96 96 96 96 96 96
18 96 96 96 96 96 96 96
19 96 96 96 96 96 96 96
20 96 96 96 96 96 96 96
21 96 96 96 96 96 96 96
22 96 96 96 96 96 96 96
23 96 96 96 96 96 96 96
24 96 96 96 96 96 96 96
25 96 96 96 96 96 96 96
26 96 96 96 96 96 96 96
27 96 96 96 96 96 96 96
28 96 96 96 96 96 96 96
29 96 96 96 96 96 96 96
30 96 96 96 96 96 96 96
[*,*,2] : 1 2 3 4 5 6 7 :=
1 104 104 104 104 104 104 104
2 104 104 104 104 104 104 104
3 104 104 104 104 104 104 104
4 104 104 104 104 104 104 104
5 104 104 104 104 104 104 104
6 104 104 104 104 104 104 104
7 104 104 104 104 104 104 104
8 104 104 104 104 104 104 104
9 104 104 104 104 104 104 104
10 104 104 104 104 104 104 104
11 104 104 104 104 104 104 104
12 104 104 104 104 104 104 104
13 104 104 104 104 104 104 104
14 104 104 104 104 104 104 104
15 104 104 104 104 104 104 104
16 104 104 104 104 104 104 104
17 104 104 104 104 104 104 104
18 104 104 104 104 104 104 104
19 104 104 104 104 104 104 104
20 104 104 104 104 104 104 104
21 104 104 104 104 104 104 104
22 104 104 104 104 104 104 104
23 104 104 104 104 104 104 104
24 104 104 104 104 104 104 104
25 104 104 104 104 104 104 104
26 104 104 104 104 104 104 104
27 104 104 104 104 104 104 104
28 104 104 104 104 104 104 104
29 104 104 104 104 104 104 104
30 104 104 104 104 104 104 104
[*,*,3] : 1 2 3 4 5 6 7 :=
1 120 120 120 120 120 120 120
2 120 120 120 120 120 120 120
3 120 120 120 120 120 120 120
4 120 120 120 120 120 120 120
5 120 120 120 120 120 120 120
6 120 120 120 120 120 120 120
7 120 120 120 120 120 120 120
8 120 120 120 120 120 120 120
9 120 120 120 120 120 120 120
10 120 120 120 120 120 120 120
11 120 120 120 120 120 120 120
12 120 120 120 120 120 120 120
13 120 120 120 120 120 120 120
14 120 120 120 120 120 120 120
15 120 120 120 120 120 120 120
16 120 120 120 120 120 120 120
17 120 120 120 120 120 120 120
18 120 120 120 120 120 120 120
19 120 120 120 120 120 120 120
20 120 120 120 120 120 120 120
21 120 120 120 120 120 120 120
22 120 120 120 120 120 120 120
23 120 120 120 120 120 120 120
24 120 120 120 120 120 120 120
25 120 120 120 120 120 120 120
26 120 120 120 120 120 120 120
27 120 120 120 120 120 120 120
28 120 120 120 120 120 120 120
29 120 120 120 120 120 120 120
30 120 120 120 120 120 120 120;