Scheduling (misole01)
/****************************************************************/
/* */
/* S A S S A M P L E L I B R A R Y */
/* */
/* NAME: misole01 */
/* TITLE: Scheduling (misole01) */
/* PRODUCT: OR */
/* SYSTEM: ALL */
/* KEYS: OR */
/* PROCS: OPTMODEL */
/* DATA: */
/* */
/* SUPPORT: UPDATE: */
/* REF: */
/* MISC: Example 1 from the Mixed Integer Linear Programming */
/* Solver chapter of Mathematical Programming. */
/* */
/****************************************************************/
data preferences;
input name $ slot mon tue wed thu fri;
datalines;
marc 1 10 10 10 10 10
marc 2 9 9 9 9 9
marc 3 8 8 8 8 8
marc 4 1 1 1 1 1
marc 5 1 1 1 1 1
marc 6 1 1 1 1 1
marc 7 1 1 1 1 1
marc 8 1 1 1 1 1
mike 1 10 9 8 7 6
mike 2 10 9 8 7 6
mike 3 10 9 8 7 6
mike 4 10 3 3 3 3
mike 5 1 1 1 1 1
mike 6 1 2 3 4 5
mike 7 1 2 3 4 5
mike 8 1 2 3 4 5
bill 1 10 10 10 10 10
bill 2 9 9 9 9 9
bill 3 8 8 8 8 8
bill 4 0 0 0 0 0
bill 5 1 1 1 1 1
bill 6 1 1 1 1 1
bill 7 1 1 1 1 1
bill 8 1 1 1 1 1
bob 1 10 9 8 7 6
bob 2 10 9 8 7 6
bob 3 10 9 8 7 6
bob 4 10 3 3 3 3
bob 5 1 1 1 1 1
bob 6 1 2 3 4 5
bob 7 1 2 3 4 5
bob 8 1 2 3 4 5
;
data maxhours;
input name $ hour;
datalines;
marc 20
mike 20
bill 20
bob 20
;
proc optmodel;
/* read in the preferences and max hours from the data sets */
set <string,num> DailyEmployeeSlots;
set <string> Employees;
set <num> TimeSlots = (setof {<name,slot> in DailyEmployeeSlots} slot);
set <string> WeekDays = {"mon","tue","wed","thu","fri"};
num WeeklyMaxHours{Employees};
num PreferenceWeights{DailyEmployeeSlots,Weekdays};
num NSlots = card(TimeSlots);
read data preferences into DailyEmployeeSlots=[name slot]
{day in Weekdays} <PreferenceWeights[name,slot,day] = col(day)>;
read data maxhours into Employees=[name] WeeklyMaxHours=hour;
/* declare the binary assignment variable x[i,j,k] */
var Assign{<name,slot> in DailyEmployeeSlots, day in Weekdays} binary;
/* for each p[i,j,k] = 0, fix x[i,j,k] = 0 */
for {<name,slot> in DailyEmployeeSlots, day in Weekdays:
PreferenceWeights[name,slot,day] = 0}
fix Assign[name,slot,day] = 0;
/* declare the objective function */
max TotalPreferenceWeight =
sum{<name,slot> in DailyEmployeeSlots, day in Weekdays}
PreferenceWeights[name,slot,day] * Assign[name,slot,day];
/* declare the constraints */
con OneEmpPerSlot{slot in TimeSlots, day in Weekdays}:
sum{name in Employees} Assign[name,slot,day] = 1;
con EmpMustHaveLunch{name in Employees, day in Weekdays}:
Assign[name,4,day] + Assign[name,5,day] <= 1;
con AtMost2ConsSlots{name in Employees, start in 1..NSlots-2,
day in Weekdays}:
Assign[name,start,day] + Assign[name,start+1,day]
+ Assign[name,start+2,day] <= 2 ;
con WeeklyHoursLimit{name in Employees}:
sum{slot in TimeSlots, day in Weekdays} Assign[name,slot,day]
<= WeeklyMaxHours[name];
/* solve the model */
solve with milp;
/* clean up the solution */
for {<name,slot> in DailyEmployeeSlots, day in Weekdays}
Assign[name,slot,day] = round(Assign[name,slot,day],1e-6);
create data report from [name slot]={<name,slot> in DailyEmployeeSlots:
max {day in Weekdays} Assign[name,slot,day] > 0}
{day in Weekdays} <col(day)=(if Assign[name,slot,day] > 0
then Assign[name,slot,day] else .)>;
quit;
title 'Reported Solution';
proc format;
value xfmt 1=' xxx ';
run;
proc tabulate data=report;
class name slot;
var mon--fri;
table (slot * name), (mon tue wed thu fri)*sum=' '*f=xfmt.
/misstext=' ';
run;