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);

   str assigned_employee {TimeSlots, Weekdays} init '';
   for {slot in TimeSlots, day in Weekdays} do;
      for {name in Employees: Assign[name,slot,day] > 0} do;
         assigned_employee[slot,day] = name;
         leave;
      end;
   end;

   create data report from [slot]=TimeSlots
      {day in Weekdays} <col(day)=assigned_employee[slot,day]>;
quit;

title 'Reported Solution';
proc print data=report;
   id slot;
run;