Corvee assignments

/* Number of people */
param P_count, integer, > 0;

/* Number of jobs */
param J_count, integer, > 0;

/* Number of days */
param D_count, integer, > 0;

param WL, integer, > 0;
param WH, integer, > 0;

set P := 1..P_count;
set J := 1..J_count;
set D := 1..D_count;

/* Person p likes to solve jobs j */
param L{p in P, j in J} default 0, binary;

/* Person p hates to solve jobs j */
param H{p in P, j in J} default 0, binary;

/* Person p is capable to perform job j */
param C{p in P, j in J} default 1, binary;

/* How many jobs need to be done on what day */
param R{j in J, d in D}, integer, >= 0;

/* Person p is allocated to do job j on day d */
var A{p in P, j in J, d in D}, binary;

/* A person only has one task per day, at most */
s.t. max_load_person{p in P, d in D}: sum{j in J} A[p,j,d] <= 1;

/* A person has at least D-1 tasks */
s.t. min_load_person{p in P}: sum{j in J, d in D} A[p,j,d] >= D_count-1;

/* A person does not perform the same job on all days */
s.t. duplicate_jobs{p in P, j in J}: sum{d in D} A[p,j,d] <= D_count-1;

/* Each task is allocated */
s.t. all_allocated{j in J, d in D}: sum{p in P} A[p,j,d] == R[j, d];

/* A person only performs what (s)he is capable of */
s.t. capability_person{p in P, j in J, d in D}: A[p,j,d] <= C[p,j];

/* Maximize enjoyment */
maximize enjoyment: sum{p in P, d in D, j in J} A[p,j,d] * (L[p, j] * WL - H[p, j] * WH);

solve;

printf "Sum %d\n", enjoyment;
printf{p in P, d in D, j in J : A[p,j,d] > 0} "%d %d %d %d\n", p, d, j, A[p,j,d] * (L[p, j] * WL - H[p, j] * WH);

data;

/* Test example */

param P_count := 3;
param J_count := 2;
param D_count := 2;
param WL := 3;
param WH := 9;

param L : 1 2 :=
	1 0 1
	2 1 0
	3 0 0;

param H : 1 2 :=
	1 1 0
	2 0 1
	3 0 1;

param R : 1 2 :=
	1 1 2
	2 2 1;

param C[3,2] := 0;

end;