劳动力4_c.c
/ *版权所有2019，Gurobi 狗万app足彩Optimization，LLC * / / *分配工人转移;每个工人都可能或可能无法在特定日期上使用。我们使用帕累托优化来解决模型：首先，我们最大限度地减少了松弛的线性和。然后，我们限制了懈怠的总和，我们最小化了试图平衡工人之间的工作量的二次目标。* / #include #include #include #include #include“gurobi_c.h”int solveandprint（grbmodel * model，int nshifts，int nworkers，Char **工人，int *状态）;#define xcol（w，s）nshifts * w + s #define slackcl（s）nshifts * nworkers + s #define totslackcol nshifts *（nworkers + 1）#define totshiftscol（w）nshifts *（nworkers + 1）+1+w #define avgshiftscol（nshifts + 1）*（nworkers + 1）#define diffshiftscol（w）（nshifts + 1）*（nworkers + 1）+ 1 + w #define maxstr 128 int main（int argc，char * argv []）{grbenv * env = null;grbmodel * model = null;int ERROR = 0，状态;int s，w，col; int *cbeg = NULL; int *cind = NULL; int idx; double *cval = NULL; char *sense = NULL; char vname[MAXSTR], cname[MAXSTR]; double val; /* Sample data */ const int nShifts = 14; const int nWorkers = 7; /* Sets of days and workers */ char* Shifts[] = { "Mon1", "Tue2", "Wed3", "Thu4", "Fri5", "Sat6", "Sun7", "Mon8", "Tue9", "Wed10", "Thu11", "Fri12", "Sat13", "Sun14" }; char* Workers[] = { "Amy", "Bob", "Cathy", "Dan", "Ed", "Fred", "Gu" }; /* Number of workers required for each shift */ double shiftRequirements[] = { 3, 2, 4, 4, 5, 6, 5, 2, 2, 3, 4, 6, 7, 5 }; /* Worker availability: 0 if the worker is unavailable for a shift */ double availability[][14] = { { 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1 }, { 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0 }, { 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1 }, { 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1 }, { 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1 }, { 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1 }, { 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 } }; /* Create environment */ error = GRBloadenv(&env, "workforce4.log"); if (error) goto QUIT; /* Create initial model */ error = GRBnewmodel(env, &model, "workforce4", (nShifts + 1) * (nWorkers + 1), NULL, NULL, NULL, NULL, NULL); if (error) goto QUIT; /* Initialize assignment decision variables: x[w][s] == 1 if worker w is assigned to shift s. This is no longer a pure assignment model, so we must use binary variables. */ for (w = 0; w < nWorkers; ++w) { for (s = 0; s < nShifts; ++s) { col = xcol(w, s); sprintf(vname, "%s.%s", Workers[w], Shifts[s]); error = GRBsetcharattrelement(model, "VType", col, GRB_BINARY); if (error) goto QUIT; error = GRBsetdblattrelement(model, "UB", col, availability[w][s]); if (error) goto QUIT; error = GRBsetstrattrelement(model, "VarName", col, vname); if (error) goto QUIT; } } /* Initialize slack decision variables */ for (s = 0; s < nShifts; ++s) { sprintf(vname, "%sSlack", Shifts[s]); error = GRBsetstrattrelement(model, "VarName", slackcol(s), vname); if (error) goto QUIT; } /* Initialize total slack decision variable */ error = GRBsetstrattrelement(model, "VarName", totSlackcol, "totSlack"); if (error) goto QUIT; /* Initialize variables to count the total shifts worked by each worker */ for (w = 0; w < nWorkers; ++w) { sprintf(vname, "%sTotShifts", Workers[w]); error = GRBsetstrattrelement(model, "VarName", totShiftscol(w), vname); if (error) goto QUIT; } /* The objective is to minimize the sum of the slacks */ error = GRBsetintattr(model, "ModelSense", GRB_MINIMIZE); if (error) goto QUIT; error = GRBsetdblattrelement(model, "Obj", totSlackcol, 1.0); if (error) goto QUIT; /* Make space for constraint data */ cbeg = malloc(sizeof(int) * nShifts); if (!cbeg) goto QUIT; cind = malloc(sizeof(int) * nShifts * (nWorkers + 1)); if (!cind) goto QUIT; cval = malloc(sizeof(double) * nShifts * (nWorkers + 1)); if (!cval) goto QUIT; sense = malloc(sizeof(char) * nShifts); if (!sense) goto QUIT; /* Constraint: assign exactly shiftRequirements[s] workers to each shift s, plus the slack */ idx = 0; for (s = 0; s < nShifts; ++s) { cbeg[s] = idx; sense[s] = GRB_EQUAL; for (w = 0; w < nWorkers; ++w) { cind[idx] = xcol(w, s); cval[idx++] = 1.0; } cind[idx] = slackcol(s); cval[idx++] = 1.0; } error = GRBaddconstrs(model, nShifts, idx, cbeg, cind, cval, sense, shiftRequirements, Shifts); if (error) goto QUIT; /* Constraint: set totSlack column equal to the total slack */ idx = 0; for (s = 0; s < nShifts; ++s) { cind[idx] = slackcol(s); cval[idx++] = 1.0; } cind[idx] = totSlackcol; cval[idx++] = -1.0; error = GRBaddconstr(model, idx, cind, cval, GRB_EQUAL, 0.0, "totSlack"); if (error) goto QUIT; /* Constraint: compute the total number of shifts for each worker */ for (w = 0; w < nWorkers; ++w) { idx = 0; for (s = 0; s < nShifts; ++s) { cind[idx] = xcol(w,s); cval[idx++] = 1.0; } sprintf(cname, "totShifts%s", Workers[w]); cind[idx] = totShiftscol(w); cval[idx++] = -1.0; error = GRBaddconstr(model, idx, cind, cval, GRB_EQUAL, 0.0, cname); if (error) goto QUIT; } /* Optimize */ error = solveAndPrint(model, nShifts, nWorkers, Workers, &status); if (error) goto QUIT; if (status != GRB_OPTIMAL) goto QUIT; /* Constrain the slack by setting its upper and lower bounds */ error = GRBgetdblattrelement(model, "X", totSlackcol, &val); if (error) goto QUIT; error = GRBsetdblattrelement(model, "UB", totSlackcol, val); if (error) goto QUIT; error = GRBsetdblattrelement(model, "LB", totSlackcol, val); if (error) goto QUIT; /* Variable to count the average number of shifts worked */ error = GRBaddvar(model, 0, NULL, NULL, 0, 0, GRB_INFINITY, GRB_CONTINUOUS, "avgShifts"); if (error) goto QUIT; /* Variables to count the difference from average for each worker; note that these variables can take negative values. */ error = GRBaddvars(model, nWorkers, 0, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL); if (error) goto QUIT; for (w = 0; w < nWorkers; ++w) { sprintf(vname, "%sDiff", Workers[w]); error = GRBsetstrattrelement(model, "VarName", diffShiftscol(w), vname); if (error) goto QUIT; error = GRBsetdblattrelement(model, "LB", diffShiftscol(w), -GRB_INFINITY); if (error) goto QUIT; } /* Constraint: compute the average number of shifts worked */ idx = 0; for (w = 0; w < nWorkers; ++w) { cind[idx] = totShiftscol(w); cval[idx++] = 1.0; } cind[idx] = avgShiftscol; cval[idx++] = -nWorkers; error = GRBaddconstr(model, idx, cind, cval, GRB_EQUAL, 0.0, "avgShifts"); if (error) goto QUIT; /* Constraint: compute the difference from the average number of shifts */ for (w = 0; w < nWorkers; ++w) { cind[0] = totShiftscol(w); cval[0] = 1.0; cind[1] = avgShiftscol; cval[1] = -1.0; cind[2] = diffShiftscol(w); cval[2] = -1.0; sprintf(cname, "%sDiff", Workers[w]); error = GRBaddconstr(model, 3, cind, cval, GRB_EQUAL, 0.0, cname); if (error) goto QUIT; } /* Objective: minimize the sum of the square of the difference from the average number of shifts worked */ error = GRBsetdblattrelement(model, "Obj", totSlackcol, 0.0); if (error) goto QUIT; for (w = 0; w < nWorkers; ++w) { cind[w] = diffShiftscol(w); cval[w] = 1.0; } error = GRBaddqpterms(model, nWorkers, cind, cind, cval); if (error) goto QUIT; /* Optimize */ error = solveAndPrint(model, nShifts, nWorkers, Workers, &status); if (error) goto QUIT; if (status != GRB_OPTIMAL) goto QUIT; QUIT: /* Error reporting */ if (error) { printf("ERROR: %s\n", GRBgeterrormsg(env)); exit(1); } /* Free data */ free(cbeg); free(cind); free(cval); free(sense); /* Free model */ GRBfreemodel(model); /* Free environment */ GRBfreeenv(env); return 0; } int solveAndPrint(GRBmodel* model, int nShifts, int nWorkers, char** Workers, int* status) { int error, w; double val; error = GRBoptimize(model); if (error) return error; error = GRBgetintattr(model, "Status", status); if (error) return error; if ((*status == GRB_INF_OR_UNBD) || (*status == GRB_INFEASIBLE) || (*status == GRB_UNBOUNDED)) { printf("The model cannot be solved " "because it is infeasible or unbounded\n"); return 0; } if (*status != GRB_OPTIMAL) { printf("Optimization was stopped with status %i\n", *status); return 0; } /* Print total slack and the number of shifts worked for each worker */ error = GRBgetdblattrelement(model, "X", totSlackcol, &val); if (error) return error; printf("\nTotal slack required: %f\n", val); for (w = 0; w < nWorkers; ++w) { error = GRBgetdblattrelement(model, "X", totShiftscol(w), &val); if (error) return error; printf("%s worked %f shifts\n", Workers[w], val); } printf("\n"); return 0; }
